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Handbook of Knot Theory book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry.
* Survey of mathematical knot theory * Articles by leading world authorities * Clear exposition, not over-technical * Accessible to readers with undergraduate background in mathematics | 677.169 | 1 |
books.google.com - This distinguished little book is a brisk introduction to a series of mathematical concepts, a history of their development, and a concise summary of how today's reader may use them.... Introduction to Mathematics | 677.169 | 1 |
This book covers the following topics: Sequences, limits, and difference equations; functions ...
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This book covers the following topics: Sequences, limits, and difference equations; functions and their properties; best affine approximations; integration; polynomial approximations and Taylor series; transcendental functions; the complex plane; differential equations.
Less | 677.169 | 1 |
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Unit
Description: resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting started.
In this mini-lesson you'll learn how to factor the binomials and polynomials. It is an important step in solving problems in a good number of algebraic applications. In factoring polynomials, we determine all the terms that were multiplied together to get the given polynomial. We then try to factor each of the terms we found in the first step. This continues until we can't factor anymore. For Example, here is the complete factorization of the polynomial
x4 – 16 = (x2 + 4)(x + 2)(x – 2)
This might seem complicated here as it is written in text, but it will be easy to follow once you hear the instructor explain it in the video here. resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting Started - Circles.
This mini-lesson introduces and walks you through the basic concepts of the circles. You'll learn it with the help of some examples, practice questions with solution,and using video explanation by the instructor that brings in an element of real-class room experience. You can see here the overview of the important basics of the circle, radius, chord etc.
A circle is the set of points that are equidistant from a special point in the plane. If the special point O is the center, it is called circle O. Some real-world examples of a circle are: a wheel, surface of a coin.
The radius is a line segment joining the center of the circle with a point on the circle. If any point A is on the circle with center O, then OA is the radius of circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus the diameter of a circle is twice as long as the radius, E.g. a circle with 5 cms radius, will have 10 cms diameter.
A chord is a line segment joining two endpoints that lie on a circle. Further you may note that the diameter of a circle is the longest chord since it passes through the center and it can be stated every diameter is a chord, but not every chord is a diameter.
This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.
In this mini-lesson you'll learn how to factor an expression of exponents with the same base. Generally speaking, for factoring exponents with the same base, we need to take a common factor out of the expression, and this factor is the base raised to the lowest exponent. For example, x2 is the common factor in the expression x2 + x6, and hence the expression can be rewritten as x2(1 + x4). mini-lesson shows you how to factor a quadratic into binomials. As is the case in Algebra many times, the overview provided here in text might seem a little complicated, but don't worry -- it will be easy to follow once you hear the instructor explain it in the video provided. Some quadratics can be factored into two identical binomials. Such quadratics are called perfect square trinomials. As quadratic expression is the product of two binomials, factoring a quadratic means breaking the quadratic back into its binomial parts. Here factoring is done using the rule of LIOF (FOIL in reverse). A couple of general rules to keep in mind how to factor a quadratic using the perfect square method. In such cases, not only can the quadratic can be factored into two expressions, but the expressions are the same. If we try to explain it in text, here is the general rule -- if we have a quadratic equation in which first and last term are both perfect squares and middle term is two times the square root of the first and last terms multiplied, it simplifies the quadratic to a binomial product or just one binomial raised to the second power. Reading this explanation in text is confusing to many of us -- just click on the video of our instructor explaining it and you'll understand the concept much more easily. Note that perfect square trinomials are often expressions of one of the following forms:
(x2 + 2ax + a2), which is the same as (x + a)2
(x2 – 2ax + a2), which is the same as (x – a)2 with the help of several examples how to factor 3rd degree polynomial into 2nd degree polynomial and 1st degree polynomial factor. As you know, if you write a polynomial as the product of two or more polynomials, you have factored it. It is fairly common to come across certain interesting forms of third degree polynomials, and here are a few rules to keep in mind in factoring them is a part of the interactive online tutorial for Geometry learning with the help of audio visual lessons. It has been created to help you learn the concept, perception with explanations and includes solution to practice questions from the topic of \' | 677.169 | 1 |
books.google.com - The growth in digital devices, which require discrete formulation of problems, has revitalized the role of combinatorics, making it indispensable to computer science. Furthermore, the challenges of new technologies have led to its use in industrial processes, communications systems, electrical networks,... to Combinatorics | 677.169 | 1 |
...This grouping includes numerical operations, basic geometry, identifying patterns, data analysis, and basic statistics. Often students require a review of basic arithmetic skills in order to be successful. Most of these concepts will be seen in future math classes/proficiency tests | 677.169 | 1 |
Britannica Web sites
Algebra is a method of thinking about mathematics in a general way. It provides rules about how equations must be put together and how they can be changed. The word algebra comes from the title of a book on mathematics written in the early 800s. The book was written by an Arab astronomer and mathematician named al-Khwarizmi. The rules of algebra are older than that, however. The ancient Greeks wrote down some of the rules that make up algebra, and others came later.
An important branch of mathematics, algebra today is studied not only in high school and college but, increasingly, in the lower grades as well. Taught with insight and understanding of the new mathematics programs, it can be an enjoyable subject. Algebra is as useful as all the other branches of mathematics-to which it is closely related. For some careers, such as those in engineering and science, a knowledge of algebra is indispensable. (See also arithmetic; calculus; geometry; mathematics; numeration systems and numbers.) | 677.169 | 1 |
Curious about quarks, quasers and the fantastic universe around you? Ever wanted to explore mathematical proof? Need some trigonometry fast? Want to swap up physics, chemistry, or learn some new biology? Ever wondered why your scratches itch before you go to sleep? Beautifully illustrated and packed with fascinating and useful information, SCIENCIA is the ultimate one-stop science reference book for inquisitive readers for all ages. Whether you just want to bursh up on what you learnt at school, still are at school, or never went to school, these pages will test you, stretch you, and make you brainier.
Essential Statistics, Regression, and Econometrics aims to help students in an introductory statistics course develop the statistical reasoning they need for econometric. Many students mistakenly believe that statistics courses are too abstract, mathematical, and tedious to be useful or interesting. To demonstrate the power, elegance, and even beauty of statistical reasoning, this textbook provides hundreds of interesting and relevant examples, and discusses not only the uses but also the abuses of statistics. these examples show how statistical reasoning can be used to answer important questions and also to expose the errors-accidental or intentional-that people often make.
Mathematics is everywhere, and this is the secind book Derek Holtin shows how the ordinary can become the extraordinary when viewed through a mathematical prim. be prepared to slice through cubes, lick stamps and fill jugs of water - along the way spot the patterns, make conjectures and see it through to a mathematical result and its proof. here are everyday problems to taunt, delight - and to solve.
Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique.
Each teacher and student brings many identities to the classroom. What is their impact on the student's learning and the teacher's teaching of mathematics? this book invites K-8 teachers to reflect on their own and their studnets' multiple identities. Rich possibilities for learning result when teachers draw on these identities to offer high-quality, equity-based teaching to all studnets.
One Equals Zero! Every number is greater than itself! All triangles are isosceles! Suprised? Welcome to the world of One Equals Zero and Other Mathematical Supirses. In this engaging book of blackline activity masters, all men are bald, mistakes are lucky, and teachers can never spring suprise tests on their students!
The transition from classroom teacher to elementary mathematics specialist is challenging, but the principal can smooth specialist's path by reassuring teachers that the new specialist is there to support them, not judge them the specialised pedagogical content knowledge that you need to teach multiplication and division effectively in grades 3-5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with these computations - not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of multiplication and division. Use the oppertunities that these and similar tasks provide to build on their own understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning.
The wonder of recreational mathematics.... This book is a compilation of 30 articles originally issued as a series entitled "enjoying maths" for the japanese magazine Rikeieno Sugaku (Mathematics for Science).
The book is a collection of 50 original essays contributed by a wide variety of authors. It contains articles by some of the best expositors of the subject (du Sautoy, Singh and Stewart for example) together with entertaining biographical pieces and articles of relevance to our everyday lives (such as Spiegelhalter on risk and Elwes on medical imaging).
This Practical book provides primary teachers and secondary with advice and resources to develop a visual and active approach to teaching mathematics. Our exciting new edition comes with a helpful CD, offering resources and practical activities that make it easy for readers to try out the ideas in the book for themselves. The new edition has: New resource materials, PowerPoint presentions for each chapter, to use in the classroom, a new section in time, specific examples of teaching strategies and lots more ideas for lesson activities.
The Essential Guide to Navigating Your First Years of Teaching Secondary Mathematics "Too much advcice for teachers is either to abstract to be useful or consists of cute ideas for tomorrow that offer no lasting support. Wieman and Arbaugh hit the coveted middle ground - practical ideas for teachers drawn from sound principles of learning and teachin. Because their focus is directly on middle and secondary school mathematics, thye have produced a rare practical guide for upper-grade teachers that is easily accessible and rewardingly substantive. Middle and high school math teachers who want to improve their teaching, with the Common Core State Standards in mind, cannot go wrong by reading this book, cover to cover." - James Hiebert University of Delaware Based on classroom observations and interviews with seasoned and beginning teachers, Success from the Start: Your First Years Teaching Secondary Mathematics offers valuable suggestions to improve your teaching and your studnets oppertunities to learn.
MyMaths for Key Stage 3
MyMaths for KeyStage 3 is a brand new series that fully addresses the new National Curriculum for KeyStage 3 Mathematics in England. Student Book 1B is for students starting KS3 that already have a secure understanding of upper KS2 topics, allowing them to consolidate their knowledge and progress to KS3 maths standards. MyMaths for Key Stage 3 is the only course to provide: - Coherent progression through KS3, with a 'learn it once and learn it well' philosophy leading to secure knowledge. - A truly differentiated structure so that all levels of ability can access the new curriculum, including all the new topics. - A Clear Approach to attainment with the emphasis on visible progress.
Written by a highly experienced and respected author team, the third edition of STP Mathematics provides complete andcomprehensive coverage of the 2014 Key Stage 3 programme of Study. Maintaining its rigorous and authoritative approach, this fully updated textbook also develops students' problem-solving skills, preparing them for a high level of achievement at key stage 3 leading onto the higher tier at GCSE.
The subject of the Calculus seems a mystery to all but the most numerate of people, but J F Riley writes with a dry humour tat engages the general reader in an informed acquantance with its history. The book describes the trials and tribulations that the topic of motion and therefore variability and change encountered from its beginnings in ancient Greece up to its discovery in the 17th century and the subsequent period of development. It is is a story behind the evolution of the 'algebra of change and shape' we call the Calculus, and about what it is, why we needed it and who made it happen.
It is not the ugly sister that it is often presented as being; it can be the 'Belle of the Ball' if the correct make-up is applied. This book will show you what 'make-up' ypu can slap on the subject to make it alluring for young people, and will hopefully encourage you to dress maths up in the way that best suits you and your pupils. By picking up this little collection of ramblings you have made the first step: you are clearly interested in what you do and want to be better at it. This was exactly how I felt about teaching maths. I realised I had a deficiency, and that only thinking positively about it would start me on the road to being good at it.See if it wors for you too.
The development of children's language and their mathematical understanding takes place from the earliest years. Research evidence suggests that teacher-facilitated 'mathematical talk' in the early years has the potential to stimulate growth in children's understanding of mathematics. It is argued that acquiring the language of mathematics is important to the acquisition of mathematical concepts and to the use and application of mathematics in a variety of situations.
City of Zombies builds speed and confidence with number play and rewards players as their maths improve. Co-operative gameplay encourages players to work together and help each other to win. Players of mixed abilities share learning through a positive play.
If you are teaching or learning to teach primary mathematics, this is the toolkit to support you! Not only does it cover the essential knowledge and understanding that you and your pupils need to know. It also offers 176 great ideas for teaching primary mathematics - adaptable for use within different areas of mathematics and for different ages and abilities. | 677.169 | 1 |
to allow students to analyze a situation using
multiple representations;
to prepare students to use computers in later
mathematics courses.
Traditionally, the focus of mathematical problem solving in high
school has been the development and solution of algebraic equations;
however many students rush through textbook exercises using word
clues and available numbers in predictable routines to arrive
at answers. They are frequently nervous about tackling any problem
that does not mimic a type already "learned".
Computer programs can provide new insight by adding to the
algebraic model the ability to analyze complicated numerical data
through charts and graphs. This can help students visualize aspects
of a problem which may not be apparent in the algebraic solution.
Spreadsheets facilitate experimentation with numerical data
which gives students the freedom to play with different possibilities
and to really try to understand the problem.
Spreadsheet addresses are concrete examples of variables.
They can dynamically take on different values and can be manipulated
to create formulas and equations to model simple linear relations
in grade 9, or periodic and exponential functions in senior grades.
This unit was very well received by four grade 9 mixed ability classes.
The students were actively involved in solving the problems.
Although some students later had difficulty setting up and solving the
problems algebraically without the computer they
were frequently successful at solving even quite complicated problems
by drawing up a handmade spreadsheet.
Three results stood out:
students employed a wide variety of solutions when they were not limited by "problem
type",
they displayed considerable skill in creating and manipulating formulas, and
they approached new and different problems with confidence.
Unit Outline
This unit takes four days in the lab and a follow up day in class.
Before students begin this unit they should have:
Used a spreadsheet such as MSWorks or ClarisWorksfor listing data and plotting points.
For an introduction, see Jan Garner's
Spreadsheet Basics. | 677.169 | 1 |
SC310 Linear Algebra and Matrix Comp
Course Description
The course includes the study of vectors in the plane and space, systems of linear equations, matrices, determinants, vectors, vector spaces, linear transformations, inner products, eigenvalues and eigenvectors. The course will approach the study of linear algebra through computer based exercises. Technology will be an integral part of this course. Students will also develop experience applying abstract concepts to concrete problems drawn from engineering and computer Science
Learning Outcomes
Perform basic matrix calculations
Use matrices to solve systems of linear equations
Find least-square solution of linear systems
Set up and solve linear systems in applied problems
Explain the basic concepts of linear algebra such as subspace, span, linear independence, basis, and dimension
Identify a linear transformation and find and use its matrix representation | 677.169 | 1 |
TERM 2 – Geometry 1 (angles in polygons, tessellations, construction of triangles, geometric reasoning and proof). Statistics 1 (scatter graphs and correlation, time series graphs, two way tables, comparing sets of data, statistical investigations). Geometry 2 (circumference and area of a circle, metric units of area and volume, surface area and volume of prisms).
TERM 3 – Number 2 (powers of 10, rounding and estimation, multiplying and dividing decimals, using a calculator and solving problems). Algebra 4 (factorising, index notation with algebra, squares and cubes and roots, distance time and real life graphs). Statistics 2 (probability, experimental probability and expected frequency).
TERM 5 – Geometry 4 (Pythagoras and trigonometry). Remainder of term is taking to support revision activities for end of KS3 formal assessment .
TERM 6 – Revision to support end of KS3 formal assessment.
Students will sit their end of KS3 formal assessment during the first 2 weeks of June. The remainder of the term will be used to start Module 1 of the GCSE Modular course.
Homework is set weekly for all students. Every other week homework will take the form of an online exercise which is marked immediately and monitored by teachers. The type of written homework set is varied, and could take the form of an investigation, creation of a powerpoint, creation of bank of questions, though more often homework will be designed to ensure that students have the opportunity to practise and consolidate the concepts developed in class. Homework is marked and graded, and students will be given feedback on what they need to do to improve and make further progress in the subject. | 677.169 | 1 |
Getting to Know the Mathematical Foundation of Signals and Systems
The study of signals and systems establishes a mathematical formalism for analyzing, modeling, and simulating electrical systems in the time, frequency, and s- or z-domains. Signals exist naturally and are also created by people. Some operate continuously (known as continuous-time signals); others are active at specific instants of time (and are called discrete-time signals).
Signals pass through systems to be modified or enhanced in some way. Systems that operate on signals are also categorized as continuous- or discrete-time.
Mathematics plays a central role in all facets of signals and systems. Specifically, complex arithmetic, trigonometry, and geometry are mainstays of this dynamic and (ahem) electrifying field of work and study. This article highlights the most applicable concepts from each of these areas of math for signals and systems work.
Complex arithmetic for signals and systems
Here are some of the most important complex arithmetic operations and formulas that relate to signals and systems.
Trigonometry and Euler's formulas
This table presents the key formulas of trigonometry that apply to signals and systems:
Geometric series
Among the most important geometry equations to know for signals and systems are these three: | 677.169 | 1 |
Complex variables is a beautiful area from a purely
mathematical point of view, as well as a powerful tool for solving a
wide array of applied problems. It is related to many mathematical
disciplines, including in particular real analysis, differential
equations, algebra and topology. The numerous applications include all
kinds of wave propagation phenomena such as those occurring in
electrodynamics, optics, fluid mechanics and quantum mechanics,
diffusion problems such as heat and contaminant diffusion, engineering
tasks such as the computation of buoyancy and resistance of wings, the
flows in turbines and the design of optimal car bodies, and signal
processing and communication theory.
Historically, complex numbers originated from the
desire to find a uniform representation of solutions of algebraic
equations. From this perspective, the field of complex numbers is a
natural extension of the field of real numbers with the property
that it is algebraically closed, that is, every polynomial can be
factorized into linear polynomials. After analysis has been
introduced, it became a natural task to extend the concepts of
differential and integral calculus and function series to complex
variables. In the 19th century complex analysis emerged as an
independent mathematical discipline, most notably through the work
of Augustin-Louis Cauchy (1789-1857), Karl Weierstrass (1815-1897),
and Bernhard Riemann (1826-1866).
The purpose of this course is an introduction to the
theory and application of complex variables and complex functions. Part
I is devoted to the basic mathematical theory, and Part II to selected
applications.
Part I: Fundamentals and Techniques of
Complex Function Theory
We begin, in Chapter 1, by introducing complex numbers,
elementary complex functions, and concepts from analysis such as limits,
continuity and differentiability. It will be seen that complex numbers
have a simple two-dimensional character that admits a straightforward
geometric description. While many results of real analysis carry over,
some important novel notions appear in the calculus of complex
functions. Applications to differential equations are briefly discussed.
In Chapter 2, we study the notion of analytic functions
and their properties. It will be shown that a complex function is
differentiable if and only if an important compatibility relationship
between its real and imaginary parts is satisfied, which is referred to
as Cauchy Riemann equations. The concepts of multivalued functions and
complex integration are considered in some detail. The technique of
integration in the complex plane is discussed and two very important
results of complex analysis are derived: Cauchy's theorem and a
corollary: Cauchy's integral formula.
Chapter 3 deals with sequences, series and singularities
of complex functions. It turns out that the representation of complex
functions frequently requires the use of infinite series expansions. The
best known are the Taylor and Laurent series, which represent analytic
functions in appropriate domains. Applications often require that we
manipulate series by termwise differentiation and integration. These
operations may be substantiated by employing the notion of uniform
convergence. Series expansion breaks down at points or curves where the
represented function is not analytic. Such locations are termed singular
points or singularities of the function. The study of singularities is
vitally important in many applications including contour integration,
differential equations, and conformal mappings.
In Chapter 4 we extend Cauchy's theorem to cases where
the integrand is not analytic, for example, if the integrand has
isolated singular points. Each isolated singular point contributes to
what is called the residue of the singularity. This extension, called
residue theorem, is very useful in applications such as the evaluation
of definite integrals of various types. The residue theorem provides a
straightforward and sometimes the only method to compute these
integrals, which include real integrals that cannot be computed on the
basis of real integral calculus alone. We also show how to use contour
integrals to compute the solutions of certain partial differential
equations by the techniques of Fourier and Laplace transforms.
Part II: Applications of Complex Function
Theory
A number of problems arising in fluid mechanics,
electrostatics, heat conduction, and many other physical situations can
be formulated in terms of Laplace's equation in a two-dimensional domain
with given boundary conditions. Conformal mappings are transformations
through which a given domain is transformed to a simple domain such as a
half plane, in which the problem is greatly simplified. Chapter 5 is
devoted to general properties of conformal mappings and a number of
applications including problems from fluid flow, steady state heat
conduction, and electrostatics.
The second application concerns the asymptotic
evaluation of integrals. This is motivated by the fact that the solution
of a large class of physically important problems can be represented in
terms of definite integrals. Although such integrals provide exact
solutions, their content is often not obvious. In order to decipher
their main mathematical and physical properties, it is often useful to
study their behavior in the limit of large values of a certain parameter
which, for example, gives insight into the far field of a scattered
wave. In Chapter 6 techniques for evaluating definite integrals
asymptotically are discussed and related to other methods such as the
WKB method. The most well-known methods to study integrals containing a
large parameter are Laplace's method, the method of stationary phase,
and the steepest descent method. | 677.169 | 1 |
The life sciences deal with a vast array of problems at different spatial, temporal, and organizational scales. The mathematics necessary to describe, model, and analyze these problems is similarly diverse, incorporating quantitative techniques that are rarely taught in standard undergraduate courses. This textbook provides an accessible introduction to these critical mathematical concepts, linking them to biological observation and theory while also presenting the computational tools needed to address problems not readily investigated using mathematics alone.
Proven in the classroom and requiring only a background in high school math, Mathematics for the Life Sciences doesn't just focus on calculus as do most other textbooks on the subject. It covers deterministic methods and those that incorporate uncertainty, problems in discrete and continuous time, probability, graphing and data analysis, matrix modeling, difference equations, differential equations, and much more. The book uses MATLAB throughout, explaining how to use it, write code, and connect models to data in examples chosen from across the life sciences.
Provides undergraduate life science students with a succinct overview of major mathematical concepts that are essential for modern biology
Covers all the major quantitative concepts that national reports have identified as the ideal components of an entry-level course for life science students
Provides good background for the MCAT, which now includes data-based and statistical reasoning
Erin N. Bodine is assistant professor of mathematics at Rhodes College. Suzanne Lenhart is Chancellor's Professor of Mathematics at the University of Tennessee. Louis J. Gross is Distinguished Professor of Ecology and Evolutionary Biology and Mathematics at the University of Tennessee.
Endorsements:
"This is the book I always wanted to write, a masterful and thorough introduction to the basic mathematical, statistical, and computational tools one needs to address biological problems, punctuated with solid and motivational applications to biology. The book is a seamless and authoritative treatment, with broad scope, that makes an ideal text for an introductory course."--Simon A. Levin, editor of The Princeton Guide to Ecology
"This book presents mathematics as the Esperanto of science, which it truly is. The authors provide salient topics in understandable form, selecting examples that capture the interest of biologists. Mathematics for the Life Sciences is as useful as it is stimulating."--Rita Colwell, University of Maryland Institute for Advanced Computer Studies
"This book does an admirable job of covering the mathematical topics that are essential for studying and analyzing biological systems. By bringing them together in a single coherent and well-written volume, the authors have produced a text that will truly serve undergraduate students in biology. The exercises are particularly well done."--Alan Hastings, University of California, Davis
"This is a thorough, self-contained introductory textbook for training undergraduate students in basic mathematical and statistical methods that are important in biological sciences. Students are introduced to topics ranging from probability and statistics to matrix theory and calculus, with a brief introduction to modeling using difference and differential equations. Two unique features of this textbook are the inclusion of real-world biological data to motivate particular methods and the use of MATLAB for computational purposes."--Linda J. S. Allen, Texas Tech University | 677.169 | 1 |
1 2 3 4 5 6 7 8 9 10 066 14 13 12 11 10 09 08 ... The exercises are designed to aid your study of mathematics by reinforcing important ... and lesson, with two practice worksheets for every lesson in Glencoe Pre-Algebra. ... The answers to these worksheets are available at the end of each Chapter Resource Masters booklet. | 677.169 | 1 |
"Engineering Mathematics Through Applications" is a new textbook for all students on first-year engineering and pre-degree courses. It teaches mathematics in a step-by-step fashion, putting the mathematics into its engineering context at every stage. A comprehensive first-year course. Hundreds of examples and exercises, the majority set in an applied engineering context so that the students immediately see the purpose of what they are learning. Introductory chapter revises indices, fractions, decimals, percentages and ratios. Fully worked solutions to every problem on the companion website at www palgrave.com/science/engineering/singh Includes calculator and mathematical software examples and exercises. Student-friendly style encouraging active participation.
More About the Author
My interest in mathematics began at school. I am originally of Asian descent, and as a young child often found English difficult to comprehend, but I discovered an affinity with mathematics, a universal language that I could begin to learn from the same start point as my peers. I did my undergraduate studies on a part-time basis at Birkbeck College, University of London whilst working full time for Lucas Aerospace developing underwater guidance systems. After this I did my post graduate study at Imperial College, London. My passion has always been to teach, and I have taught mathematics at the University of Hertfordshire since 1992. I am the author of 'Engineering Mathematics through Applications', a book that I am proud to say is used widely as the basis for undergraduate studies in many different countries. I am also the author of Linear Algebra Step by Step which is published by Oxford University Press in October 2013. I also host and regularly update a website dedicated to mathematics; My family and career leave little room for outside interest, but I am a keen football fan and occasional cyclist. Born: Hertfordshire UK Religion: Sikh Interests: Cycling, walking, watching football, boxercise. Heroes: Sant Jarnail Singh Ji Bhindranwale, Bobby Sands, Malala.
Product Description
Review
'The unique quality of this book is the wealth of examples applying the mathematical techniques taught here. These examples span mechanics, aerodynamics, electronics, engineering, fluid dynamics and other areas of applied mathematics. These are not just the usual examples involving differential equations and equations of motion, but real and thoughtful applications that will be relevant to the student.' - Jill Russell, Open University 'If you teach a first year mathematics module to a diverse engineering group, this book should be at the top of your list for consideration as a core text. It aims to encourage their [the students] learning through setting the mathematics within the context of engineering examples. With its very readable text it is suitable for both self-study and as support for a taught module. The book covers the requirements of most first year engineering mathematics modules with a fairly gentle reminder of arithmetic and algebra by way of introduction. Examples are drawn from such diverse subjects as electricity, control theory, heat flow, structures, fluid mechanics, signal processing, thermodynamics etc with the largest group being from mechanics. The examples are simple enough to be understood by most engineering students but sufficiently specific to allow students to see that mathematics is relevant to their own engineering discipline. I liked the presentation of the text - the questions posed to the reader, the full labelling in diagrams and the indication to students of the discipline of the examples. Helpful extra information is occasionally provided in subscript format to indicate the method used to move from one line to the next.' - Dr Ian Taylor, Faculty of Engineering at The University of Ulster, Engineering Subject Centre 'The book starts with the basics of mathematics making it suitable for those with little background in mathematics. This also makes it appealing to a wide variety of readers with different mathematical backgrounds. The book is a good size covering all the essential topics to adequate depth. It covers topics similar to other books targeted at the same audience; however it differs in that it does not assume readers to have a mathematical background. The book's approach of using examples is effective. Its use of examples is motivating. The engineering example generates interest by illustrating the importance and relevance of mathematics in engineering. A definite plus is the provision of online interactive questions, which enable users to test their understanding. This extra support makes it an ideal text for self-study and distance learning.' - Dr Lawrence Chirwa, School of Electrical and Mechanical Engineering at The University of Ulster, Engineering Subject Centre 'This is a book that is designed to cover the basics thoroughly and then move on. As a reminder of useful techniques, the book is definitely valuable. What is most refreshing is that it explains everything that you need to know in order to cover the basics of a given subject. The fact that there is almost no assumed knowledge is reassuring, and takes some of the mental strain away from getting your head around eigenvectors again... Essentially, if you want to remind yourself how to do those things that you once thought were straightforward, this is the book for you. A very useful book to have on your shelf.' --Edward Hoare, The Institution of Structural Engineers
The book is excellent, and I'm finding it tremendously helpful. I've been using it as a companion to the legendary title, Engineering Mathematics, by K. Stroud. Both books are first rate. student I'm finding that the examples and problems provided by Mr. Singh give me additional insight and understanding of the topics, relating them directly to my mechanical engineering course work. This makes it easier to actually use the maths I'm learning in a useful way. --student
From the Author
It took me six years to write this book and I am pleased with the outcome. There have been excellent independent reviews of the book. Have a look at the Amazon and other reviews below.
Most Helpful Customer Reviews
This book is a very worthwhile investment for undergraduate engineering students and experienced engineers alike. The layout is modern, crisp and user friendly; this combined with the refreshing approach taken by the author makes for an excellent resource for learning and quick reference. Each topic is covered adequately from transposition of formulae to differentiation; the sections start with a description of the topic, then the properties & execution, examples and a summary. The author has also included some useful tips throughout the sections. As a Consulting Engineer in the field of Building Services Engineering and a Post Grad Student I have found the reference within the worked examples to various engineering disciplines to be particularly useful, which makes reference to thermodynamics, mechanics, fluid mechanics, electrical etc. So the reader can process many different forms of the maths theory as well finding an example more compatible with their own discipline. Finally, a number of exercises are provided with solutions in the rear to enable the reader to apply what has been taught. This book is well worth the outlay !
I am very grateful for the book "Engineering Mathematics Through Applications" and suggest that Mr.Singh is probably the best teacher in the world for the subject of mathematics. I mean that quite sincerely. I have found none superior.
I have recently re-discovered his book in my collection to help with a bit of revision for my daughter, prior to her commencing A-Level studies. I confess that I had not properly read the early chapters. A huge error on my part, as both my daughter and I were delighted to find his eloquent execution of the subject - in particular the basics. I have many books on the subject, but none impart comprehension in the way he does, with such brilliantly clear and logical instruction. And definitely not in the category of current GCSE and A-Level study publications. I certainly remember my studies many years ago and wish I had had a teacher like Mr.Singh at the helm.
Knowing a subject and knowing how to teach it are two entirely different skills which are for the most part these days, sadly lost in the modern education system. He has clearly mastered both arts.
I would whole-heartedly recommend his publications and teachings to anyone looking to better understand the "why's" and "how's", in addition to the usual "mechanics" of maths, from the most simple through to the complex. I have long been of the opinion that a student's interest and success in a subject is in direct proportion to the enthusiasm, ability and teaching skill of the teacher, and that students become more involved when they have clear comprehension of subject. He has achieved all the above superbly.
This is the first book I have seen which places mathematics in an engineering context. Singh deserves praise for writing such a thorough book on what most engineering students find diffcult. The book will be most useful to engineering students as well as other disciplines having a mathematics content. I am not surprised it has taken Singh 6 years to write this book, it clearly shows the effort. It has a good layout and the topics are well sign posted. Each section begins with the objectives and ends with a summary and a set of exercises. The exercises are all in an engineering discipline. Also full solutions are on the book's web site which I found very useful. There are a series of on line tests on the web site but some of the maths symbols are missing. An engineering student will find this book a great asset.
I'm not one to review books normally, but I had to stress how much this book has helped me get to grips with some very complex math... 4 weeks ago I would have just stared in terror at the stuff I am doing now. Each section starts at a simple pace, with plenty of examples to work through, then follows with questions of increasing difficulty.
It started, with the 'Introduction' chapter, with the very basics, but as I hadn't had any reason to do math for about 20 yrs it was very welcome! It has quickly increased in complexity, but I haven't had any trouble getting through the examples / questions and knowledge retention has been high, each section building on the last.
It's also interesting to see questions / examples relating to real world engineering / physics... I can finally see math as a language for solving problems rather than a series of manipulations with no real relevance to anything, so it has helped a lot in this regard too :)
The most amazing and the best Maths book in the World. I am a teacher myself and recommend it to everyone - although I have its first edition and bought it as a good second hand book, it's better than any Maths book I have ever seen. I assume that new editions must be even better.
This is the best book on mathematics i have ever read so far, simplified and applied. Books like this one would create interest among students and motivate them for self learning. I congratulate author for this mammoth effort. | 677.169 | 1 |
Importance of maths not fully understood by students
June 25, 2014
Too many sixth form students do not have a realistic understanding of either the relevance of Mathematics and Statistics to their discipline or of the demands that will be put upon them in undergraduate study, according to a new report published today by the Higher Education Academy (HEA). The report examines the mathematical and statistical needs of students in undergraduate disciplines including Business and Management, Chemistry, Economics, Geography, Sociology and Psychology.
Professor Jeremy Hodgen, lead author of the report from the Department of Education & Professional Studies, said: 'Too few students in the UK study Mathematics after the age of 16, yet the study demonstrates that Mathematics matters across a range of subjects at university. The report recommends that prospective undergraduates are better informed of this when applying to higher education.'
Lack of confidence and anxiety about Mathematics and Statistics is also a problem for many students, making the transition into higher education particularly challenging. A number of recommendations are made within the report to address this problem, but overall it calls for better dialogue between the sectors so that pre-university students have a better understanding of what is expected of them and the higher education sector has a better understanding of what their undergraduates can do.
The report also draws attention to developments at pre-university level, where new 'Core Maths' courses are being designed to meet the needs of the many students (the report estimates at least 200,000 a year) who need Mathematics but for whom a full A-level would not be appropriate. It calls for higher education to become actively involved in and to influence this work.
Dr Mary McAlinden, Discipline Lead for Mathematics, Statistics and Operational Research at the HEA said: 'Many students are surprised at the amount of mathematical content in their undergraduate programmes and some struggle to cope with this content.
'This project, and the accompanying reports, seeks to promote greater understanding between the higher education and pre-university sectors so that students will arrive at university better prepared and better able to cope with the mathematical and statistical demands of their undergraduate studies.'
Dr Janet De Wilde, Head of STEM at the HEA said: 'This report demonstrates the importance that the HEA places on this topic. The recommendations it contains are valuable to the sector to help further the discussion between the secondary and tertiary sector to inform policy development and teaching practice to address the importance of mathematical and statistical skills.'
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For many years, studies have shown that American students score significantly lower than students worldwide in mathematics achievement, ranking 25th among 34 countries. Now, researchers from the University of Missouri | 677.169 | 1 |
Elementary Education
Mathematics for Elementary Teaching II
Class Level: Junior
Credits: 2
Department: Education
Term:
Description: This course is the second foundational course in the mathematics content area for elementary education majors. It includes exploration of our number system including properties, basic operations and algorithms, probability, statistics, measurement, coordinate geometry, graphs, and 2- and 3-dimensional geometry. Problem solving is stressed in each unit. The NCTM Principles and Standards and Indiana?s Academic Standards for Mathematics are introduced. Prerequisite: MAT 323. Taken concurrently with EDE 337, EDE 345, EDE 366, and EFE 385. Additional prerequisite: 2.50 GPA and admission to the teacher education program. Spring, junior | 677.169 | 1 |
YOU WILL NEED
1. Students will be able to analyze the basic properties of
functions.
2. Students will be able to manipulate algebraic expressions
at the level appropriate to the course.
3. Students will be able to graph algebraic and transcendental
functions and their transformations.
4. Students will be able to correctly model a real world
situation using algebra, geometry, exponentials, logarithms and/or trigonometry
and use this model to solve problems.
TESTS: Worth
50% of your grade.
There will be Five comprehensive exams, the dates of
which you can find in the calendars. In the event that you miss an
exam, that exam will be replaced by the Final exam.No make-up exams. If you can not take an exam due to a
documented excuse, you must notify me prior to the exam with a written
statement or a document.All missed
exams without appropriate reasons and/or documentation will receive a score of
zero.Exams will be brought to the
classroom once after they have been graded. If you are absent from class on the
day the exams are returned, you must pick up your exam on the next lecture
day.10 points will be deducted from
your exam score if your cell phone device rings or you go outside during an
exam.
The final exam is cumulative and is worth 25% of your
grade.
CLASS-WORK:Worth
10% of your grade.
In class, you will be assigned group-work to help you better
prepare for the homework and the tests. All members of the group are expected
to work on each problem. Although I will help you out with difficult problems,
I encourage you to talk to EACH OTHER first before asking me questions. You
will work with 2 or 3 different groups throughout the semester. Students who
are absent may submit missed group work for that day for a maximum score of 8
points at the end of the next lecture.
QUIZZES: Worth
10% of your grade.
Quizzes will be given in accordance with your homework
assignments AND unannounced unexpectadly. Quizzes often include problems
directly taken from the homework/classwork assignment. One of your lowest
scoring quizzes will be dropped. NO MAKEUP!
WEBSITE INFORMATION
You can find my page by visiting Pasadena college website at
and then doing PCC
people search for Alina Daych at the top right corner.Then click on my name when it comes up on
the screen.You will see your class
link under WINTER 2011 on the right.There you will find your syllabus, calendar and homework assignment, as
well as other assignment throughout the semester.
SPRING 2011:PASADENA CITY COLLEGE
MATHEMATICAL ANALYSIS 1:MATH 7A,#5241
HOMEWORK
It is recommended that
students spend at least 3 hours each day to review the class notes, read the
pertinent sections in the
textbook, solve the homework problems and pre-read and take notes for
the sections which will be
covered in the next class session. Homework is to be completed via WebAssign.
The code to access WebAssign is available with a purchase of a new book.Alternatively, it can also be purchased at can use PCC computer lab in the lower
level of the D-building. Instructions for registering are on the inside cover
of the textbook.
Homework problems should
be written up neatly in a spiral notebook or a binder,solved completely and with sufficient
explanations. Bring your HW-notebook/binder to every lecture so that you can
ask questions and make corrections in class. Do not get behind in your
homework. It will be difficult to catch up with the class.
If you cannot complete a
problem, click on "show an example or "help me solve this".If after several attempts you are still
unable to complete the problem, click "ask my instructor" and tell me what you
think is wrong with your approach.At
the next class meeting I will attempt to go over all your questions (or as many
as time allows). I will only go over questions that are sent to me.
The homework assignment
are required in order to take the homework quizzes. There are no deadline to
complete the homework, but there are deadlines for the homework quizzes.
HOMEWORK QUIZZES:Worth 10% of your grade.
You can complete the
homework quizzes on WebAssign.You will
be able to access the quiz once you have completed the homework
prerequisite.There will be a 2 point
deduction on the exam for each quiz not taken for that exam.
GRADING
50%=Chapter Tests20%=Final Exam
10%=Quizzes10%=Homework
Quizzes
10%=Classwork
90-100% is an A; 80-89% is a B; 70-79% is a C; 60-69% is a
D; 0-59% is an F.
STUDENT CONDUCT
If you have a pager/cellular
phone, please turn off while you are in class. If it rings during the class it
will be kept with the instructor until the end of the class and 10 points
deducted from your exam. Please do not have unnecessary talking and gossiping,
food or drinks, chewing gum, going in and out during the class, sleeping, rude
yawning, disrespect for one another, writing on desktops, retractable
erasers.Cheating of any kind will be
punished in according with Pasadena City College guidelines.
DROP AND ATTENDANCE POLICY
You are allowed for a maximum of 10 missed
class-hours; the equivalent to 4 classes.Three tardies are equivalent to an absence. If you are more than 15
minutes late or leave more than 15 minutes before class, that will account as
an absence.If you leave during class
and then return you will be assessed a tardy.You can be dropped for the poor attendance. | 677.169 | 1 |
... for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package. Features includes Graphics, algebra and tables are connected and fully dynamic, Easy-to-use ... mathematical objects of several types used for calculus, algebra and geometry. Since this is a Java-based application, ...
... Excel) give P(X less than A) and using algebra other results can be found whereas ESBPDF Analysis is Probability Analysis Software that handles all the combinations for you. Features include Binomial, Poisson, Hypergeometric, Normal, Exponential, Student t, Chi Squared, F, Beta and Lognormal Distributions; Inverses of Normal, Student t, Chi ...
The Matrix ActiveX Component is a useful tool that can simplify the use of matrix operations for mathematical computations in application development. It provides for matrix operations such as addition, subtraction, multiplication, inversion, transpose, and computation of determinant, LU and Cholesky decompositions. Advanced edition additionally supports QR and Singular Value (SVD) ...
... way. The program covers the areas Analysis, Geometry, Algebra, Stochastics,Vector algebra.MathProf helps Junior High School students with problems in Geometry and Algebra. High School and College students, seeking to expand ...
... perform matrix mathematics plus solve sets of linear algebraic equations. There is also an integrated context sensitive help system with numerous tutorials in .wmv file format which will significantly reduce the time it takes to learn Math Mechanixs. ...
Build whole number and fraction computation skills. Number by number problem exercises. Includes whole number math facts, addition, subtraction, multiplication and division of whole numbers and fractions. Also includes English and Metric measurements. Simple to complex problem generation. Printed worksheets for testing in all areas. Suitable for all age, grade and ...
Simple Solver is a free Windows application that can simplify computer logic systems, Boolean equations, and truth tables. The application includes six different tools:Logic Design Draw, Logic Simulation, Logic Design Auto, Boolean, Permutation and Random Number. These tools are built on years of engineering design experience and are intended for both ...
Logic Minimizer is an innovative, versatile application for simplifying Karnaugh maps and logical expressions step by step. It is geared for those involved in engineering fields, more precisely digital and formal logic scholars and academics, digital devices constructors or anybody involved with logical expressions. With its powerful minimization capabilities and full-fledged ... | 677.169 | 1 |
The Problems of the Week are designed to challenge students with non-routine problems and to encourage them
to verbalize their solutions. There are Elementary, Middle School, Algebra, Geometry, Trigonometry &
Calculus, and Discrete Mathematics Problems of the Week. The Problem of the week is a mentored environment in which students submit
solutions to a math challenge. Each submission is responded to by a mentor.
The Math Forum has collected, organized, cataloged and annotated thousands of math related web sites from diverse sources to create its Internet Mathematics Library. You can browse or search this gold mine of mathematics, organized under the headings of Mathematics Topics, Resource Types, Mathematics Education Topics or Educational Level. Clicking on any of these headings yields a hierarchical outline. Clicking on a category in the outline takes you to a page showing subcategories, selected sites, and all sites in the category. This format is consistent as you 'drill down'.
Teacher2Teacher is like a virtual teacher's lounge in that people pose questions and share opinions about topics ranging from classroom teaching techniques to good Internet resources for professional development. The initial responses are provided by mentor teachers, most of whom are Presidential Awardees for Excellence in Mathematics Teaching.
Ask Dr. Math is an ask-an-expert service in which math
questions at all levels are asked of our volunteer doctors. A
searchable archive is available by level and topic, together with a FAQ and Classic Problems
section.
We have over 300,000 pages, so this is quite an extensive search arena. You may also search a specific area, which may give you a more focused, and in the case of the discussion groups, a more thorough search.
The Math Forum's discussion archives
include mathematics and math education-related newsgroups, mailing lists, and Web-based discussions.
(E.g., Math-Teach, Numeracy, Geometry-Pre-College, K-12 Math Education, Math History List, NCTM
Standards 2000, etc.) For example, we host discussions for AMTE, the Association of Mathematics Teacher
Educators. Many of these groups are open to the public.
An electronic newsletter is sent out via e-mail once a week to those who subscribe, and is archived on the Web and as a Web discussion. It offers site tips (what we have at the Math Forum and how to find it), notes about new items on the site or on the Internet, questions and answers from the Math Forum's interactive math projects (Ask Dr. Math, Problems of the Week), suggestions for K-12 teachers and students, and pointers to key issues in mathematics and math education.
You might want to browse through an issue or two. You are welcome to subscribe to the newsletter as one immediate way to join the community. | 677.169 | 1 |
During this webinar we will present a number of examples of mathematics in film, including those done capably, as well as questionable and downright "creative" treatments. See relevant, exciting examples that you can use to engage your students, or attend this webinar simply for its entertainment value. Have you ever wondered if the bus could really have jumped the gap in "Speed?" We've got the answer! Anyone with an interest in mathematics, especially high school and early college math educators, will be both entertained and informed by attending this webinar. At the end of the webinar you'll be given an opportunity to download an application containing all of the Hollywood examples that we demonstrate.
This webinar will highlight the wide variety of statistics questions that are available for use in Maple T.A. See how Maple graded, mathematical formula, and other question types can enhance your statistics assessments. The presentation will also demonstrate a simple example of how to create your own statistics questions in Maple T.A. | 677.169 | 1 |
A resource written specifically for the Principles of Mathematics 10 (MPM2D) course. Principles of Mathematics 10 will help students learn the mathematics skills and concepts they need to succeed in school and beyond.
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books.google.com - Aimed primarily at higher level undergraduates in the mathematical sciences, the author provides the reader with a deep understanding of the uses and limitations of multivariate calculus by the integrated use of geometric insight, intuitive arguments, detailed explanations and mathematical reasoning.... Calculus and Geometry | 677.169 | 1 |
Description: This an introduction to linear algebra with solutions to all exercises. It covers linear equations, matrices, subspaces, determinants, complex numbers, eigenvalues and eigenvectors, identifying second degree equations, and three–dimensional geometry. | 677.169 | 1 |
Linear Algebra
9780135367971
ISBN:
0135367972
Edition: 2 Pub Date: 1971 Publisher: Prentice Hall
Summary: This introduction to linear algebra features intuitive introductions and examples to motivate important ideas and to illustrate the use of results of theorems. Linear Equations; Vector Spaces; Linear Transformations; Polynomials; Determinants; Elementary canonical Forms; Rational and Jordan Forms; Inner Product Spaces; Operators on Inner Product Spaces; Bilinear Forms For all readers interested in linear algebra. ...> Hoffman, Kenneth is the author of Linear Algebra, published 1971 under ISBN 9780135367971 and 0135367972. Four hundred thirty eight Linear Algebra textbooks are available for sale on ValoreBooks.com, twenty five used from the cheapest price of $60.85, or buy new starting at $170 Ship | 677.169 | 1 |
Video: Up and Running with Mathematica 9: Welcome
Hi, I'm Curt Frye. Welcome to Up and Running with Mathematica 9. In this course, I'll show you how to use Mathematica to perform calculations on your data. I'll start by showing you how to run Mathematica, manage Mathematica Notebooks and get help if you need it. Next I'll show you how to assign values to variables, use built-in commands to control Mathematica and perform calculations using mathematical operators and built-in functions.
Mathematica is a computational platform with the power and flexibility you need to analyze data and make good decisions for your company. Similar to a programming language, it provides a complete environment for doing math. This course shows information workers how to perform advanced data analysis using Mathematica 9.
Curt Frye teaches you how to set up Mathematica notebooks, assign values to variables, perform simple calculations, create and manipulate matrices, enter equations in linear and descriptive form, write and debug Mathematica scripts, and visualize data with charts.
NOTE: Basic knowledge of linear algebra is helpful for this course, but not required.
Welcome
Hi, I'm Curt Frye.Welcome to Up and Running with Mathematica 9.In this course, I'll show you how touse Mathematica to perform calculations on your data.I'll start by showing you how to run Mathematica,manage Mathematica Notebooks and get help if you need it.Next I'll show you how to assign values to variables, use built-incommands to control Mathematica and performcalculations using mathematical operators and built-in functions.
Chapter Three shows you how to performcalculations on matrix and vector data, whileChapter Four demonstrates how to use externaldata, comment your code, and debug your scripts.Finally, Chapter Five demonstrates how to plot yourdata using the capabilities built in to Mathematica 9.All of these methods provide the power and flexibility you need toanalyze your data, so you can make good decisions for you company.I'm sure you'll find that your time with Upand Running with Mathematica 9 will be time well spent | 677.169 | 1 |
Description: At first blush one might think that of all areas of mathematics certainly arithmetic should be the simplest, but it is a surprisingly deep subject. We assume that students have some familiarity with basic set theory, and calculus. To a great extent the book is self-contained. It requires only a certain amount of mathematical maturity. Before the course is over students will be introduced to the symbolic programming language Maple which is an excellent tool for exploring number theoretic questions. | 677.169 | 1 |
Now even the most uncertain students can overcome math anxiety and confidently master key mathematical concepts and their business applications with Brechner/Bergeman CONTEMPORARY MATHEMATICS FOR BUSINESS AND CONSUMERS, 7E. This unique modular approach invites students into a successful, interactive learning experience with numerous real-world business examples and integrated teaching technology. The author continues to incorporate a proven step-by-step instructional model that allows students to progress one topic at a time without being intimidated or overwhelmed. This new edition offers a fresh, reader-friendly design with a wealth of revised and new engaging learning features that connect the latest business news to chapter topics and provide helpful personal money tips. Students...
Less
Now in its 8th edition, MATHEMATICS FOR PLUMBERS AND PIPEFITTERS delivers the essential math skills necessary in the plumbing and pipefitting professions. Starting with a thorough math review to ensure a solid foundation, the book progresses into specific on-the-job applications, such as pipe length calculations, sheet metal work, and the builder's level.Broad-based subjects like physics, volume, pressures, and capacities round out your knowledge, while a new chapter on the business of plumbing invites you to consider an exciting entrepreneurial venture. Written by a Master Plumber and experienced vocational educator, MATHEMATICS FOR PLUMBERS AND PIPEFITTERS, 8th Edition includes a multitude of real- world examples, reference tables, and formulas to help you build a rewarding career | 677.169 | 1 |
Course Learning Outcomes The student will:
• Be able to solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion.
• Be able to carry out matrix operations, including inverses and determinants.
• Demonstrate understanding of the concepts of vector space and subspace.
• Demonstrate understanding of linear independence, span, and basis.
• Be able to determine eigenvalues and eigenvectors and solve problems involving eigenvalues.
• Apply principles of matrix algebra to linear transformations.
• Demonstrate application of inner products and associated norms.
• Construct proofs using definitions and basic theorems.
Graphing Calculator required. TI 83, TI 84 or TI 86 series calculators recommended.
Calculators capable of symbolic manipulation will not be allowed on tests. Examples include, but are not limited to, TI 89, TI 92, and Nspire CAS models and HP 48 models.
Neither cell phones nor PDA's can be used as calculators. Calculators may be cleared before tests. | 677.169 | 1 |
Details about Intermediate Algebra through Applications:
KEY MESSAGE: Presented in a clear and concise style, the Akst/Bragg series teaches by example while expanding understanding with applications that are fully integrated throughout the text and exercise sets. Akst/Bragg's user-friendly design offers a distinctive side-by-side format that pairs each example and its solution with a corresponding practice exercise. The concise writing style keeps readers' interest and attention by presenting the mathematics with minimal distractions, and the motivating real-world applications demonstrate how integral mathematical understanding is to a variety of disciplines, careers, and everyday situations. KEY TOPICS: Algebra Basics; Linear Equations and Inequalities; Graphs, Linear Equations and Inequalities, and Functions; Systems of Linear Equations and Inequalities; Polynomials; Rational Expressions and Equations; Radical Expressions and Equations; Quadratic Equations, Functions, and Inequalities; Exponential and Logarithmic Functions; Conic Sections MARKET: for all readers interested in intermediate algebra. | 677.169 | 1 |
College Algebra (3rd Edition)
9780321466075
ISBN:
0321466071
Edition: 3 Pub Date: 2007 Publisher: Addison Wesley
Summary: These authors have created a book to really help students visualize mathematics for better comprehension. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition, the authors have added a variety of new tools to help students better use the book for maximum effecti...veness to not only pass the course, but truly understand the material.
Judith A. Beecher is the author of College Algebra (3rd Edition), published 2007 under ISBN 9780321466075 and 0321466071. Three hundred sixteen College Algebra (3rd Edition) textbooks are available for sale on ValoreBooks.com, one hundred thirty six used from the cheapest price of $2.48, or buy new starting at $34 | 677.169 | 1 |
Traditional optimization techniques, such as those based on classical calculus, are
useful and work well in decision environments that are not complex. When a decision
environment becomes complex either due to resource limitations or the presence of
interdependent goals and alternatives, traditional optimization techniques do not
always produce the best results. Given that most decision environments are complex,
one needs to use more efficient tools like mathematical programming that can deal
with these complexities more effectively. Mathematical programming is a generic term
used for a group of programming models where each model is based on a set of
interrelated, but well-defined structures, equations, and assumptions. Models are
abstract representations of the real world. As abstractions of the real world, they can
only deal with the most important elements of the world. It is not possible for any
model to capture every single element of a system in all its intricate details; it is costly,
time consuming, and even difficult to analyze. Mathematical programming models are
no exception. As quantitative tools, they attempt to capture only the most important
elements and relationships that exist in a real system using mathematical relations. As
a general rule, the more complex a system, the more complex the relations.
This chapter presents four of the most widely discussed programming models: linear
programming, integer programming, dynamic programming, and heuristic programming. Because of its widespread use and importance, the chapter examines the linear
programming model in much greater detail than the rest of the models.
LINEAR PROGRAMMING
Linear programming is the most well known among all mathematical programming
models. Developed during World War II as a mathematical technique to deal with the
problems of military logistics,
1 it has since been applied to a wide variety of problems
and disciplines ranging from industrial technology to education to medicine to
economics and business. It is the forerunner of all mathematical programming models
Print this page
While we understand printed pages are helpful to our users, this limitation is necessary
to help protect our publishers' copyrighted material and prevent its unlawful distribution.
We are sorry for any inconvenience. | 677.169 | 1 |
New Zealand Mathematics 10 Homework Book
This Homework Book is designed to be used in conjunction with New Zealand Mathematics for Year 10 textbook.
The aim of this Mathematics Homework Book is to assist students to become more proficient in the skills which they have learned in class. About 500 questions are provided for Chapters 1-14 in the textbook, covering the basic course for Year 10. (Questions are not provided for the two extension chapters 15 "NCEA Test Types for Level 5" and 16 "Extension Algebra".)
The questions are carefully graded and answers are provided in a centre section which can be removed easily, should the teacher so desire. Worked Examples and Reminders are sprinkled throughout as helpful references for students when working independently at home. | 677.169 | 1 |
Introduction to Finite Fields and their Applications
2nd Edition
University of Tasmania
National University of Singapore
Hardback
Manufactured on demand: supplied direct from the printer
(Stock level updated: 01:59 GMT, 29 August 2015)
£99.99
The theory of finite fields is a branch of modern algebra that has come to the fore in recent years because of its diverse applications in such areas as combinatorics, coding theory, cryptology and the mathematical study of switching circuits. The first part of this updated edition presents an introduction to this theory, emphasising those aspects that are relevant for application. The second part is devoted to a discussion of the most important applications of finite fields, especially to information theory, algebraic coding theory and cryptology. There is also a chapter on applications within mathematics, such as finite geometries, combinatorics and pseudo-random sequences. The book is meant to be used as a textbook: worked examples and copious exercises that range from the routine, to those giving alternative proofs of key theorems, to extensions of material covered in the text, are provided throughout. It will appeal to advanced undergraduates and graduate students taking courses on topics in algebra, whether they have backgrounds in mathematics, electrical engineering or computer science. Non-specialists will also find this a readily accessible introduction to an active and increasingly important subject.
• Includes many examples and exercises
• Few prerequisites
• Contains many applications
Reviews
' … a model of how a text book should be written; it is clear, unfussy and contains lots of examples … of particular interest to anybody wishing to teach a course in concrete algebra'
Mathematika
' … a very useful and highly readable introduction to the classical theory and the standard applications of finite fields. It has a clear and precise presentation with many examples and a large selection of exercises.'
The Mathematical Gazette | 677.169 | 1 |
will continue to build on
this foundation as they expand their understanding through other mathematical
experiences.
(2) Algebraic thinking and symbolic reasoning.
Symbolic reasoning plays a critical role in algebra; symbols provide powerful
ways to represent mathematical situations and to express generalizations.
Students use symbols in a variety of ways to study relationships among quantities.
(3) Function concepts. A function is a fundamental
mathematical concept; it expresses a special kind of relationship between
two quantities. Students use functions to determine one quantity from another,
to represent and model problem situations, and to analyze and interpret relationships.
(4) Relationship between equations and functions.
Equations and inequalities arise as a way of asking and answering questions
involving functional relationships. Students work in many situations to set
up equations and inequalities and use a variety of methods to solve them understands
that a function represents a dependence of one quantity on another and can
be described in a variety of ways. The student is expected to:
(B) identify mathematical domains and ranges
and determine reasonable domain and range values for given situations, both
continuous and discrete;
(C) interpret situations in terms of given
graphs or creates situations that fit given graphs; and
(D) collect and organize data, make and interpret
scatterplots (including recognizing positive, negative, or no correlation
for data approximating linear situations), and model, predict, and make decisions
and critical judgments in problem situations.
(3) Foundations for functions. The student understands
how algebra can be used to express generalizations and recognizes and uses
the power of symbols to represent situations. The student is expected to:
(A) use symbols to represent unknowns and
variables; and
(B) look for patterns and represent generalizations
algebraically.
(45) Linear functions. The student understands
that linear functions can be represented in different ways and translates
among their various representations. The student is expected to:
(A) determine whether or not given situations
can be represented by linear functions;
(B) determine the domain and range for linear
functions in given situations; and
(C) use, translate, and make connections among
algebraic, tabular, graphical, or verbal descriptions of linear functions.
(6) Linear functions. The student understands
the meaning of the slope and intercepts of the graphs of linear functions
and zeros of linear functions and interprets and describes the effects of
changes in parameters of linear functions in real-world and mathematical situations.
The student is expected to:
(A) develop the concept of slope as rate of
change and determine slopes from graphs, tables, and algebraic representations;
(B) interpret the meaning of slope and intercepts
in situations using data, symbolic representations, or graphs;
(C) investigate, describe, and predict the
effects of changes in m and b on the graph of y = mx + b;
(D) graph and write equations of lines given
characteristics such as two points, a point and a slope, or a slope and y‑intercept;
(E) determine the intercepts of the graphs
of linear functions and zeros of linear functions from graphs, tables, and
algebraic representations;
(F) interpret and predict the effects of changing
slope and y-intercept in applied situations; and
(7) Linear functions. The student formulates
equations and inequalities based on linear functions, uses a variety of methods
to solve them, and analyzes the solutions in terms of the situation. The student
is expected to:
(B) investigate methods for solving linear
equations and inequalities using concrete models, graphs, and the properties
of equality, select a method, and solve the equations and inequalities; and
(C) interpret and determine the reasonableness
of solutions to linear equations and inequalities.
(8) Linear functions. The student formulates
systems of linear equations from problem situations, uses a variety of methods
to solve them, and analyzes the solutions in terms of the situation. The student
is expected to:
(A) analyze situations and formulate systems
of linear equations in two unknowns to solve problems;
(C) interpret and determine the reasonableness
of solutions to systems of linear equations.
(9) Quadratic and other nonlinear functions.
The student understands that the graphs of quadratic functions are affected
by the parameters of the function and can interpret and describe the effects
of changes in the parameters of quadratic functions. The student is expected
to:
(A) determine the domain and range for quadratic
functions in given situations;
(B) investigate, describe, and predict the
effects of changes in a on the graph of y = ax2 + c;
(C) investigate, describe, and predict the
effects of changes in c on the graph of y = ax2 + c; and
(D) analyze graphs of quadratic functions
and draw conclusions.
(10) Quadratic and other nonlinear functions.
The student understands there is more than one way to solve a quadratic equation
and solves them using appropriate methods. The student is expected to:
(B) make connections among the solutions (roots)
of quadratic equations, the zeros of their related functions, and the horizontal
intercepts (x-intercepts) of the graph of the function.
(11) Quadratic and other nonlinear functions.
The student understands there are situations modeled by functions that are
neither linear nor quadratic and models the situations. The student is expected
to:
(A) use patterns to generate the laws of exponents
and apply them in problem-solving situations; Algebraic thinking and symbolic reasoning.
Symbolic reasoning plays a critical role in algebra; symbols provide powerful
ways to represent mathematical situations and to express generalizations.
Students study algebraic concepts and the relationships among them to better
understand the structure of algebra.
(3) Functions, equations, and their relationship.
The study of functions, equations, and their relationship is central to all
of mathematics. Students perceive functions and equations as means for analyzing
and understanding a broad variety of relationships and as a useful tool for
expressing generalizations.
(4) Relationship between algebra and geometry.
Equations and functions are algebraic tools that can be used to represent
geometric curves and figures; similarly, geometric figures can illustrate
algebraic relationships. Students perceive the connections between algebra
and geometry and use the tools of one to help solve problems in the other uses
properties and attributes of functions and applies functions to problem situations.
The student is expected to:
(A) identify the mathematical domains and
ranges of functions and determine reasonable domain and range values for continuous
and discrete situations; and
(B) collect and organize data, make and interpret
scatterplots, fit the graph of a function to the data, interpret the results,
and proceed to model, predict, and make decisions and critical judgments.
(2A) use tools including factoring and properties
of exponents to simplify expressions and to transform and solve equations;
and
(B) use complex numbers to describe the solutions
of quadratic equations.
(3) Foundations for functions. The student formulates
systems of equations and inequalities from problem situations, uses a variety
of methods to solve them, and analyzes the solutions in terms of the situations.
The student is expected to:
(A) analyze situations and formulate systems
of equations in two or more unknowns or inequalities in two unknowns to solve
problems;
(B) use algebraic methods, graphs, tables,
or matrices, to solve systems of equations or inequalities; and
(C) interpret and determine the reasonableness
of solutions to systems of equations or inequalities for given contexts.
(4) Algebra and geometry. The student connects
algebraic and geometric representations of functions. The student is expected
to:
(B) extend parent functions with parameters
such as a in f (x) = a/x and describe the
effects of the parameter changes on the graph of parent functions; and
(C) describe and analyze the relationship
between a function and its inverse.
(5) Algebra and geometry. The student knows the
relationship between the geometric and algebraic descriptions of conic sections.
The student is expected to:
(A) describe a conic section as the intersection
of a plane and a cone;
(B) sketch graphs of conic sections to relate
simple parameter changes in the equation to corresponding changes in the graph;
(C) identify symmetries from graphs of conic
sections;
(D) identify the conic section from a given
equation; and
(E) use the method of completing the square.
(6) Quadratic and square root functions. The
student understands that quadratic functions can be represented in different
ways and translates among their various representations. The student is expected
to:
(A) determine the reasonable domain and range
values of quadratic functions, as well as interpret and determine the reasonableness
of solutions to quadratic equations and inequalities;
(B) relate representations of quadratic functions,
such as algebraic, tabular, graphical, and verbal descriptions; and
(C) determine a quadratic function from its
roots (real and complex) or a graph.
(7) Quadratic and square root functions. The
student interprets and describes the effects of changes in the parameters
of quadratic functions in applied and mathematical situations. The student
is expected to:
(A) use characteristics of the quadratic parent
function to sketch the related graphs and connect between
the y = ax2 + bx + c and the y = a (x - h)2 + k symbolic
representations of quadratic
functions; and
(B) use the parent function to investigate,
describe, and predict the effects of changes in a, h, and k
on the graphs of y = a (x - h)2 + k
form of a function in applied and purely mathematical situations.
(8) Quadratic and square root functions. The
student formulates equations and inequalities based on quadratic functions,
uses a variety of methods to solve them, and analyzes the solutions in terms
of the situation. The student is expected to:
(9) Quadratic and square root functions. The
student formulates equations and inequalities based on square root functions,
uses a variety of methods to solve them, and analyzes the solutions in terms
of the situation. The student is expected to:
(A) use the parent function to investigate,
describe, and predict the effects of parameter changes on the graphs of square
root functions and describe limitations on the domains and ranges;
(10) Rational functions. The student formulates
equations and inequalities based on rational functions, uses a variety of
methods to solve them, and analyzes the solutions in terms of the situation.
The student is expected to:
(A) use quotients of polynomials to describe
the graphs of rational functions, predict the effects of parameter changes,
describe limitations on the domains and ranges, and examine asymptotic behavior;
(B) analyze various representations of rational
functions with respect to problem situations;
(C) determine the reasonable domain and range
values of rational functions, as well as interpret and determine the reasonableness
of solutions to rational equations and inequalities;
(D) determine the solutions of rational equations
using graphs, tables, and algebraic methods;
(E) determine solutions of rational inequalities
using graphs and tables;
(F) analyze a situation modeled by a rational
function, formulate an equation or inequality composed of a linear or quadratic
function, and solve the problem; and
(G) use functions to model and make predictions
in problem situations involving direct and inverse variation.
(11) Exponential and logarithmic functions. The
student formulates equations and inequalities based on exponential and logarithmic
functions, uses a variety of methods to solve them, and analyzes the solutions
in terms of the situation. The student is expected to:
(A) develop the definition of logarithms by
exploring and describing the relationship between exponential functions and
their inverses;
(B) use the parent functions to investigate,
describe, and predict the effects of parameter changes on the graphs of exponential
and logarithmic functions, describe limitations on the domains and ranges,
and examine asymptotic behavior;
(C) determine the reasonable domain and range
values of exponential and logarithmic functions, as well as interpret and
determine the reasonableness of solutions to exponential and logarithmic equations
and inequalities;
(E) determine solutions of exponential and
logarithmic inequalities using graphs and tables; and
(F) analyze a situation modeled by an exponential
function, formulate an equation or inequality, and solve the problem.
Source: The provisions of this §111.33 adopted to be effective
September 1, 1996, 21 TexReg 7371; amended to be effective August 1, 2006,
30 TexReg 1931; amended to be effective February 22, 2009, 34 TexReg 1056. Geometric thinking and spatial reasoning.
Spatial reasoning plays a critical role in geometry; geometric figures provide
powerful ways to represent mathematical situations and to express generalizations
about space and spatial relationships. Students use geometric thinking to
understand mathematical concepts and the relationships among them.
(3) Geometric figures and their properties. Geometry
consists of the study of geometric figures of zero, one, two, and three dimensions
and the relationships among them. Students study properties and relationships
having to do with size, shape, location, direction, and orientation of these
figures.
(4) The relationship between geometry, other
mathematics, and other disciplines. Geometry can be used to model and represent
many mathematical and real-world situations. Students perceive the connection
between geometry and the real and mathematical worlds and use geometric ideas,
relationships, and properties to solve problems.
(5) Tools for geometric thinking. Techniques
for working with spatial figures and their properties are essential in understanding
underlying relationships. Students use a variety of representations (concrete,
pictorial, numerical, symbolic, graphical, and verbal), tools, and technology
(including, but not limited to, calculators with graphing capabilities, data
collection devices, and computers) to solve meaningful problems by representing
and transforming figures and analyzing relationships.
(6) Underlying mathematical processes. Many processes
underlie all content areas in mathematics. As they do mathematics, students
continually use problem-solving, language and communication, connections within
and outside mathematics, and reasoning (justification and proof). Students
also use multiple representations, technology, applications and modeling,
and numerical fluency in problem solving contexts.
(b) Knowledge and skills.
(1) Geometric structure. The student understands
the structure of, and relationships within, an axiomatic system. The student
is expected to:
(A) develop an awareness of the structure
of a mathematical system, connecting definitions, postulates, logical reasoning,
and theorems;
(B) recognize the historical development of
geometric systems and know mathematics is developed for a variety of purposes;
and
(C) compare and contrast the structures and
implications of Euclidean and non-Euclidean geometries.
(2) Geometric structure. The student analyzes
geometric relationships in order to make and verify conjectures. The student
is expected to:
(A) use constructions to explore attributes
of geometric figures and to make conjectures about geometric relationships;
and
(B) make conjectures about angles, lines,
polygons, circles, and three-dimensional figures and determine the validity
of the conjectures, choosing from a variety of approaches such as coordinate,
transformational, or axiomatic.
(A) determine the validity of a conditional
statement, its converse, inverse, and contrapositive;
(B) construct and justify statements about
geometric figures and their properties;
(C) use logical reasoning to prove statements
are true and find counter examples to disprove statements that are false;
(D) use inductive reasoning to formulate a
conjecture; and
(E) use deductive reasoning to prove a statement.
(4)Geometric structure. The student uses
a variety of representations to describe geometric relationships and solve
problems. The student is expected to select an appropriate representation
(concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems.
(5) Geometric patterns. The student uses a variety
of representations to describe geometric relationships and solve problems.
The student is expected to:
(B) use numeric and geometric patterns to
make generalizations about geometric properties, including properties of polygons,
ratios in similar figures and solids, and angle relationships in polygons
and circles;
(C) use properties of transformations and
their compositions to make connections between mathematics and the real world,
such as tessellations; and
(D) identify and apply patterns from right
triangles to solve meaningful problems, including special right triangles
(45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.
(6) Dimensionality and the geometry of location.
The student analyzes the relationship between three-dimensional geometric
figures and related two-dimensional representations and uses these representations
to solve problems. The student is expected to:
(A) describe and draw the intersection of
a given plane with various three-dimensional geometric figures;
(B) use nets to represent and construct three-dimensional
geometric figures; and
(C) use orthographic and isometric views of
three-dimensional geometric figures to represent and construct three-dimensional
geometric figures and solve problems.
(7) Dimensionality and the geometry of location.
The student understands that coordinate systems provide convenient and efficient
ways of representing geometric figures and uses them accordingly. The student
is expected to:
(A) use one- and two-dimensional coordinate
systems to represent points, lines, rays, line segments, and figures;
(B) use slopes and equations of lines to investigate
geometric relationships, including parallel lines, perpendicular lines, and
special segments of triangles and other polygons; and
(C) derive and use formulas involving length,
slope, and midpoint.
(8) Congruence and the geometry of size. The
student uses tools to determine measurements of geometric figures and extends
measurement concepts to find perimeter, area, and volume in problem situations.
The student is expected to:
(A) find areas of regular polygons, circles,
and composite figures;
(B) find areas of sectors and arc lengths
of circles using proportional reasoning;
(C) derive, extend, and use the Pythagorean
Theorem;
(D) find surface areas and volumes of prisms,
pyramids, spheres, cones, cylinders, and composites of these figures in problem
situations;
(E) use area models to connect geometry to
probability and statistics; and
(F) use conversions between measurement systems
to solve problems in real-world situations.
(9) Congruence and the geometry of size. The
student analyzes properties and describes relationships in geometric figures.
The student is expected to:
(A) formulate and test conjectures about the
properties of parallel and perpendicular lines based on explorations and concrete
models;
(B) formulate and test conjectures about the
properties and attributes of polygons and their component parts based on explorations
and concrete models;
(C) formulate and test conjectures about the
properties and attributes of circles and the lines that intersect them based
on explorations and concrete models; and
(D) analyze the characteristics of polyhedra
and other three-dimensional figures and their component parts based on explorations
and concrete models.
(10) Congruence and the geometry of size. The
student applies the concept of congruence to justify properties of figures
and solve problems. The student is expected to:
(A) use congruence transformations to make
conjectures and justify properties of geometric figures including figures
represented on a coordinate plane; and
(B) justify and apply triangle congruence
relationships.
(11) Similarity and the geometry of shape. The
student applies the concepts of similarity to justify properties of figures
and solve problems. The student is expected to:
(A) use and extend similarity properties and
transformations to explore and justify conjectures about geometric figures;
(B) use ratios to solve problems involving
similar figures;
(C) develop, apply, and justify triangle similarity
relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean
triples using a variety of methods; and
(D) describe the effect on perimeter, area,
and volume when one or more dimensions of a figure are changed and apply this
idea in solving problems.
Source: The provisions of this §111.34 adopted to be effective
September 1, 1996, 21 TexReg 7371; amended to be effective August 1, 2006,
30 TexReg 1931; amended to be effective February 22, 2009, 34 TexReg 1056.
(a) General requirements. The provisions of
this section shall be implemented beginning September 1, 1998, and at that
time shall supersede §75.63(bb) of this title (relating to Mathematics). Students
can be awarded one-half to one credit for successful completion of this course.
Recommended prerequisites: Algebra II, Geometry.
(b) Introduction.
(1) In Precalculus, students continue to build
on the K-8, Algebra I, Algebra II, and Geometry foundations as they expand
their understanding through other mathematical experiences. Students use symbolic
reasoning and analytical methods to represent mathematical situations, to
express generalizations, and to study mathematical concepts and the relationships
among them. Students use functions, equations, and limits as useful tools
for expressing generalizations and as means for analyzing and understanding
a broad variety of mathematical relationships. Students also use functions
as well as symbolic reasoning to represent and connect ideas in geometry,
probability, statistics, trigonometry, and calculus and to model physical
situations functions and equations and solve real-lifeB) determine the domain and range of functions
using graphs, tables, and symbols;
(C) describe symmetry of graphs of even and
odd functions;
(D) recognize and use connections among significant
values of a function (zeros, maximum values, minimum values, etc.), points
on the graph of a function, and the symbolic representation of a function;
and
(E) investigate the concepts of continuity,
end behavior, asymptotes, and limits and connect these characteristics to
functions represented graphically and numerically.
(2) The student interprets the meaning of the
symbolic representations of functions and operations on functions to solve
meaningful problems. The student is expected to:
(a) General requirements. The provisions of
this section shall be implemented beginning September 1, 1998. Students can
be awarded one-half to one credit for successful completion of this course.
Recommended prerequisite: Algebra I.
(b) Introduction.
(1) In Mathematical Models with Applications,
students continue to build on the K-8 and Algebra I foundations as they expand
their understanding through other mathematical experiences. Students use algebraic,
graphical, and geometric reasoning to recognize patterns and structure, to
model information, and to solve problems from various disciplines. Students
use mathematical methods to model and solve real-life applied problems involving
money, data, chance, patterns, music, design, and science. Students use mathematical
models from algebra, geometry, probability, and statistics and connections
among these to solve problems from a wide variety of advanced applications
in both mathematical and nonmathematical situations. Students use a variety
of representations (concrete, pictorial, numerical, symbolic, graphical, and
verbal), tools, and technology (including, but not limited to, calculators
with graphing capabilities, data collection devices, and computers) to link
modeling techniques and purely mathematical concepts and to solve appliedc) Knowledge and skills.
(1) The student uses a variety of strategies
and approaches to solve both routine and non-routine problems. The student
is expected to:
(A) compare and analyze various methods for
solving a real-life problem;
(B) use multiple approaches (algebraic, graphical,
and geometric methods) to solve problems from a variety of disciplines; and
(C) select a method to solve a problem, defend
the method, and justify the reasonableness of the results.
(2) The student uses graphical and numerical
techniques to study patterns and analyze data. The student is expected to:
(A) interpret information from various graphs,
including line graphs, bar graphs, circle graphs, histograms, scatterplots,
line plots, stem and leaf plots, and box and whisker plots to draw conclusions
from the data;
(B) analyze numerical data using measures
of central tendency, variability, and correlation in order to make inferences;
(C) analyze graphs from journals, newspapers,
and other sources to determine the validity of stated arguments; and
(D) use regression methods available through
technology to describe various models for data such as linear, quadratic,
exponential, etc., select the most appropriate model, and use the model to
interpret information.
(3) The student develops and implements a plan
for collecting and analyzing data (qualitative and quantitative) in order
to make decisions. The student is expected to:
(8) The student uses algebraic and geometric
models to describe situations and solve problems. The student is expected
to:
(A) use geometric models available through
technology to model growth and decay in areas such as population, biology,
and ecology;
(B) use trigonometric ratios and functions
available through technology to calculate distances and model periodic motion;
and
(C) use direct and inverse variation to describe
physical laws such as Hook's, Newton's, and Boyle's laws.
(9) The student uses algebraic and geometric
models to represent patterns and structures. The student is expected to:
(A) use geometric transformations, symmetry,
and perspective drawings to describe mathematical patterns and structure in
art and architecture; and
(B) use geometric transformations, proportions,
and periodic motion to describe mathematical patterns and structure in music.
Source: The provisions of this §111.36 adopted to be effective
September 1, 1998, 22 TexReg 7623; amended to be effective August 1, 2006,
30 TexReg 1931; amended to be effective February 22, 2009, 34 TexReg 1056.
§111.37. Advanced Quantitative
Reasoning (One Credit).
(a) General requirements. Students shall be
awarded one credit for successful completion of this course. Prerequisite:
Algebra II.
(b) Introduction.
(1) In Advanced Quantitative Reasoning, students
continue to build upon the K-8, Algebra I, Algebra II, and Geometry foundations
as they expand their understanding through further mathematical experiences.
Advanced Quantitative Reasoning includes the analysis of information using
statistical methods and probability, modeling change and mathematical relationships,
and spatial and geometric modeling for mathematical reasoning. Students learn
to become critical consumers of real-world quantitative data, knowledgeable
problem solvers who use logical reasoning, and mathematical thinkers who can
use their quantitative skills to solve authentic problems. Students develop
critical skills for success in college and careers, including investigation,
research, collaboration, and both written and oral communication of their
work, as they solve problems in many types of applied situations.
(2) As students work with these mathematical
topics, they continually rely on mathematical processes, including problem-solving
techniques, appropriate mathematical language and communication skills, connections
within and outside mathematics, and reasoning. Students also use multiple
representations, technology, applications and modeling, and numerical fluency
in problem-solving contexts.
(c) Knowledge and skills.
(1) The student develops and applies skills used
in college and careers, including reasoning, planning, and communication,
to make decisions and solve problems in applied situations involving numerical
reasoning, probability, statistical analysis, finance, mathematical selection,
and modeling with algebra, geometry, trigonometry, and discrete mathematics.
The student is expected to:
(A) gather data, conduct investigations, and
apply mathematical concepts and models to solve problems in mathematics and
other disciplines;
(B) demonstrate reasoning skills in developing,
explaining, and justifying sound mathematical arguments, and analyze the soundness
of mathematical arguments of others; and
(C) communicate with mathematics orally and
in writing as part of independent and collaborative work, including making
accurate and clear presentations of solutions to problems.
(2) The student analyzes real-world numerical
data using a variety of quantitative measures and numerical processes. The
student is expected to:
(3) The student analyzes and evaluates risk and
return in the context of real-world problems. The student is expected to:
(A) determine and interpret conditional probabilities
and probabilities of compound events by constructing and analyzing representations,
including tree diagrams, Venn diagrams, and area models, to make decisions
in problem situations;
(B) use probabilities to make and justify
decisions about risks in everyday life; and
(B) justify the design and the conclusion(s)
of statistical studies, including the methods used for each; and
(C) communicate statistical results in both
oral and written formats using appropriate statistical language.
(7) The student analyzes the mathematics behind
various methods of ranking and selection. The student is expected to:
(A) apply, analyze, and compare various ranking
algorithms to determine an appropriate method to solve a real-world problem;
and
(B) analyze and compare various voting and
selection processes to determine an appropriate method to solve a real-world
problem.
(8) The student models data, makes predictions,
and judges the validity of a prediction. The student is expected to:
(A) determine if there is a linear relationship
in a set of bivariate data by finding the correlation coefficient for the
data, and interpret the coefficient as a measure of the strength and direction
of the linear relationship;
(B) collect numerical bivariate data; use
the data to create a scatterplot; and select a function such as linear, exponential,
logistic, or trigonometric to model the data; and
(C) justify the selection of a function to
model data, and use the model to make predictions.
(a) The provisions of §§111.39-111.45 of this
subchapter shall be implemented by school districts.
(b) No later than June 30, 2015, the commissioner
of education shall determine whether instructional materials funding has been
made available to Texas public schools for materials that cover the essential
knowledge and skills for mathematics as adopted in §§111.39-111.45 of this
subchapter.
(c) If the commissioner makes the determination
that instructional materials funding has been made available under subsection
(b) of this section, §§111.39-111.45 of this subchapter shall be implemented
beginning with the 2015-2016 school year and apply to the 2015-2016 and subsequent
school years.
(d) If the commissioner does not make the determination
that instructional materials funding has been made available under subsection
(b) of this section, the commissioner shall determine no later than June 30
of each subsequent school year whether instructional materials funding has
been made available. If the commissioner determines that instructional materials
funding has been made available, the commissioner shall notify the State Board
of Education and school districts that §§111.39-111.45 of this subchapter
shall be implemented for the following school year.
(e) Sections 111.31-111.37 of this subchapter
shall be superseded by the implementation of §§111.38-111.45 under this section.
Source: The provisions of this §111.38 adopted to be effective
September 10, 2012, 37 TexReg 7109.
§111.39. Algebra I,
Adopted 2012 (One Credit).
(a) General requirements. Students shall be
awarded one credit for successful completion of this course. This course is
recommended for students in Grade 8 or 9. Prerequisite: Mathematics, Grade
8 or its equivalent I, students will build on the
knowledge and skills for mathematics in Grades 6-8, which provide a foundation
in linear relationships, number and operations, and proportionality. Students
will study linear, quadratic, and exponential functions and their related
transformations, equations, and associated solutions. Students will connect
functions and their associated solutions in both mathematical and real-world
situations. Students will use technology to collect and explore data and analyze
statistical relationships. In addition, students will study polynomials of
degree one and two, radical expressions, sequences, and laws of exponents.
Students will generate and solve linear systems with two equations and two
variables and will create new functions through transformations form Linear functions, equations, and inequalities.
The student applies the mathematical process standards when using properties
of linear functions to write and represent in multiple ways, with and without
technology, linear equations, inequalities, and systems of equations. The
student is expected to:
(A) determine the domain and range of a linear
function in mathematical problems; determine
reasonable domain and range values for real-world situations, both continuous
and discrete; and represent domain and range using inequalities;
(B) write linear equations in two variables in various forms, including
y = mx + b, Ax + By = C, and y - y1= m(x
- x1), given one point and the slope and given two points;
(C) write linear
equations in two variables given a table of values, a graph, and a verbal
description;
(D) write and solve equations involving direct
variation;
(E) write the equation of a line that contains
a given point and is parallel to a given line;
(F) write the equation of a line that contains
a given point and is perpendicular to a given line;
(G) write an equation of a line that is parallel
or perpendicular to the X or Y axis and determine whether the slope of the line is zero or undefined;
(H) write linear
inequalities in two variables given a table of values, a graph, and a verbal
description; and
(I) write systems of two linear equations
given a table of values, a graph, and a verbal description.
(3) Linear functions, equations, and inequalities.
The student applies the mathematical process standards when using graphs of
linear functions, key features, and related transformations to represent in
multiple ways and solve, with and without technology, equations, inequalities,
and systems of equations. The student is expected to:
(A) determine the slope of a line given a
table of values, a graph, two points on the line, and an equation written
in various forms, including y = mx + b, Ax + By = C, and y
- y1= m(x - x1);
(B) calculate the rate of change of a linear
function represented
tabularly, graphically, or algebraically in context of mathematical
and
real-world problems;
(C) graph linear functions on the coordinate
plane and identify key features, including x-intercept, y-intercept,
zeros, and slope, in mathematical and real-world problems;
(D) graph the solution setof
linear inequalities in two variables on the coordinate plane;
(E) determine the effects on the graph of
the parent
function f(x) = x when f(x) is replaced by af(x),
f(x) + d, f(x - c), f(bx) for specific values of a, b, c,
and d;
(F) graph systems of two linear equations
in two variables on the coordinate plane and determine the solutions if they
exist;
(G) estimate graphically the solutions
to systems
of two linear equations with two variables in real-world problems; and
(H) graph the solution setof
systems
of two linear inequalities in two variables on the coordinate plane.
(4) Linear functions, equations, and inequalities.
The student applies the mathematical process standards to formulate statistical
relationships and evaluate their reasonableness based on real-world data.
The student is expected to:
(A) calculate, using technology,
the correlation coefficient between two quantitative variables and interpret
this quantity as a measure of the strength of the linear association;
(B) compare and contrast association and causation
in real-world problems; and
(C) write, with and without technology, linear
functions that provide a reasonable fit to data to estimate solutions andmake predictions
for real-world problems.
(5) Linear functions, equations, and inequalities.
The student applies the mathematical process standards to solve, with and
without technology, linear equations and evaluate the reasonableness of their
solutions. The student is expected to:
(A) solve linear equations in one variable,
including those for which the application of the distributive property is
necessary and for which variables are included on both sides;
(B) solve linear inequalities in one variable,
including those for which the application of the distributive property is
necessary and for which variables are included on both sides; and
(C) solve systems of two linear equations
with two variables for mathematical and real-world problems.
(6) Quadratic functions and equations. The student
applies the mathematical process standards when using properties of quadratic
functions to write and represent in multiple ways, with and without technology,
quadratic equations. The student is expected to:
(A) determine the domain and range of quadratic
functions and represent the domain and range using inequalities;
(B) write equations of quadratic functions
given the vertex and another point on the graph, write the equation in vertex
form (f(x)
= a(x - h)2+ k),
and rewrite the equation from vertex form to standard form (f(x) = ax2+
bx + c); and
(C) write quadratic
functions when given real solutionsand graphs of their related equations.
(7) Quadratic functions and equations. The student
applies the mathematical process standards when using graphs of quadratic
functions and their related transformations to represent in multiple ways
and determine, with and without technology, the solutions to equations. The
student is expected to:
(A) graph quadratic functions on the coordinate
plane and use the graph to identify key attributes, if possible, including
x-intercept, y-intercept, zeros, maximum value, minimum values,
vertex, and the equation of the axis of symmetry;
(B) describe the relationship between the linear
factors of quadratic expressionsand the zeros of their associated quadratic
functions; and
(C) determine the effects on the graph of
the parent
function f(x) = x2 when f(x) is replaced by af(x),
f(x) + d, f(x - c), f(bx) for specific values of a, b, c,
and d.
(8) Quadratic functions and equations. The student
applies the mathematical process standards to solve, with and without technology,
quadratic equations and evaluate the reasonableness of their solutions. The
student formulates statistical relationships and evaluates their reasonableness
based on real-world data. The student is expected to:
(9) Exponential functions and equations. The
student applies the mathematical process standards when using properties of
exponential functions and their related transformations to write, graph, and
represent in multiple ways exponential equations and evaluate, with and without
technology, the reasonableness of their solutions. The student formulates
statistical relationships and evaluates their reasonableness based on real-world
data. The student is expected to:
(A) determine the domain and range of exponential
functions of the form f(x) = abx and
represent the domain and range using inequalities;
(B) interpret the meaning of the values of
a and b in exponential functions of the form f(x) = abx
in real-world problems;
(C) write exponential functions
in the form f(x) = abx (where b is a rational
number) to describe problems arising from mathematical and real-world situations,
including growth and decay;
(D) graph exponential functions
that model growth and decay and identify key features, including y-intercept
and asymptote, in mathematical and real-world problems; and
(10) Number and algebraic methods. The student
applies the mathematical process standards and algebraic methods to rewrite
in equivalent forms and perform operations on polynomial expressions. The
student is expected to:
(A) add and subtract polynomials of degree
one and
degree two;
(B) multiply polynomials of degree one and degree two;
(C) determine the quotient of a polynomial
of degree one and polynomial of degree two when divided by a polynomial
of degree one and polynomial of degree two when the degree of the divisor
does not exceed the degree of the dividend;
(D) rewrite polynomial expressions of degree
one and
degree two in equivalent forms using the distributive property;
(E) factor, if possible, trinomials with real
factors in the form ax2 + bx + c,
including perfect square trinomials of
degree two; and
(F)decide if a binomial
can be written as the difference of two squares and, if possible,use the structure
of a difference of two squares to rewrite the binomial.
(11) Number and algebraic methods. The student
applies the mathematical process standards and algebraic methods to rewrite
algebraic expressions into equivalent forms. The student is expected to:
(B) simplify numeric and algebraic expressions
using the laws of exponents, including integral and rational exponents.
(12) Number and algebraic methods. The student
applies the mathematical process standards and algebraic methods to write,
solve, analyze, and evaluate equations, relations, and functions. The student
is expected to:
(B) evaluate functions, expressed in function
notation, given one or more elements in their
domains;
(C) identify terms of arithmetic and
geometric sequences when the sequencesare given in function form using recursive
processes;
(D) write a formula for the nthterm
of arithmetic and geometric sequences, given the value
of several of their terms; and
(E) solve mathematic and scientific formulas,
and other literal equations, for a specified variable.
Source: The provisions of this §111.39 adopted to be effective
September 10, 2012, 37 TexReg 7109.
§111.40. Algebra II,
Adopted 2012 (One-Half to One Credit).
(a) General requirements. Students shall be
awarded one-half to II, students will build on the
knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I.
Students will broaden their knowledge of quadratic functions, exponential
functions, and systems of equations. Students will study logarithmic, square
root, cubic, cube root, absolute value, rational functions, and their related
equations. Students will connect functions to their inverses and associated
equations and solutions in both mathematical and real-world situations. In
addition, students will extend their knowledge of data analysis and numeric
and algebraic methods or justifymathematical ideas and arguments using precise
mathematical language in written or oral communication.
(2) Attributes of functions and their inverses.
The student applies mathematical processes to understand that functions have
distinct key attributes and understand the relationship between a function
and its inverse. The student is expected to:
(A) graph the functions f(x)=√x,
f(x)=1/x, f(x)=x3, f(x)= 3√x,
f(x)=bx, f(x)=|x|, and f(x)=logb (x) where
b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain,
range, intercepts, symmetries, asymptotic behavior, and maximum and minimum
given an interval;
(B) graph and write the inverse of a function using notation such as
f-1 (x);
(C) describe and
analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential),
including the restriction(s) on domain, which will restrict its range; and
(D) use the composition
of two functions, including the necessary restrictions on the domain, to determine
if the functions are inverses of each other.
(3) Systems of equations and inequalities. The
student applies mathematical processes to formulate systems of equations and
inequalities, use a variety of methods to solve, and analyze reasonableness
of solutions. The student is expected to:
(A) formulate systems of equations, including systems consisting
of three linear equations in three variables and systems
consisting of two equations, the first linear and the second quadratic;
(B) solve systems of three linear equations
in
three variables by using Gaussianelimination, technology with matrices, and substitution;
(C) solve, algebraically, systems of two equations
in two variables consisting of a linear equation
and a quadratic equation;
(D) determine the reasonableness of solutions
to systems of a linear equation and a quadratic equation in two variables;
(E) formulate systems of at least two linear inequalities in two
variables;
(F) solve systems of two or more linear inequalities
in two variables; and
(G) determine possible solutions in the solution set of
systems of two or more linear inequalities in two variables.
(4) Quadratic and square root functions, equations,
and inequalities. The student applies mathematical processes to understand
that quadratic and square root functions, equations, and quadratic inequalities
can be used to model situations, solve problems, and make predictions. The
student is expected to:
(A) writethequadratic
function given three specified points in the plane;
(B) write the equation of a parabola using given attributes,including vertex,
focus, directrix, axis of symmetry, and direction of opening;
(C) determine the effect on the graph of f(x)
= √x when f(x) is replaced by af(x), f(x) + d,
f(bx), and f(x - c)
for specific positive and negative values of a, b, c, and d;
(E) formulate quadratic and square root equations
using technology given a table of data;
(F) solve quadratic and square root equations;
(G) identifyextraneous solutions of square root equations; and
(H) solve quadratic inequalities.
(5) Exponential and logarithmic functions and
equations. The student applies mathematical processes to understand that exponential
and logarithmic functions can be used to model situations and solve problems.
The student is expected to:
(A) determine the effects on the key attributes on the graphs of f(x) = bx
and f(x) = logb (x)where b is 2, 10, and e when f(x) is
replaced by af(x), f(x) + d, andf(x
- c) for specific positive and negative real values of a,
c, and d;
(A) analyze data to select the appropriate
model from among linear, quadratic, and exponential models;
(B) use regression
methods available through technology to write a linear function, a quadratic
function, and an exponential function from a given set of data; and
(C) predict and make decisions and critical
judgments from a given set of data using linear, quadratic, and exponential
models.
Source: The provisions of this §111.40 adopted to be effective
September 10, 2012, 37 TexReg 7109.
§111.41. Geometry,
Adopted 2012 Geometry, students will build on the knowledge
and skills for mathematics in Kindergarten-Grade 8 and Algebra I to strengthen
their mathematical reasoning skills in geometric contexts. Within the course,
students will begin to focus on more precise terminology, symbolic representations,
and the development of proofs. Students will explore concepts covering coordinate
and transformational geometry; logical argument and constructions; proof and
congruence; similarity, proof, and trigonometry; two- and three-dimensional
figures; circles; and probability. Students will connect previous knowledge
from Algebra I to Geometry through the coordinate and transformational geometry
strand. In the logical arguments and constructions strand, students are expected
to create formal constructions using a straight edge and compass. Though this
course is primarily Euclidean geometry, students should complete the course
with an understanding that non-Euclidean geometries exist. In proof and congruence,
students will use deductive reasoning to justify, prove and apply theorems
about geometric figures. Throughout the standards, the term "prove"
means a formal proof to be shown in a paragraph, a flow chart, or two-column
formats. Proportionality is the unifying component of the similarity, proof,
and trigonometry strand. Students will use their proportional reasoning skills
to prove and apply theorems and solve problems in this strand. The two- and
three-dimensional figure strand focuses on the application of formulas in
multi-step situations since students have developed background knowledge in
two- and three-dimensional figures. Using patterns to identify geometric properties,
students will apply theorems about circles to determine relationships between
special segments and angles in circles. Due to the emphasis of probability
and statistics in the college and career readiness standards, standards dealing
with probability have been added to the geometry curriculum to ensure students
have proper exposure to these topics before pursuing their post-secondary
education.
(4) These standards are meant to provide clarity
and specificity in regards to the content covered in the high school geometry
course. These standards are not meant to limit the methodologies used to convey
this knowledge to students. Though the standards are written in a particular
order, they are not necessarily meant to be taught in the given order. In
the standards, the phrase "to solve problems" includes both contextual
and non-contextual problems unless specifically stated Coordinate and transformational geometry.
The student uses the process skills to understand the connections between
algebra and geometry and uses the one- and two-dimensional coordinate systems
to verify geometric conjectures. The student is expected to:
(A) determine the coordinates of a point that
is a given fractional distance less than one from one end of a line segment
to the other in one- and two-dimensional coordinate systems,
including finding the midpoint;
(B) derive and use the distance, slope, and midpoint formulas to verify geometric
relationships, including congruence of segments and parallelism or perpendicularity
of pairs of lines; and
(C) determine
an equation of a line parallel or perpendicular to a given line that passes
through a given point.
(3) Coordinate and transformational geometry.
The student uses the process skills to generate and describe rigid transformations
(translation, reflection, and rotation) and non-rigid transformations (dilations
that preserve similarity and reductions and enlargements that do not preserve
similarity). The student is expected to:
(A) describe and perform transformations of figures in a plane using coordinate
notation;
(B) determine the image or pre-image of a given two-dimensional figure under
a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both,including dilations where the center can
be any point in the plane;
(C) identify the sequence of transformations
that will carry a given pre-image onto an image on and off the coordinate
plane; and
(D) identify and distinguish between reflectional
and rotational symmetry in a plane figure.
(B) identify and determine the validity of the converse, inverse, and contrapositive
of a conditional statement and recognize the connection between a biconditional statement and a true
conditional statement with a true converse;
(C) verify that a conjecture is false using
a counterexample; and
(D) compare geometric relationshipsbetween Euclidean and spherical
geometries, including parallel lines
and the sum of the angles in a triangle.
(A) investigate patterns to make conjectures about geometric relationships,
including angles formed by parallel lines cut by a transversal, criteria required
for triangle congruence, special segments of triangles, diagonals of quadrilaterals,
interior and exterior angles of polygons, and special segments and angles
of circles choosing from a variety of tools;
(B) construct congruent segments, congruent angles, a segment bisector, an angle
bisector, perpendicular lines, the perpendicular bisector of a line segment,
and a line parallel to a given line through a point not on a line using a
compass and a straightedge;
(C) use the constructions
of congruent segments, congruent angles, angle bisectors, and perpendicular
bisectors to make conjectures about geometric relationships; and
(D) verify the Triangle Inequality theorem using constructions and apply the
theorem to solve problems.
(6) Proof and congruence. The student uses the process skills with deductive
reasoning to prove and apply theorems by using a variety of methods such as
coordinate, transformational, and axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected to:
(A) verify theorems about angles formed by the intersection of lines and line segments,
including vertical angles, and angles formed by parallel lines cut by a transversal
and prove equidistance between the endpoints of a segment and points on its
perpendicular bisector and applythese relationships
to solve problems;
(C) apply the definition of congruence, in terms of rigid transformations,
to identify congruent figures and their corresponding sides and angles;
(D) verify theorems about therelationships in triangles, including proof of the Pythagorean Theorem,
the sum of interior angles, base angles of isosceles triangles, midsegments,
and medians,and apply these relationships to solve problems; and
(E)prove
a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite
sides, opposite angles, or diagonals and apply these relationshipsto solve problems.
(7) Similarity, proof, and trigonometry. The student uses the process skills
in applying similarity to solve problems. The student is expected to:
(A) apply the definition of similarity in
terms of a dilation to identify similar figures and
their proportional sides and the congruent corresponding angles;
and
(B) apply the Angle-Angle
criterion to verify similar triangles and apply the proportionality of the
corresponding sides to solve
problems.
(8) Similarity, proof, and trigonometry. The student uses the process skills
with deductive reasoning to prove and apply theorems by using a variety of
methods such as coordinate, transformational, and axiomatic and formats such
as two-column, paragraph, and flow chart. The student is expected to:
(A) prove theorems about similar triangles,including the Triangle Proportionality
theorem, and apply
these theorems to solve problems; and
(B) identify and
apply the relationships that exist when an altitude is drawn to the hypotenuse
of a right triangle, including the geometric mean, to solve problems.
(9) Similarity, proof, and trigonometry. The student uses the process skills
to understand and apply relationships in right triangles. The student is expected
to:
(A) determine the lengths of sides and measures of angles in a right
triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems; and
(B) apply the
relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the
Pythagorean theorem, including Pythagorean triples,to solve problems.
(10) Two-dimensional and three-dimensional figures. The student
uses the process skills to recognize characteristics and dimensional changes
of two- and three-dimensional figures. The student is expected to:
(A) identify the shapes of two-dimensional
cross-sections of prisms, pyramids, cylinders, cones, and
spheres and identify three-dimensional objects generated by
rotations of two-dimensional shapes; and
(B) determine
and describe how changes in the linear dimensions
of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional
change.
(11) Two-dimensional and three-dimensional figures. The student
uses the process skills in the application of formulas to determine measures
of two- and three-dimensional figures. The student is expected to:
(A) apply the formula for the area of regular polygons to solve problems using appropriate units of measure;
(B) determine
the area of composite two-dimensional figures comprised of a combination of
triangles, parallelograms, trapezoids, kites, regular polygons, or sectors
of circles to solve problems using appropriate units of measure;
(C) apply the formulas for
the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres,
and composite figures,to solve problems using appropriate units of measure; and
(D) apply the formulas for
the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures,to solve problems using appropriate units of measure.
(12) Circles. The student uses the process skills
to understand geometric relationships and apply theorems and equations about
circles. The student is expected to:
(B) apply the
proportional relationship between the measure of an
arc length of a circle and the circumference of the circle to solve problems;
(C) apply the
proportional relationship between the measure of the area of a sector of a
circle and the area of the circle to solve
problems;
(D) describe radian
measure of an angle as the ratio of the length of an arc intercepted by a
central angle and the radius of the circle; and
(E) show that the equation of a circle with center at the origin and radius
r is x2 + y2 = r2and determine the equation
for the graph of a circle with radius r and center (h, k),
(x - h)2 + (y - k)2 =r2.
(13) Probability. The student uses the process
skills to understand probability in real-world situations and how to apply
independence and dependence of events. The student is expected to:
(A) develop strategies to use permutations
and combinations to solve contextual problems;
(B) determine
probabilities based on area to solve contextual problems;
(C) identify whether
two events are independent and compute the probability of the two events occurring together
with or without replacement;
(D) apply conditional
probability in contextual problems; and
(E) apply independence in contextual problems.
Source: The provisions of this §111.41 adopted to be effective
September 10, 2012, 37 TexReg 7109.
§111.42. Precalculus,
Adopted 2012 (One-Half to One Credit).
(a) General requirements. Students shall be
awarded one-half to one credit for successful completion of this course. Prerequisites:
Algebra I, Geometry, Precalculus is the preparation for calculus.
The course approaches topics from a function point of view, where appropriate,
and is designed to strengthen and enhance conceptual understanding and mathematical
reasoning used when modeling and solving mathematical and real-world problems.
Students systematically work with functions and their multiple representations.
The study of Precalculus deepens students' mathematical understanding and
fluency with algebra and trigonometry and extends their ability to make connections
and apply concepts and procedures at higher levels. Students investigate and
explore mathematical ideas, develop multiple strategies for analyzing complex
situations, and use technology to build understanding, make connections between
representations, and provide support in solving problems Functions. The student uses process standards
in mathematics to explore, describe, and analyze the attributes of functions.
The student makes connections between multiple representations of functions
and algebraically constructs new functions. The student analyzes and uses
functions to model real-world problems. The student is expected to:
(A) use the composition of two functions to
model and solve real-world problems;
(B) demonstrate that function composition is not
always commutative;
(C) represent
a given function as a composite function of two or more functions;
(D) describe symmetry of graphs of even and
odd functions;
(E) determine an inverse function, when it
exists, for a given function over its domain or a subset of its domain and
represent the inverse using multiple representations;
(H) graph arcsin
x and arccos xand describe the limitations on the domain;
(I) determine and analyze the key features of
exponential, logarithmic, rational, polynomial, power,trigonometric, inverse trigonometric, and piecewise defined
functions, including step functions such as domain, range, symmetry,
relative maximum, relative minimum, zeros, asymptotes, and intervals over
which the function is increasing or decreasing;
(J) analyze and describe end behavior of functions, including
exponential, logarithmic, rational, polynomial, and power functions,
using infinity notation to communicate this characteristic in mathematical
and real-world problems;
(K) analyze characteristics of rational functions
and the behavior of
the function around the asymptotes, including horizontal, vertical, and oblique asymptotes;
(L) determine various types of discontinuities
in the interval (-∞, ∞) as they relate to functions and explore
the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities;
(M) describe the left-sided behavior and the right-sided
behavior of the graph of a function around discontinuities;
(C) use parametric equations to model and solve mathematical
and real-world problems;
(D) graph points in the polar coordinate system
and convert between rectangular coordinates and polar coordinates;
(E) graph polar equations by plotting points and using technology;
(F) determine the conic section formed when a plane
intersects a double-napped cone;
(G) make connections between the locus definition
of conic sections and their equations in rectangular coordinates;
(H) use the characteristics of an ellipse to write
the equation of an ellipse with center (h, k); and
(I) use the characteristics of a hyperbola to write
the equation of a hyperbola with center (h, k).
(4) Number and measure. The student uses process
standards in mathematics to apply appropriate techniques, tools, and formulas
to calculate measures in mathematical and real-world problems. The student
is expected to:
(A) determine the relationship between the
unit circleand the definition of a periodic function to
evaluate trigonometric functions in mathematical and real-world problems;
(B) describe the relationship between degree and radian measure
on the unit circle;
(C) represent angles in radians or degrees
based on the concept of rotation and find the measure of reference angles
and angles in standard position;
(D) represent angles in radians or degrees
based on the concept of rotation in mathematical and real-world problems,
including linear and angular velocity;
(J) solve polynomial equations with real coefficients
by applying a variety of techniques in mathematical and real-world problems;
(K) solve polynomial inequalities with real
coefficients by applying a variety
of techniques and write the solution set of the polynomial inequality
in interval notation in mathematical and real-world problems;
(L) solve rational inequalities with real
coefficients by applying a variety of techniques and write the solution set
of the rational inequality
in interval notation in mathematical and real-world problems;
(M) use trigonometric identities such as reciprocal,
quotient, Pythagorean, cofunctions, even/odd, and sum and difference identities
for cosine and sine to simplify trigonometric expressions; and
(a) General requirements. Students can be awarded
one credit for successful completion of this course. Prerequisite: Algebra
I Mathematical Models with Applications is
designed to build on the knowledge and skills for mathematics in Kindergarten-Grade
8 and Algebra I. This mathematics course provides a path for students to succeed
in Algebra II and prepares them for various post-secondary choices. Students
learn to apply mathematics through experiences in personal finance, science,
engineering, fine arts, and social sciences. Students use algebraic, graphical,
and geometric reasoning to recognize patterns and structure, model information,
solve problems, and communicate solutions. Students will select from tools
such as physical objects; manipulatives; technology, including graphing calculators,
data collection devices, and computers; and paper and pencil and from methods
such as algebraic techniques, geometric reasoning, patterns, and mental math
to solve problems.
(4) In Mathematical Models with Applications,
students will use a mathematical modeling cycle to analyze problems, understand
problems better, and improve decisions. A basic mathematical modeling cycle
is summarized in this paragraph. The student will:
(A) represent:
(i) identify the variables in the problem and select
those that represent essential features; and
(ii) formulate a model by creating and selecting
from representations such as geometric, graphical, tabular, algebraic, or
statistical that describe the relationships between the variables;
(B) compute: analyze and perform operations
on the relationships between the variables to draw conclusions;
(C) interpret: interpret the results of the
mathematics in terms of the original problem;
(D) revise: confirm the conclusions by comparing
the conclusions with the problem and revising as necessary; and
(E) report: report on the conclusions and
the reasoning behind the conclusions communicate mathematical5) Mathematical modeling in science and engineering.
The student applies mathematical processes with algebraic
techniques to study patterns and analyze data as it applies to science. The
student is expected to:
(A) use proportionality and inverse variation
to describe physical laws such as Hook's Law, Newton's Second
Law of Motion, and Boyle's Law;
(B) use exponential models available through
technology to model growth and decay in areas, including radioactive
decay; and
(C) use quadratic
functions to model motion.
(6) Mathematical modeling in science and engineering.
The student applies mathematical processes with algebra
and geometry to study patterns and analyze data as it applies to architecture
and engineering. The student is expected to:
(B) use scale factors with two-dimensional
and three-dimensional objects to demonstrate proportional and non-proportional
changes in surface area and volume as applied to fields;
(C) use the Pythagorean Theorem and special
right-triangle relationships to calculate distances; and
(D) use trigonometric ratios to calculate
distances and angle measures as applied to fields.
(7) Mathematical modeling in fine arts. The student
uses mathematical processes with algebra and geometry to study patterns and
analyze data as it applies to fine arts. The student is expected to:
(A) use trigonometric ratios and functions
available through technology to model periodic behavior in art
and music;
(B) use similarity, geometric
transformations, symmetry, and perspective drawings to describe mathematical
patterns and structure in art and photography;
(C) use geometric transformations,
proportions, and periodic motion to describe mathematical patterns and structure
in music; and
(D) use scale factors with two-dimensional
and three-dimensional objects to demonstrate proportional and non-proportional
changes in surface area and volume as applied to fields.
(8) Mathematical modeling in social sciences.
The student applies mathematical processes to determine the number of elements in a finite
sample space and compute the probability of an event. The student is expected
to:
(A) determine the number of ways an event
may occur using combinations, permutations, and the Fundamental Counting Principle;
(B) compare theoretical
to empirical probability; and
(C) use experiments to determine
the reasonableness of a theoretical model such as binomial or geometric.
(9) Mathematical modeling in social sciences.
The student applies mathematical processes and mathematical models to analyze data as
it applies to social sciences. The student is expected to:
(A) interpret information from
various graphs, including line graphs, bar graphs, circle graphs, histograms,
scatterplots, dot plots, stem-and-leaf plots, and box and whisker plots, to
draw conclusions from the data and determine the strengths and weaknesses
of conclusions;
(B) analyze numerical data using measures
of central tendency (mean, median, and mode) and variability (range, interquartile
range or IQR, and standard deviation) in order to make inferences with normal
distributions;
(C) distinguish the purposes and differences
among types of research, including surveys, experiments, and observational
studies;
(D) use data from a sample to estimate population
mean or population proportion;
(E) analyze marketing claims based on graphs
and statistics from electronic and print media and justify the validity of
stated or implied conclusions; and
(F) use regression methods available through
technology to model linear and exponential functions, interpret correlations,
and make predictions.
(10) Mathematical modeling in social sciences.
The student applies mathematical processes to design a study and use graphical, numerical,
and analytical techniques to communicate the results of the study. The student
is expected to:
(A) formulate a meaningful question,
determine the data needed to answer the question, gather the appropriate data,
analyze the data, and draw reasonable conclusions; and
(B) communicate methods used, analyses conducted,
and conclusions drawn for a data-analysis project through
the use of one or more of the following: a written report, a
visual display, an oral report, or a multi-media presentation.
Statutory Authority: The provisions of this §111.43 issued
under the Texas Education Code, §§7.102(c)(4), 28.002, and 28.025.
Source: The provisions of this §111.43 adopted to be effective
September 10, 2012, 37 TexReg 7109; amended to be effective August 24, 2015,
40 TexReg 5330.
(a) General requirements. Students shall be
awarded one-half to one credit for successful completion of this course. Prerequisites:
Geometry Advanced Quantitative Reasoning, students
will develop and apply skills necessary for college, careers, and life. Course
content consists primarily of applications of high school mathematics concepts
to prepare students to become well-educated and highly informed 21st century
citizens. Students will develop and apply reasoning, planning, and communication
to make decisions and solve problems in applied situations involving numerical
reasoning, probability, statistical analysis, finance, mathematical selection,
and modeling with algebra, geometry, trigonometry, and discrete Numeric reasoning. The student applies the
process standards in mathematics to generate new understandings by extending
existing knowledge. The student generates new mathematical understandings
through problems involving numerical data that arise in everyday life, society,
and the workplace. The student extends existing knowledge and skills to analyze
real-world situations. The student is expected to:
(A) use precision and accuracy in real-life
situations related to measurement and significant figures;
(B) apply and analyzepublished
ratings, weighted averages, and indices to make informed decisions;
(C) solve problems
involving quantities that are not easily measured using proportionality;
(D) solve geometric problems involving indirect
measurement, including similar triangles, the Pythagorean Theorem, Law of
Sines, Law of Cosines, and the use of dynamic geometry software;
(E) solve problems involving large quantities
using combinatorics;
(F) use arrays toefficiently
manage large collections of data and add, subtract, and multiply
matrices to solve applied problems, including geometric transformations;
(G) analyze various voting and selection processes
to compare results in given
situations; and
(H) select and
apply an algorithm of interest to solve real-life problems such as problems
using recursion or iteration involving population growth or decline, fractals,
and compound interest; the validity in recorded and transmitted data using
checksums and hashing; sports rankings, weighted class
rankings, and search engine rankings; and problems involving
scheduling or routing situations using vertex-edge graphs, critical paths,
Euler paths, and minimal spanning trees and communicate to peers the application
of the algorithm in precise mathematical and nontechnical language.
(3) Algebraic reasoning (expressions, equations,
and generalized relationships). The student applies the process standards
in mathematics to create and analyze mathematical models of everyday situations
to make informed decisions related to earning, investing, spending, and borrowing
money by appropriate, proficient, and efficient use of tools, including technology.
The student uses mathematical relationships to make connections and predictions.
The student judges the validity of a prediction and uses mathematical models
to represent, analyze, and solve dynamic real-world problems. The student
is expected to:
(A) collect numerical bivariate datato create a scatterplot,
select a function to model the data, justify the model selection, and
use the model to interpret results and make predictions;
(B) describe the degree to which uncorrelated
variables may or may not be related and analyze situations where correlated
variables do or do not indicate a cause-and-effect relationship;
(C) determine or analyze an appropriate growth
or decay model for problem situations, including linear, exponential, and
logistic functions;
(D) determine or analyze an appropriate cyclical
model for problem situations that can be modeled with periodic
functions;
(F) create, represent, and analyze mathematical models for various
types of income calculations to determine the best option for a given situation;
(G) create, represent, and analyze mathematical models for expenditures,
including those involving credit, to determine the best option for a given
situation; and
(H) create, represent, and analyze mathematical models and appropriate
representations, including formulas and amortization tables, for
various types of loans and investments to determine the best option
for a given situation.
(4) Probabilistic and statistical reasoning.
The student uses the process standards in mathematics to generate new understandings
of probability and statistics. The student analyzes statistical information
and evaluates risk and return to connect mathematical ideas and make informed
decisions. The student applies a problem-solving model and statistical methods
to design and conduct a study that addresses one or more particular question(s).
The student uses multiple representations to communicate effectively the results
of student-generated statistical studies and the critical analysis of published
statistical studies. The student is expected to:
(A) use a two-way frequency table as a sample
space to identify whether two events are independent and to interpret the
results;
(I) interpret and compare statistical
results using
appropriate technology given a margin of error;
(J) identify potential misuses of statistics
to justify particular conclusions, including assertions of a cause-and-effect
relationship rather than an association, and missteps or fallacies in logical reasoning;
(K) describe strengths
and weaknesses of sampling techniques, data and graphical displays, and interpretations
of summary statistics and other results appearing in a study, including reports
published in the media;
(L) determine the need for and purpose of
a statistical investigation and what type of statistical analysis can be used
to answer a specific question or set of questions;
(M) identify the population of interest for a
statistical investigation, select an appropriate sampling technique,
and collect data;
(N) identify the variables to be used in a
study;
(O) determine possible sources of statistical
bias in a study and how bias may affect the validity
of the results;
(P) create data displays for given data sets
to investigate, compare, and estimate center, shape, spread, and unusual features
of the data;
(Q) analyze possible sources of data variability, including those that can be controlled and those that cannot
be controlled;
(R) report results of statistical studies
to a particular audience, including selecting an appropriate presentation
format, creating graphical data displays, and interpreting results in terms
of the question studied;
(S) justify the design and the conclusion(s)
of statistical studies, including the methods used; and
(T) communicate statistical results in oral
and written formats using appropriate statistical and nontechnical language.
Source: The provisions of this §111.44 adopted to be effective
September 10, 2012, 37 TexReg 7109.
(1) Students shall be awarded one-half to one
credit for successful completion of this course. Prerequisites: Geometry and
Algebra II.
(2) Students may repeat this course with different
course content for up to three credits.
(3) The requirements for each course must be
approved by the local district before the course begins.
(4) If this course is being used to satisfy requirements
for the Distinguished Achievement Program, student research/products must
be presented before a panel of professionals or approved by the student's
mentor Independent Study in Mathematics, students
will extend their mathematical understanding beyond the Algebra II level in
a specific area or areas of mathematics such as theory of equations, number
theory, non-Euclidean geometry, linear algebra, advanced survey of mathematics,
or history of mathematics.
(4) Statements that contain the word "including"
reference content that must be mastered, while those containing the phrase
"such as" are intended as possible illustrative examples.
(1) apply mathematics to problems arising in
everyday life, society, and the workplace;
(23) select tools, including real objects, manipulatives, paper and pencil, and
technology as appropriate, and techniques,
including mental math, estimation,
and number sense as appropriate, to solve
problems;
(4) communicatemathematical ideas, reasoning, and their implications using
multiple representations, including
symbols, diagrams, graphs, and language as appropriate;
(5) create and use representations to organize,
record, and communicate mathematical ideas;
(a) General requirements. Students shall be
awarded one-half to one credit for successful completion of this course. Prerequisite:
Al Discrete Mathematics for Problem Solving,
students are introduced to the improved efficiency of mathematical analysis
and quantitative techniques over trial-and-error approaches to management
problems involving organization, scheduling, project planning, strategy, and
decision making. Students will learn how mathematical topics such as graph
theory, planning and scheduling, group decision making, fair division, game
theory, and theory of moves can be applied to management and decision making.
Students will research mathematicians of the past whose work is relevant to
these topics today and read articles about current mathematicians who either
teach and conduct research at major universities or work in business and industry
solving real-world logistical problems. Through the study of the applications
of mathematics to society's problems today, students will become better prepared
for and gain an appreciation for the value of a career inA) use the adjusted winner procedure to determine
a fair allocation of property;
(B) use the adjusted winner procedure to resolve
a dispute;
(C) explain how to reach a fair division using
the Knaster inheritance procedure;
(D) solve fair division problems with three
or more players using the Knaster inheritance procedure;
(E) explain the conditions under which the
trimming procedure can be applied to indivisible goods;
(F) identify situations appropriate for the
techniques of fair division;
(G) compare the advantages of the divider
and the chooser in the divider-chooser method;
(H) discuss the rules and strategies of the
divider-chooser method;
(I) resolve cake-division problems for three
players using the last-diminisher method;
(J) analyze the relative importance of the
three desirable properties of fair division: equitability, envy-freeness,
and Pareto optimality; and
(K) identify fair division procedures that
exhibit envy-freeness.
(6) Game (or competition) theory. The student
uses knowledge of basic game theory concepts to calculate optimal strategies.
The student analyzes situations and identifies the use of gaming strategies.
The student is expected to:
(A) recognize competitive game situations;
(B) represent a game with a matrix;
(C) identify basic game theory concepts and
vocabulary;
(D) determine the optimal pure strategies
and value of a game with a saddle point by means of the minimax technique;
(E) explain the concept of and need for a
mixed strategy;
(F) compute the optimal mixed strategy and
the expected value for a player in a game who has only two pure strategies;
(G) model simple two-by-two, bimatrix games
of partial conflict;
(H) identify the nature and implications of
the game called "Prisoners' Dilemma";
(I) explain the game known as "chicken";
(J) identify examples that illustrate the
prevalence of Prisoners' Dilemma and chicken in our society; and
(K) determine when a pair of strategies for
two players is in equilibrium.
(7) Theory of moves. The student analyzes the
theory of moves (TOM). The student uses the TOM and game theory to analyze
conflicts. The student is expected to:
(A) compare and contrast TOM and game theory;
(B) explain the rules of TOM;
(C) describe what is meant by a cyclic game;
(D) use a game tree to analyze a two-person
game;
(E) determine the effect of approaching Prisoners'
Dilemma and chicken from the standpoint of TOM and contrast that to the effect
of approaching them from the standpoint of game theory;
(F) describe the use of TOM in a larger, more
complicated game; and
(G) model a conflict from literature or from
a real-life situation as a two-by-two strict ordinal game and compare the
results predicted by game theory and by TOM.
Statutory Authority: The provisions of this §111.46
issued under the Texas Education Code, §§7.102(c)(4), 28.002, and 28.025,
as that section existed before amendment by House Bill 5, 83rd Texas Legislature,
Regular Session, 2013.
Source: The provisions of this §111.46 adopted to be effective
August 25, 2014, 38 TexReg 9027.
§111.47. Statistics,
Ad predictions. Students will analyze mathematical relationships to connect
and communicate mathematical ideas. Students will display, explain, or justify
mathematical ideas and arguments using precise mathematical language in written
or oral communication.
(3) In Statistics, students will build on the
knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I.
Students will broaden their knowledge of variability and statistical processes.
Students will study sampling and experimentation, categorical and quantitative
data, probability and random variables, inference, and bivariate data. Students
will connect data and statistical processes to real-world situations. In addition,
students will extend their knowledge of data analysisand evaluating the problem-solving processand the reasonableness
of the solution;
(G) display,explain, or justifymathematical ideas and arguments using precise mathematical language
in written or oral communication.
(2) Statistical process sampling and experimentation.
The student applies mathematical processes to apply understandings about statistical
studies, surveys, and experiments to design and conduct a study and use graphical,
numerical, and analytical techniques to communicate the results of the study.
The student is expected to:
(A) compare and contrast the benefits of different
sampling techniques, including random sampling and convenience sampling methods;
(F) communicate methods used, analyses conducted,
and conclusions drawn for a data-analysis project through the use of one or
more of the following: a written report, a visual display, an oral report,
or a multi-media presentation; and
(5) Probability and random variables. The student
applies the mathematical process standards to connect probability and statistics.
The student is expected to:
(A) determine probabilities, including the
use of a two-way table;
(B) describe the relationship between theoretical
and empirical probabilities using the Law of Large Numbers;
(C) construct a distribution based on a technology-generated
simulation or collected samples for a discrete random variable; and
(D) compare statistical measures such as sample
mean and standard deviation from a technology-simulated sampling distribution
to the theoretical sampling distribution.
(6) Inference. The student applies the mathematical
process standards to make inferences and justify conclusions from statistical
studies. The student is expected to:
(A) explain how a sample statistic and a confidence
level are used in the construction of a confidence interval;
(B) explain how changes in the sample size,
confidence level, and standard deviation affect the margin of error of a confidence
interval;
(C) calculate a confidence interval for the
mean of a normally distributed population with a known standard deviation;
(D) calculate a confidence interval for a
population proportion;
(E) interpret confidence intervals for a population
parameter, including confidence intervals from media or statistical reports;
(F) explain how a sample statistic provides
evidence against a claim about a population parameter when using a hypothesis
test;
(G) construct null and alternative hypothesis
statements about a population parameter;
(H) explain the meaning of the p-value in
relation to the significance level in providing evidence to reject or fail
to reject the null hypothesis in the context of the situation;
(I) interpret the results of a hypothesis
test using technology-generated results such as large sample tests for proportion,
mean, difference between two proportions, and difference between two independent
means; and
(B) transform a linear parent function to
determine a line of best fit;
(C) compare different linear models for the
same set of data to determine best fit, including discussions about error;
(D) compare different methods for determining
best fit, including median-median and absolute value;
(E) describe the relationship between influential
points and lines of best fit using dynamic graphing technology; and
(F) identify and interpret the reasonableness
of attributes of lines of best fit within the context, including slope and
y-intercept.
Statutory Authority: The provisions of this §111.47
issued under the Texas Education Code, §§7.102(c)(4), 28.002, and 28.025.
Source: The provisions of this §111.47 adopted to be effective
March 18, 2015, 40 TexReg 1371.
§111.48. Algebraic
Reasoning, Adic Reasoning, students will build
on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra
I, continue with the development of mathematical reasoning related to algebraic
understandings and processes, and deepen a foundation for studies in subsequent
mathematics courses. Students will broaden their knowledge of functions and
relationships, including linear, quadratic, square root, rational, cubic,
cube root, exponential, absolute value, and logarithmic functions. Students
will study these functions through analysis and application that includes
explorations of patterns and structure, number and algebraic methods, and
modeling from data using tools that build to workforce and college readiness
such as probes, measurement tools, and software tools, including spreadsheets incorporatesG) display, explain, or justify mathematical
ideas and arguments using precise mathematical language in written or oral
communication.
(2) Patterns and structure. The student applies
mathematical processes to connect finite differences or common ratios to attributes
of functions. The student is expected to:
(A) determine the patterns that identify the
relationship between a function and its common ratio or related finite differences
as appropriate, including linear, quadratic, cubic, and exponential functions;
(B) classify a function as linear, quadratic,
cubic, and exponential when a function is represented tabularly using finite
differences or common ratios as appropriate;
(C) determine the function that models a given
table of related values using finite differences and its restricted domain
and range; and
(D) determine a function that models real-world
data and mathematical contexts using finite differences such as the age of
a tree and its circumference, figurative numbers, average velocity, and average
acceleration.
(A) compare and contrast the key attributes,
including domain, range, maxima, minima, and intercepts, of a set of functions
such as a set comprised of a linear, a quadratic, and an exponential function
or a set comprised of an absolute value, a quadratic, and a square root function
tabularly, graphically, and symbolically;
(B) compare and contrast the key attributes
of a function and its inverse when it exists, including domain, range, maxima,
minima, and intercepts, tabularly, graphically, and symbolically;
(C) verify that two functions are inverses
of each other tabularly and graphically such as situations involving compound
interest and interest rate, velocity and braking distance, and Fahrenheit-Celsius
conversions;
(D) represent a resulting function tabularly,
graphically, and symbolically when functions are combined or separated using
arithmetic operations such as combining a 20% discount and a 6% sales tax
on a sale to determine h(x), the total sale, f(x)
= 0.8x, g(x) = 0.06(0.8x), and h(x)
= f(x) + g(x);
(E) model a situation using function notation
when the output of one function is the input of a second function such as
determining a function h(x) = g(f(x)) =
1.06(0.8x) for the final purchase price, h(x) of an item
with price x dollars representing a 20% discount, f(x)
= 0.8x followed by a 6% sales tax, g(x) = 1.06x;
and
(F) compare and contrast a function and possible
functions that can be used to build it tabularly, graphically, and symbolically
such as a quadratic function that results from multiplying two linear functions.
(4) Number and algebraic methods. The student
applies mathematical processes to simplify and perform operations on functions
represented in a variety of ways, including real-world situations. The student
is expected to:
(A) connect tabular representations to symbolic
representations when adding, subtracting, and multiplying polynomial functions
arising from mathematical and real-world situations such as applications involving
surface area and volume;
(B) compare and contrast the results when
adding two linear functions and multiplying two linear functions that are
represented tabularly, graphically, and symbolically;
(C) determine the quotient of a polynomial
function of degree three and of degree four when divided by a polynomial function
of degree one and of degree two when represented tabularly and symbolically;
and
(D) determine the linear factors of a polynomial
function of degree two and of degree three when represented symbolically and
tabularly and graphically where appropriate.
(5) Number and algebraic methods. The student
applies mathematical processes to represent, simplify, and perform operations
on matrices and to solve systems of equations using matrices. The student
is expected to:
(A) add and subtract matrices;
(B) multiply matrices;
(C) multiply matrices by a scalar;
(D) represent and solve systems of two linear
equations arising from mathematical and real-world situations using matrices;
and
(E) represent and solve systems of three linear
equations arising from mathematical and real-world situations using matrices
and technology.
(6) Number and algebraic methods. The student
applies mathematical processes to estimate and determine solutions to equations
resulting from functions and real-world applications with fluency. The student
is expected to:
(A) estimate a reasonable input value that
results in a given output value for a given function, including quadratic,
rational, and exponential functions;
(B) solve equations arising from questions
asked about functions that model real-world applications, including linear
and quadratic functions, tabularly, graphically, and symbolically; and
(7) Modeling from data. The student applies mathematical
processes to analyze and model data based on real-world situations with corresponding
functions. The student is expected to:
(A) represent domain and range of a function
using interval notation, inequalities, and set (builder) notation;
(B) compare and contrast between the mathematical
and reasonable domain and range of functions modeling real-world situations,
including linear, quadratic, exponential, and rational functions;
(C) determine the accuracy of a prediction
from a function that models a set of data compared to the actual data using
comparisons between average rates of change and finite differences such as
gathering data from an emptying tank and comparing the average rate of change
of the volume or the second differences in the volume to key attributes of
the given model;
(D) determine an appropriate function model,
including linear, quadratic, and exponential functions, for a set of data
arising from real-world situations using finite differences and average rates
of change; and
(E) determine if a given linear function is
a reasonable model for a set of data arising from a real-world situation.
Statutory Authority: The provisions of this §111.48
issued under the Texas Education Code, §§7.102(c)(4), 28.002, and 28.025.
Source: The provisions of this §111.48 adopted to be effective
May 31, 2015, 40 TexReg 3146. | 677.169 | 1 |
Mathematical Finance (FINC3021)
UNIT OF STUDY
The aim of this unit is to provide students with a thorough understanding of some standard financial models from a mathematical perspective. Many of the greatest innovations in finance have been mathematical in nature and it is our aim to study the models along those lines. Specifically, we will concern ourselves with portfolio theory, CAPM, fundamental theorems of asset pricing and derivative valuation through the Black-Scholes and binomial models. Though some topics may appear familiar from previous courses, we will undertake a more quantitative approach to these models, starting from first principles, which will provide a greater depth of understanding. While the background mathematics will be taught as part of this unit, students are expected to be competent with basic mathematics | 677.169 | 1 |
An integrated body of resource material for a high school general mathematics course. The integrating theme, twentieth-century America, provides the general area to be considered; five foci supply specific subtopics...
Math resources for both students and teachers are given on this site, spanning the general topics of arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos with clear...
This page from the Meeting 21st-Century Cybersecurity Needs Through Advanced Technological Education project provides resources for students. These are designed to give students a "hands on fun opportunities to discover...
Created by the University of Texas's Department of Mathematics, mp_arc is an electronic archive for research papers in Mathematical Physics and related areas. This service, which is completely free to users, allows one... | 677.169 | 1 |
Salient Features:
• Exhaustive coverage of entire syllabus. • Covers answers to all Textual and Miscellaneous Exercises. • Precise theory for every topic. • Neat, labelled and authentic diagrams. • Written in a systematic manner. • Self evaluative in nature. • Includes Board Question Papers of March, October 2013, 2014 and March 2015.
Preface:
In the case of good books, the point is not how many of them you can get through, but rather how many can get through to you.
"Std. XII Sci. : PERFECT MATHS - II" is a complete and thorough guide critically analysed and extensively drafted to boost the students confidence. The book is prepared as per the Maharashtra State board syllabus and provides answers to all textual questions. Neatly labelled diagrams have been provided wherever required.
Multiple Choice Questions help the students to test their range of preparation and the amount of knowledge of each topic. Important theories and formulae are the highlights of this book. The steps are written in a systematic manner for easy and effective understanding.
The journey to create a complete book is strewn with triumphs, failures and near misses. If you think we've nearly missed something or want to applaud us for our triumphs, we'd love to hear from you. | 677.169 | 1 |
This course incorporates the Common Core Learning Standards with instructional time focusing on the number system, expressions and equations, functions, geometry, and stastistics and probability. Lessons and units vary in length. Students . . . | 677.169 | 1 |
Details about Mathematics and Politics:
This book teaches humanities majors the accessibility and beauty of discrete and deductive mathematics. political science, and could be offered at the freshman or sophomore level. models of international conflict, political power, and social choice. problems in international conflict resolution. quantitative methods are presented in strongly applied settings for political science and the social sciences.
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Rent Mathematics and Politics 1st edition today, or search our site for Taylor textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Springer. | 677.169 | 1 |
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About the book:
This title offers the language of mathematics at your fingertips. Derived from the world-renowned "McGraw-Hill Dictionary of Scientific and Technical Terms, Sixth Edition", this vital reference offers a wealth of essential information in a portable, convenient, quick-find format. Whether you're a professional, a student, a writer, or a general reader with an interest in science, there is no better or more authoritative way to stay up-to-speed with the current language of mathematics or gain an understanding of its key ideas and concepts. Written in clear, simple language understandable to the general reader, yet in-depth enough for scientists, educators, and advanced students, "The McGraw-Hill Dictionary of Mathematics, Second Edition" has been extensively revised, with 4,000 entries encompassing the language of mathematics and statistics.It includes synonyms, acronyms, and abbreviations. It provides pronunciations for all terms. It covers such topics as algebra, analysis, arithmetic, logic and set theory, number theory, probability and statistics, topology, and trigonometry. It also includes an appendix containing tables of useful data and information. It is based on the "McGraw-Hill Dictionary of Scientific and Technical Terms" - for more than a quarter-of-a-century the standard international reference. Carefully reviewed for clarity, completeness, and accuracy, the "McGraw-Hill Dictionary of Mathematics, Second Edition", offers a standard of excellence unmatched by any similar publicationSuperfast_Bookstore via United States
Softcover, ISBN 0071410481 Publisher: McGraw-Hill Professional, 2003 0071410481 Publisher: English, 2003
Softcover, ISBN 0071410481 Publisher: McGraw-Hill Professional, 2003 0071410481 0071410481 Publisher: McGraw-Hill Professional, 2003 0071410481 Publisher: McGraw-Hill Professional, 200371410481 Publisher: McGraw-Hill Professional, 2003 0071410481 Publisher: McGraw-Hill Professional, 2003 3rd71410481 Publisher: McGraw-Hill Professional, 2003 language71410481 Publisher: McGraw-Hill Professional71410481 Publisher: McGraw-Hill Professional71410481 Publisher: McGraw-Hill Professional, 2003 Used - Good, Usually ships in 1-2 business days, Good clean copy with no missing pages might be an ex library copy; may contain marginal notes and or highlighting
Softcover, ISBN 0071410481 Publisher: McGraw-Hill Professional71410481 Publisher: McGraw-Hill Professional, 2003 Paperback. Used - Good Good . May be an ex-library copy with library markings or stickers, may have some highlighting and or textual notes. May no longer have dust jacket or accessories if applicable.
Softcover, ISBN 0071410481 Publisher: McGraw-Hill Professional, 2003 | 677.169 | 1 |
Hanover Park CalculusEdward P.
...Wrapping up the study of arithmetic on whole numbers, exponentiation and order of operations (PEMDAS) are introduced. Knowing how to work with whole numbers well is the key to the bulk of a prealgebra course. The same skills (reading and writing, basic arithmetic operations, exponentiation and PEMDAS) are introduced for fractions, mixed numbers and decimals | 677.169 | 1 |
Introduction to Matrices and Vectors
In this concise undergraduate text, the first three chapters present the basics of matrices — in later chapters the author shows how to use vectors and matrices to solve systems of linear equations. 1961 edition.See more details below
Overview
In this concise undergraduate text, the first three chapters present the basics of matrices — in later chapters the author shows how to use vectors and matrices to solve systems of linear equations. 1961 edition. | 677.169 | 1 |
Algebra
Review Problems
- The following problems are provided as examples of
algebra concepts you should know before starting MAT 111. Answers are provided
to help you evaluate your progress. Your goal should be 80% correct or better.
- The following problems are provided as examples of Trigonometry concepts you
should know if you are interested in placing into MAT 161. Answers are provided
to help you evaluate your progress. Your goal should be 90% correct or better. | 677.169 | 1 |
The student workbook includes a set of lesson review boxes accompanied by questions that provide practice for previously taught concepts and the concepts taught in the lesson. "Exploring Math Through..." sections help students understand how ordinary people use algebraic math, providing concrete examples of how math is useful in life. Students will need to supply paper to work the problems. 333 pages, softcover | 677.169 | 1 |
Math Occupations
Actuaries analyze the financial costs of risk and uncertainty. They use mathematics, statistics, and financial theory to assess the risk that an event will occur and they help businesses and clients develop policies that minimize the cost of that risk. Actuaries' work is essential to the insurance industry. | 677.169 | 1 |
National 5 Mathematics
This Course is valid from August 2013.
The National 5 Mathematics Course enables learners to select and apply mathematical techniques in a variety of mathematical and real-life situations. Learners interpret, communicate and manage information in mathematical form.
Unit assessment overview
01-JUN-2014
This document provides general advice on assessment, judging evidence and re-assessment and outlines the approach taken in SQA-produced Unit assessment support packs.
Assessors also have freedom and flexibility to produce their own assessments, or use or adapt SQA-produced Unit assessment support packs. In all cases, Unit assessments have to demonstrate competency across all Assessment Standards.
Conditions of assessment
01-JUN-2014
Assessments for Mathematics must be carried out under supervised closed-book conditions. While this is not a change to the conditions of assessment, the UAS packs will be updated to include the term 'closed-book' in order to avoid any uncertainty in the future.
Qualification content and delivery tools
The documents on this page are for teachers and lecturers.
Learners studying this qualification may also find the documents useful.
The 'Related information' panel on this page contains information that applies to all new National Qualifications in this subject.
Use the tabs below to open each section individually. Alternatively you can view allhide all the sections.
Mandatory information
Course Specification
This explains the overall structure of the Course, including its purpose and aims and information on the skills, knowledge and understanding that will be developed.
National Parent Forum Scotland have also produced their Revision in a Nutshell series to help learners to prepare for new National 5 examinations | 677.169 | 1 |
Barisan dan deret .ingg
1.
SIGMA NOTATIOM, SEQUANCES AND SERIES
2.
MAIN TOPIC <ul><li>4.1 Sequences and Series </li></ul><ul><li>4.2 Sigma Notation </li></ul><ul><li>4.3 Arithmetic Sequences and Series </li></ul><ul><li>4.3 Geometric Sequences and Series </li></ul><ul><li>4.4 Infinite Geometric Series </li></ul>
3.
OBJECTIVE <ul><li>At the end of this topic you should be able to </li></ul><ul><ul><li>Define sequences and series </li></ul></ul><ul><ul><li>Understand finite and infinite sequence, finite and infinite series </li></ul></ul><ul><ul><li>Use the sum notation to write a series </li></ul></ul>
4.
SEQUENCES and SERIES <ul><li>A sequence is a set of real numbers a 1, a 2,… an ,… which is arranged (ordered). </li></ul><ul><li>Example: </li></ul><ul><li>Each number ak is a term of the sequence. </li></ul><ul><li>We called a 1 - First term and a 45 - Forty-fifth term </li></ul><ul><li>The n th term an is called the general term of the sequence. </li></ul>
5.
INFINITE SEQUENCES <ul><li>An infinite sequence is often defined by stating a formula for the n th term, a n by using { a n } . </li></ul><ul><li>Example: </li></ul><ul><ul><li>The sequence has n th term . </li></ul></ul><ul><ul><li>Using the sequence notation, we write this sequence as follows </li></ul></ul>First three terms Fifth teen term INFINITE SEQUENCES
6.
EXERCISE 1 : Finding terms of a sequence <ul><li>List the first four terms and tenth term of each sequence: </li></ul>A B C D E F
8.
The amount of the term in the addition above can be written as (3i – 1). The term in the addition are obtained by substituting the value of i with the value of 1, 2, 3, 4, and 5 to (3i – 1) The symbol read as sigma, is used to simplify the expression of the addition of number with certain patterns. In order that you understand more, the addition above can be written as : = 2 + 5 + 8 + 11 + 14 =(3(1) – 1) + (3(2) – 1) + (3(3) – 1) + (3(4) – 1) + (3(5) – 1) + (3(6)-1) =(3(1) – 1) + (3(2) – 1) + … + (3(i) – 1) + … + (3(6)-1)
9.
<ul><li>In general, the sum of n term of number with certain pattern where the i th term is stated as U i can be written as : </li></ul>U 1 + U 2 + U 3 + … + U i + …+ U n = Where : i = 1 is the lower bound of the addition n is the upper bound of the addition
16.
OBJECTIVE <ul><li>At the end of this topic you should be able to : </li></ul><ul><ul><li>Recognize arithmetic sequences and series </li></ul></ul><ul><ul><li>Determine the n th term of an arithmetic sequences and series </li></ul></ul><ul><ul><li>Recognize and prove arithmetic mean of an arithmetic sequence of three consecutive terms a , b and c </li></ul></ul>
17.
THE n th TERM OF AN ARITHMETIC SEQUENCES <ul><li>An arithmetic sequence with first term a and common different b , can be written as follows: </li></ul><ul><li>The n th term, a n of this sequence is given by the following formula: </li></ul>a, a + b, a + 2b, … , a + (n – 1)b U n = a + (n – 1)b
22.
EXERCISE 9: Finding a specific term of an arithmetic sequence <ul><li>If given the arithmetic sequence U 6 = 50 and U 41 = 155 determine the twelfth. </li></ul><ul><li>If the fourth term of an arithmetic sequence is 5 and the ninth term is 20, find the sixth term. </li></ul>
28.
THE n th PARTIAL SUM OF AN ARITHMETIC SEQUENCES <ul><li>If a 1, a 2,… an ,… is an arithmetic sequence with common difference b, then the n th partial sum Sn (that is the sum of the first n th terms) is given by either </li></ul><ul><li>or </li></ul>
29.
OBJECTIVE <ul><li>At the end of this topic you should be able to </li></ul><ul><ul><li>Recognize geometric sequences and series </li></ul></ul><ul><ul><li>Determine the n th term of a geometric sequences and series </li></ul></ul><ul><ul><li>Recognize and prove geometric mean of an geometric sequence of three consecutive terms a , b and c </li></ul></ul><ul><ul><li>Derive and apply the summation formula for infinite geometric series </li></ul></ul><ul><ul><li>Determine the simplest fractional form of a repeated decimal number written as infinite geometric series </li></ul></ul>
41.
OBJECTIVE <ul><li>At the end of this topic you should be able to </li></ul><ul><ul><li>Solve problem involving arithmetic series </li></ul></ul><ul><ul><li>Solve problem involving geometric series </li></ul></ul>
43.
APPLICATION 2: ARITHMETIC SEQUENCE <ul><li>The first ten rows of seating in a certain section of stadium have 30 seats, 32 seats, 34 seats, and so on. The eleventh through the twentieth rows contain 50 seats. Find the total number of seats in the section. </li></ul>Figure 2
45.
APPLICATION 2: GEOMETRIC SEQUENCE <ul><li>If deposits of RM100 is made on the first day of each month into an account that pays 6% interest per year compounded monthly, determine the amount in the account after 18 years. </li></ul>Figure 4 | 677.169 | 1 |
Solve and graph one-variable inequalities
Geometry classes typically need to review Algebra I topics prior to entry into Algebra II. The fundamental concept of inequalities with one-variable was presented as preparation for more challenging topics, especially in graphing. | 677.169 | 1 |
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A Quick Tour of the Wolfram Music Theory Course Assistant for iPad
Learn music theory with the help of the Wolfram Music Theory Course Assistant iPad app. This video gives a quick overview of how the app guides you through learning, practicing, and understanding the fundamentals of music theory.
Wolfram technologies offer the world's largest integrated web of mathematical capabilities and algorithms. See the ultimate mathematical computational tools, including Mathematica and Wolfram|Alpha, in action in this ...
Wolfram technologies, including Mathematica and Wolfram|Alpha, are broadening your math education pipeline—from interactive courseware authoring to cutting-edge research collaboration. Learn more in this video.
Building on 25 years of contributions to invention, discovery, and education, Wolfram provides the ultimate computational tools and resources. This video gives an overview of how Mathematica, Wolfram|Alpha, and other Wolfram technologies are used to support math, science, engineering, ...
Wolfram technologies offer the world's largest integrated web of mathematical capabilities and algorithms. See the ultimate mathematical computational tools, including Mathematica and Wolfram|Alpha, in action in this ...
In this Wolfram Technology Conference presentation, Radim Kusak shares his experiences in creating the course, Introduction to Wolfram Mathematica for Teachers, for his colleagues at Charles University in ... | 677.169 | 1 |
Pre-Algebra
9780078651083
ISBN:
0078651085
Pub Date: 2005 Publisher: Glencoe/McGraw-Hill School Pub Co
Summary: "Glencoe Pre-Algebra" is focused, organized, and easy to follow. The program shows your students how to read, write, and understand the unique language of mathematics, so that they are prepared for every type of problem-solving and assessment situation.
Glencoe McGraw-Hill Staff is the author of Pre-Algebra, published 2005 under ISBN 9780078651083 and 0078651085. Seven hundred sixty seven Pre-Algebra textboo...ks are available for sale on ValoreBooks.com, six hundred sixty four used from the cheapest price of $5.09, or buy new starting at $55WE HAVE NUMEROUS COPIES HARDCOVER humidity uptake causing wavy pages but no staining or wrinkling, chunks of cover missing up to 2" bottom of spine, very heavy wear to co [more]
WE HAVE NUMEROUS COPIES HARDCOVER humidity uptake causing wavy pages but no staining or wrinkling, chunks of cover missing up to 2" bottom of spine, very heavy wear to cover, edges, corners and spine, lots of cardboard showing on cover, edges, corners, and spine, binding and cover solid and strong, generally clean inside with minimal writing | 677.169 | 1 |
Singapore Math Practice, Level 1a
by Frank Schaffer Publisher Comments
Welcome to Singapore Math––the leading math program in the world! This workbook features math practice and activities for first and second grade students based on the Singapore Math method. Level A is designed for the first semester and Level B... (read more)
Study of Numbers up to 20, Bk. 1
by Caleb Gattegno Publisher Comments
The title Gattegno Mathematics embodies an approach best expressed by the phrase The Subordination of Teaching to Learning. The program covered in this series envisages the use of colored rods (Algebricks) and other books and printed materials that are... (read more)
Complete Math Success Grade 3 (Complete Math Success)
by Popular Book Company Publisher Comments
The Complete Math Success series provides engaging and systematic practice for developing and improving children's math skills. These curriculum-based workbooks are developed specifically to help young students reinforce the concepts that they have... (read more)
Nordic Research in Mathematics Education
by Carl Winsl Book News Annotation
This volume contains 64 papers originally presented at the fifth
Nordic conference in research on mathematics education, held in
Copenhagen, Denmark, in April of 2008. The conference was organized
around four themes: "Didactical design in mathematics... (read more)
Math Bafflers Book 1: Logic Puzzles That Use Real-World Math
by Marilynn L. Rapp Buxton Publisher Comments
Math Bafflers requires students to use creativity, critical thinking, and logical reasoning to perform a variety of operations and skills that align with state and national math standards. The book covers real-life situations requiring math skills, such... (read more)
Key Works in Radical Constructivism
by E. Von Glasersfeld Publisher Comments
Key works on radical constructivism brings together a number of essays by Ernst von Glasersfeld that illustrate the application of a radical constructivist way of thinking in the areas of education, language, theory of knowledge, and the analysis of a... (read more)
Teaching Geometry
by Doug French Publisher Comments
This fascinating title reviews the teaching and learning of school geometry from the perspective of both the new teacher and the more experienced teacher. It is designed to extend and deepen subject knowledge and to offer practical advice and ideas for... (read more)
Common Core Geometry: Solaro Study Guide (Common Core Study Guides)
by Castle Rock Research Corporation (cor) Publisher Comments
A comprehensive geometry study guide that helps students, educators, and parents alike navigate the new Common Core State Standards With content developed by a team of teachers and curriculum specialists and reviewed by assessment experts with a minimum | 677.169 | 1 |
This book has been specifically written for the new two-tier Edexcel linear GCSE specification for first examination in 2008. The book is targeted at the B to A* grade range in the Foundation tier GCSE, and it comprises units organised clearly into homeworks designed to support the use of the Higher Plus Students' Book in the same series. Each unit offers:
BLA review test focusing on prior topics for continual reinforcement BLTwo sets of questions that relate directly to individual lessons in the unit, providing ample practice BLA synoptic homework that covers the whole unit, so students consolidate the key techniques BLFull answers in the accompanying teacher book
It forms part of a suite of four homework books at GCSE, in which the other three books cater for grade ranges G to E, E to C and D to B.
Book Description OUP Oxford, 20063353735
Book Description OUP Oxford, 20063456761
Book Description OUP Oxford347740
Book Description OUP Oxford, 2006. Paperback. Book Condition: Good. Oxford GCSE Maths for Edexcel: Higher Plus Homework Book057-MB002-K16-00061
Book Description Paperback. Book Condition: Good. The book has been read but remains in clean condition. All pages are intact and the cover is intact. Some minor wear to the spine. Bookseller Inventory # GOR0009567071721199 | 677.169 | 1 |
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Mathematica in K–12 and Community College Education: Part 2
Cliff Hastings
This is the second video in a series showing examples of Mathematica features that are especially useful for K–12 and community college educators. In this video, you'll discover how easy it is to create interactive Demonstrations, lessons, quizzes, and instructional handouts with Mathematica.
Watch an introduction to the Wolfram Demonstrations Project, a free resource that uses dynamic computation to illuminate concepts in science, technology, mathematics, art, finance, and a range of other fields.
computerbasedmath.org is a project to build a new math curriculum with computer-based computation at its heart. In this talk from the Wolfram Technology Conference 2011, Conrad Wolfram discusses the concept, ... | 677.169 | 1 |
Maplesoft Blogger Profile: Robert Lopez
Dr. Robert J. Lopez, Emeritus Professor of Mathematics at the Rose-Hulman Institute of Technology in Terre Haute, Indiana, USA, is an award winning educator in mathematics and is the author of several books including Advanced Engineering Mathematics (Addison-Wesley 2001). For over two decades, Dr. Lopez has also been a visionary figure in the introduction of Maplesoft technology into undergraduate education. Dr. Lopez earned his Ph.D. in mathematics from Purdue University, his MS from the University of Missouri - Rolla, and his BA from Marist College. He has held academic appointments at Rose-Hulman (1985-2003), Memorial University of Newfoundland (1973-1985), and the University of Nebraska - Lincoln (1970-1973). His publication and research history includes manuscripts and papers in a variety of pure and applied mathematics topics. He has received numerous awards for outstanding scholarship and teaching.
Posts by Robert Lopez
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In this webinar I am going to demonstrate how Maple can be used to get across the concept of the eigenpair, to show its meaning, to relate this concept to the by-hand algorithms taught in textbooks.
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Fourteen Clickable Calculus examples have been added to the Teaching Concepts with Maple area of the Maplesoft web site. Four are sequence and series explorations taken from algebra/precalculus, four are applications of differentiation, four are applications of integration, and two are problems from the lines-and-planes section of multivariate calculus. By my count, this means some 111 Clickable Calculus examples have now been posted to the section.
Thirteen Clickable Calculus examples have been added to the Teaching Concepts with Maple section of the Maplesoft web site. The additions include examples in algebra, differential and integral calculus, lines-and-planes in multivariate calculus, and linear algebra. By my count, this means some 97 Clickable Calculus examples are now available.
In Maple 17, the Student MultivariateCalculus package has been augmented with fifteen new commands relevant for defining and manipulating lines and planes. There already exists a functionality for this in the geom3d package whose structures differ from those in the new Student packages. Students...
Ten more Clickable Calculus solutions have been added to the Teaching Concepts with Maple section of the Maplesoft web site. Solutions to problems include examples in algebra, differential and integral calculus, lines-and-planes in multivariate calculus, linear algebra, and vector calculus.
Revision Note: I have updated the graph in the attached Maple document based on Doug Meade's comment below. CarTalkPuzzler_9-22-.mw
Car Talk, a humorous phone-in program in which Tom and Ray Magliozzi (Click and Clack, the Tappet Brothers) diagnose and offer solutions for mysterious auto-related maladies, is carried by National Public Radio...
Eleven new Clickable-Calculus examples have been added to the Teaching Concepts with Maple section of the Maplesoft website. That means some 74 of the 154 solved problems in my data-base of syntax-free calculations are now available. Once again, these examples and associated videos illustrate point-and-click computations in support of the pedagogic message of resequencing skills and concepts.
This post is a further exploration of the optimization problem of finding a point on f(x) = sinh(x) - xe-3x closest to the point (1,7). The problem is part of our Teaching Concepts with Maple web site, a collection of video examples and Maple worksheets designed to illustrate how Maple can be used to generate...
With the addition of ten new Clickable-Calculus examples to the Teaching Concepts with Maple section of the Maplesoft website, we've now posted 63 of the 154 solved problems in my data-base of syntax-free calculations. Once again, these examples and associated videos illustrate point-and-click computations, but more important, they embody the
My list of problems solved with Clickable-Calculus syntax-free techniques now numbers 154, spread over eight subject areas. Recently, Maplesoft posted to its website 44 of these problems, along with videos of their point-and-click solutions. Not only do these solutions demonstrate Maple functionalities, but they also have a pedagogic message, that is resequencing skills and concepts. They show how Maple can be used to obtain a solution, then show how Maple can be used to implement...
Being easy to use is nice, but being easy to learn with is better. Maple's ease-of-use paradigm, captured in the phrases "Clickable Calculus" and "Clickable Math" provides a syntax-free way to use Maple. The learning curve is flattened. But making Maple easy to use to use badly in the classroom helps neither student nor instructor.
A recent Tips and Techniques article in the Maple Reporter contained the following five "gems" from my Red Book of Maple Magic. These 'gems' are tricks and techniques for Maple that I've discovered in my years here at Maplesoft. The previous 15 gems have appeared in three other issues of the Reporter, as...
National Public Radio in the USA carries Car Talk, a humorous phone-in program in which Tom and Ray Magliozzi (Click and Clack, the Tappet Brothers) diagnose and offer solutions for mysterious auto-related maladies. It's an amusing hour on Saturday mornings. | 677.169 | 1 |
Class Schedule
MAT101: Fundamentals of Mathematics
MAT101: Fundamentals of Mathematics - 4 Hours
An introduction to basic and fundamental mathematics which includes reading and writing whole numbers, the operations associated with addition, subtraction, multiplication, and division of whole numbers, fractions, mixed numbers, decimals, and percents. The course also covers ratio and proportion, and the metric system. Solving word problems is emphasized throughout the course. | 677.169 | 1 |
About this book
A collection of inter-connected topics in areas of mathematics which
particularly interest the author, ranging over the two millennia from
the work of Archimedes to the "Werke" of Gauss. The book is intended
for those who love mathematics, including undergraduate students of
mathematics, more experienced students and the vast unseen host of
amateur mathematicians. It is equally a useful source of material for
those who teach mathematics. | 677.169 | 1 |
Master Mathematics
Mathematics is a broad discipline, strongly related to innovation, science and technology.
Mathematicians are very professional individuals who can have a career in many places.
Living with a constant learning desire and maintaining a sustained progress, are characteristics common to mathematicians and highly valued by employers Mathematics
Advertisement
Mathematicsisabroaddiscipline,stronglyrelatedtoinnovation,science andtechnology. Mathematiciansareveryprofessionalindividualswhocan have a career inmanyplaces.Living with aconstantlearning desire and maintaining a sustainedprogress, arecharacteristicscommontomathematiciansandhighly valued by employers.Expertstrainedin mathematicsbyCCCEareparticularlysuitable for: | 677.169 | 1 |
9780201312232 Algebra through Applications
Throughout this text, motivating real-world applications, examples, and exercises demonstrate how integral mathematical understanding is to student mastery in other disciplines, a variety of occupations, and everyday situations. A distinctive side-by-side format, pairing each example with a corresponding practice exercise, encourages students to get actively involved in the mathematical content from the start. Unique Mindstretchers target different levels and types of student understanding in one comprehensive problem set per section. Mindstretchers incorporate related investigation, critical thinking, reasoning, and pattern recognition exercises along with corresponding group work and cultural connections. To show how mathematics has evolved over the centuries, in many cultures, and throughout the world, each chapter features a compelling Cultural Note that investigates and illustrates the origins of mathematical concepts. Diverse topics include art, music, the evolution of digit notation, and the ancient practice of using a scale to find an unknown weight. | 677.169 | 1 |
make sure that they gain understanding of what it means to prove a theorem logically. In pre-algebra, the student is introduced to the abstract concepts. These concepts have to be related to the real life. am currently working as a professional musician, primarily as a saxophone player with the soul-pop band Lawrence. I | 677.169 | 1 |
Intermediate Algebra for College Students (5th Edition)
9780136007623
ISBN:
0136007627
Edition: 5 Pub Date: 2008 Publisher: Prentice Hall
Summary: The goal of this book is to provide readers with a strong foundation in algebra by developing the problem-solving and critical thinking abilities. Topics are presented in an interesting format, incorporating real world sourced data and encouraging modeling and problem-solving.
Robert F. Blitzer is the author of Intermediate Algebra for College Students (5th Edition), published 2008 under ISBN 9780136007623 a...nd 0136007627. Eleven Intermediate Algebra for College Students (5th Edition) textbooks are available for sale on ValoreBooks.com, five used from the cheapest price of $23.46, or buy new starting at $148.64 | 677.169 | 1 |
Recently changed in this version
Description
In this Math App, there are no words to explain except at index. So let me introduce the concept of Math Bridge in English. You can try free sample version on web.
This App is not Math itself, but Math-related supplemental program. Math can only exist when you are doing it as if your thinking exists when you think.
1. Calculation
In this App, there are three levels and one challenge mode in following calculations.
i) Addition:
ii) Subtraction:
iii) Multiplication:
iv) Division:
After every five questions, quick review is set to check right and wrong. All four challenge modes for calculations have a five seconds timer to answer the question. They are difficult but concentration can enable us to get right answers.
5 Differentiation
In calculus, a branch of mathematics, the derivatives is a measure to know how a function changes as its input changes. (from wikipedia)
In this App, you can find points of extreme by a quadratic derivative in trinomials.
6 Integration
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. (from wikipedia)
In this App, you can learn the calculation of an area between quadratic function and linear function. At first, the cross-points of two functions are calculated by factoring and calculate the area by integration. Please touch screen to take steps.
An Orbit of thrown object as quadratic curve can be a bridge connected between the real world and math. Math is a tool as well as a world. The difference of the real world and a world is ambiguous, because we can't see the real world without a world, which is our own world. Math has a history over 3000 years as well as language, both of which are very powerful to explore the real world. Life may be a problem much more complex than math, but logic is useful for both of them. To handle logic or theory requires much energy in brain so that doing math is a good training for thinking about the world and life with your own logic. These can be reasons why we learn math. How about you?
Have fun!
ver 1.1
"Quadratic formula" and "Trinomial" are added in Equation.
In Quadratic formula, you can see the course from a general quadratic equation to the quadratic formula by 7 steps. The logic of four arithmetic operations and notion of equal is the basic skill.
In trinomial, you can solve cubic equations by factoring. Please note that plus and minus notations are needed to be cared for as well as calculating fraction. When f(a) = 0 in f(x)=0, it means that the "a" can be factored. | 677.169 | 1 |
This book explores the life and scientific legacy of Manfred Schroeder through personal reflections, scientific essays and Schroeder?s own memoirs. Reflecting the wide range of Schroeder?s activities, the first part of the book contains thirteen articles written by his colleagues and former students. Topics discussed include his early, pioneering... more...
Arithmetic for the Mature Student provides information pertinent to the basic operations of arithmetic, including addition, subtraction, multiplication, and division. This book covers a variety of topics, including percentages, fractions, and factors. Organized into five chapters, this book begins with an overview of the instructions on how to use... more...
Tips for simplifying tricky basic math and pre-algebra operations Whether you're a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary math... more...
Generic group algorithms solve computational problems defined over algebraic groups without exploiting properties of a particular representation of group elements. This is modeled by treating the group as a black-box. The fact that a computational problem cannot be solved by a reasonably restricted class of algorithms may be seen as support towards... more...
This text introduces related fundamental mathematics in the field of blind signal processing and covers many advances. It includes results from a Shanghai Jiao Tong University study in speech signal processing, underwater signals, data compression and more. more...
Since the publication of the first edition in 1976, there has been a notable increase of interest in the development of logic. This is evidenced by the several conferences on the history of logic, by a journal devoted to the subject, and by an accumulation of new results. This increased activity and the new results - the chief one being that Boole's... more...
This book contains the proceedings of the NATO-Russia Advanced Study Institute (ASI) 'Boolean Functions in Cryptology and Information Security', which was held at September 8-18, 2007 in Zvenigorod, Moscow region, Russia. These proceedings consist of three parts. The first part contains survey lectures on various areas of Boolean function theory that... more...
This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric... more...
This book contains selected papers on the language, applications, and environments of CafeOBJ, which is a state-of -the-art algebraic specification language. The authors are speakers at a workshop held in 1998 to commemorate a large industrial/academic project dedicated to CafeOBJ. The project involved more than 40 people from more than 10 organisations,... more... | 677.169 | 1 |
From the Contributor: MathTutorDVD.com I have tutored many, many people in Math through Calculus, and I have found that if you start off with the basics and take things one step at a time - anyone can learn complex Math topics. This 2-DVD set contains 5 hours of fully worked example problems in Trig and Pre-Calculus. After viewing this DVD course in Trigonometry and Pre-Calculus you'll discover that the material isn't hard at all if it is presented in a clear manner. No knowledge is assumed on the part of the student. Each example builds in complexity so before you know it you'll be working the 'tough' problems with ease! Have a problem with your homework? Simply find a similar problem fully worked out on the Trigonometry and Pre-Calculus Tutor 2-DVD set! Total run time: 5 hours.
Topics Covered: Disk 1 Section 1: Complex Numbers Section 2: Exponential Functions Section 3: Logarithmic Functions Section 4: Solving Exponential and Logarithmic Equations Section 5: Angles Disk 2 Section 6: Finding Trig Functions Using Triangles Section 7: Finding Trig Functions Using The Unit Circle Section 8: Graphing Trig Functions Section 9: Trig Identities Product Description The Trigonometry and Pre-Calculus Tutor is the easiest way to improve your grades in Trig and Pre-Calculus! How does a baby learn to speak? By being immersed in everyday conversation. What is the best way to learn Trig and Pre-Calculus? By being immersed in it! During this course the instructor will work out hundreds of examples with each step fully narrated so no one gets lost! Most other DVDs on Trig and Pre-Calculus are 2 hours in length. This DVD set is over double the running time and costs much less! See why thousands have discovered that the easiest way to learn Trig and Pre-Calculus is to learn by examples!
The Trigonometry & Pre-Calculus Tutor- Volume 2 DVD - Factory sealed. $25ppd. Product Description Learn how to solve problems in Trigonometry and PreCalculus with fully worked example problems! Every lesson features step-by-step instruction so that every student will master the topics. This course continues the student's study of essential topics in trigonometry and pre-calculus with extensive practice of trig identities, the unit circuit, law of sines/cosines, and much more! Total Run Time: 6 Hours | 677.169 | 1 |
Mathematics - Algebra (529 results)
Bringing to life the joys and difficulties of mathematics this book is a must read for anyone with a love of puzzles, a head for figures or who is considering further study of mathematics. On the Study and Difficulties of Mathematics is a book written by accomplished mathematician Augustus De Morgan. Now republished by Forgotten Books, De Morgan discusses many different branches of the subject in some detail. He doesn't shy away from complexity but is always entertaining. One purpose of De Morgan's book is to serve as a guide for students of mathematics in selecting the most appropriate course of study as well as to identify the most challenging mental concepts a devoted learner will face. "No person commences the study of mathematics without soon discovering that it is of a very different nature from those to which he has been accustomed," states De Morgan in his introduction. The book is divided into chapters, each of which is devoted to a different mathematical concept. From the elementary rules of arithmetic, to the study of algebra, to geometrical reasoning, De Morgan touches on all of the concepts a math learner must master in order to find success in the field. While a brilliant mathematician in his own right, De Morgan's greatest skill may have been as a teacher. On the Study and Difficulties of Mathematics is a well written treatise that is concise in its explanations but broad in its scope while remaining interesting even for the layman. On the Study and Difficulties of Mathematics is an exceptional book. Serious students of mathematics would be wise to read De Morgan's work and will certainly be better mathematicians for it.
The purpose of this book, as implied in the introduction, is as follows: to obtain a vital, modern scholarly course in introductory mathematics that may serve to give such careful training in quantitative thinking and expression as well-informed citizens of a democracy should possess. It is, of course, not asserted that this ideal has been attained. Our achievements are not the measure of our desires to improve the situation. There is still a very large "safety factor of dead wood" in this text. The material purposes to present such simple and significant principles of algebra, geometry, trigonometry, practical drawing, and statistics, along with a few elementary notions of other mathematical subjects, the whole involving numerous and rigorous applications of arithmetic, as the average man (more accurately the modal man) is likely to remember and to use. There is here an attempt to teach pupils things worth knowing and to discipline them rigorously in things worth doing.<br><br>The argument for a thorough reorganization need not be stated here in great detail. But it will be helpful to enumerate some of the major errors of secondary-mathematics instruction in current practice and to indicate briefly how this work attempts to improve the situation. The following serve to illustrate its purpose and program:<br><br>1. The conventional first-year algebra course is characterized by excessive formalism; and there is much drill work largely on nonessentials.
Bertrand Russell was a British logician, nobleman, historian, social critic, philosopher, and mathematician. Known as one of the founders of analytic philosophy, Russell was considered the premier logician of the 20th century and widely admired and respected for his academic work. In his lifetime, Russell published dozens of books in wildly varying fields: philosophy, politics, logic, science, religion, and psychology, among which The Principles of Mathematics was one of the first published and remains one of the more widely known. Although remembered most prominently as a philosopher, he identified as a mathematician and a logician at heart, admitting in his own biography that his love of mathematics as a child kept him going through some of his darkest moments and gave him the will to live. With his book The Principles of Mathematics, Russell aims to instill the same deep seated passion for mathematics and logic that he has carefully cultivated in the reader. He adeptly explores mathematical problems in a logical context, and attempts to prove that the study of mathematics holds critical importance to philosophy and philosophers. Russell utilizes the text to explore the some of the most fundamental concepts of mathematics, and expounds on how these building blocks can easily be applied to philosophy. In the second part of the book, Bertrand addresses mathematicians directly, discussing arithmetic and geometry principles through the lens of logic, offering yet another unique and groundbreaking interpretation of a field long before considered static. This book affords new insight and application for many basic mathematical concepts, both in roots of and application to other fields of scholarly pursuit. Russell uses his book to establish a baseline of mathematical understanding and then expands upon that baseline to establish larger and more complex ideas about the world of mathematics and its connections to other fields of personal interest. The Principles of Mathematics is a very captivating glimpse into the logic and rational of one of history's greatest thinkers. Whether you're a mathematician at heart, a logician, or someone interested in the life and thoughts of Bertrand Russell, this book is for you. With an incredible amount of information on mathematics, philosophy, and logic, this text inspires the reader to learn more and discover the ways in which these very disparate fields can interconnect and create new possibilities at their intersections.
William F. White was a professor of mathematics at State Normal School in New Paltz, New York and held a PhD from Colgate University. He was also, very clearly, a lover of mathematics. A Scrap-Book of Elementary Mathematics: Notes, Recreations, Essays is White's love letter to math. White makes it clear early in this work that this is not a resource guide or a textbook. Rather, White has created a volume consisting primarily of puzzles, notes, and intriguing principles of mathematics. Essentially, this is the fun side of math. Repeating products, algebraic fallacies, axioms in elementary algebra, and the law of commutation are just four of the intriguing principles discussed. The real strengths of the work are the mathematical games and puzzles presented throughout. Each section of the book is brief, with topics covered in only one or two pages, and the author keeps the book moving at a rapid pace. Bibliographic notes and a detailed index conclude the work. A Scrap-Book of Elementary Mathematics: Notes, Recreations, Essays is exactly the type of text that should be introduced to students of mathematics. It demonstrates real world application of math and all of the quirks and oddities contained within its study. White has put together a lighthearted book that emphasizes enjoyment and discovery over serious analysis and strict repetition. While no replacement for a true textbook, this collection is sure to entertain. Ultimately, A Scrap-Book of Elementary Mathematics: Notes, Recreations, Essays is the rare book that can entertain both kids and adults with math. White's underappreciated work is highly recommended and deserves to sit side by side with modern math textbooks.
The Directly-Useful Technical Series requires a few words by of introduction. Technical books of the past have arranged themselves largely under two sections: the Theoretical and the Practical and the exercises are to be of a directly-useful orientalists who exploited Indian history and literature about a century ago were not always perfect in their methods of investigation and consequently promulgated many errors. Gradually, however, sounder methods have obtained and we are now able to see the facts in more correct perspective. In particular the early chronology has been largely revised and the revision in some instances has important bearings on the history of mathematics and allied subjects. According to orthodox Hindu tradition the Surya Siddhanta, the most important Indian astronomical work, was composed over two million years ago! Bailly, towards the end of the eighteenth century, considered that Indian astronomy had been founded on accurate observations made thousands of years before the Christian era. Laplace, basing his arguments on figures given by Bailly considered that some 3,000 years B. C. the Indian astronomers had recorded actual observations of the planets correct to one second; Playfair eloquently supported Bailly's views; Sir William Jones argued that correct observations must have been made at least as early as 1181 B. C.; and so on; but with the researches of Colebrooke, Whitney, Weber, Thibaut, and others more correct views were introduced and it was proved that the records used by Bailly were quite modern and that the actual period of the composition of the original Surya Siddhanta was not earliar than A. D. 400.<br><br>It may, indeed, be generally stated that the tendency of the early orientalists was towards antedating and this tendency is exhibited in discussions connected with two notable works, the Sulvasutras and the Bakhshali arithmetic, the dates of which are not even yet definitely fixed.
The Directly Useful Technical Series requires a few words by way of introduction. Technical books of the past have arranged themselves largely under two sections: the theoretical and the practical, and the exercises are to be of a directly useful present collection of Exercises, gathered from many sources, is one which has accumulated through several years, and consists of papers set weekly or bi-weekly to boys of all ages during that time. They serve to recall back work, and keep boys always ready for the examination. The First Series contains 261 papers, about half the total number, and commences with exercises in Arithmetic suitable to boys who have gone through the First Four Rules, Simple and Compound, and are beginning Fractions; and Algebraical Exercises consisting chiefly of Numerical Values, Addition, and Subtraction. From these onward, the exercises rise in difficulty by careful gradations, reaching Cube Root and Compound Interest in Arithmetic, and Quadratic Equations in Algebra, at the end of the First Series.<br><br>The Second Series is a continuation of the First, and includes problems in Higher Algebra, Logarithms, Trigonometry, and easy Mechanics, and Analytical Geometry.
The present work contains a full and complete treatment of the topics usually included in an Elementary Algebra. The author has endeavored to prepare a course sufficiently advanced for the best High Schools and Academies, and at the same time adapted to the requirements of those who are preparing for admission to college.<br><br>Particular attention has been given to the selection of examples and problems, a sufficient number of which have been given to afford ample practice in the ordinary processes of Algebra, especially in such as are most likely to be met with in the higher branches of mathematics. Problems of a character too difficult for the average student have been purposely excluded, and great care has been taken to obtain accuracy in the answers.<br><br>The author acknowledges his obligations to the elementary text-books of Todhunter and Hamblin Smith, from which much material and many of the examples and problems have been derived. He also desires to express his thanks for the assistance which he has received from experienced teachers, in the way of suggestions of practical value.
This text is prepared to meet the needs of the student who will continue his mathematics as far as the calculus, and is written in the spirit of applied mathematics. This does not imply that algebra for the engineer is a different subject from algebra for the college man or for the secondary student who is prepared to take such a course. In fact, the topics which the engineer must emphasize, such as numerical computations, checks, graphical methods, use of tables, and the solution of specific problems, are among the most vital features of the subject for any student. But important as these topics are, they do not comprise the substance of algebra, which enables it to serve as part of the foundation for future work. Rather they furnish an atmosphere in which that foundation may be well and intelligently laid.<br><br>The concise review contained in the first chapter covers the topics which have direct bearing on the work which follows. No attempt is made to repeat all of the definitions of elementary algebra. It is assumed that the student retains a certain residue from his earlier study of the subject.<br><br>The quadratic equation is treated with unusual care and thoroughness. This is done not only for the purpose of review, but because a mastery of the theory of this equation is absolutely necessary for effective work in analytic geometry and calculus. Furthermore, a student who is well grounded in this particular is in a position to appreciate the methods and results of the theory of the general equation with a minimum of effort.<br><br>The theory of equations forms the keystone of most courses in higher algebra. The chapter on this subject is developed gradually, and yet with pointed directness, in the hope that the processes which students often perform in a perfunctory manner will take on additional life and interest.
Francis William Newman was an emeritus professor of University College in London and an honorary fellow of Worcester College, Oxford. Considered quite the renaissance man, Newman's interests ranged wildly, from writings on philosophy, English reforms, Arabic, diet, grammar, political economy, Austrian Politics, Roman History, and math. He wrote at length on every subject he found of interest, and this book, Mathematical Tracts is a testament to his very successful career as a mathematician and his eloquence as an impassioned author. At its core, this book explores many of the basics theorems and principles behind geometry, aimed at the budding mathematician to encourage interest and educate. A wonderful beginners guide, but also an interesting read for anyone wanting to refresh their foundational knowledge in geometry, this book is an easy to understand and approachable guide to mathematics. After establishing the basics, this book goes in-depth on many geometrical concepts such as the treatment of ration between quantities incommensurable and primary ideas of the sphere and circle. Newman's vast knowledge of mathematics is put to excellent use in this text, expounding on mathematical concepts and explaining them with such clarity that regardless of prior mathematical knowledge, the reader is guaranteed to understand the concepts. Newman highlights a variety of shapes such as pyramids and cones in their geometric context and explains their mathematical significance. He also expands the reader's understanding of parallel straight lines and the infinite area of a plane angle, and ends the book with a plethora of tables and helpful mathematical examples intended to further clarify the core concepts of the text. Truly a one of a kind, Mathematical Tracts is the perfect book for anyone interested in mathematics. Whether you're an early learner or a seasoned professional, you will find new information that is communicated in such a passionate and compelling way that it is impossible not to be enthused and excited about the topic. An incredibly approachable book laden with mathematical concepts that are made both interesting and exciting by the overwhelming passion of the author, this book is highly recommended for all readers.
It is the business of schools to give children during the first six years of school life that kind of instruction in mathematics which will lead them to a quick recognition and a ready knowledge of number combinations and number operations, and then enable them to apply these number combinations and number operations to the solution of simple problems. The instruction for this period, if it is to serve its purpose, must be definite and specific.<br><br>At the end of the sixth year the pupil should have a thorough mastery of the number combinations in integers; of the four fundamental operations with integers, common fractions, and decimal fractions; of the common measurements; and of the use of all of these in the solution of problems. Since eternal review is the price of excellence in all mathematical work, especially in computations, this book contains a complete but not lengthy review of the work of the first six years. The reviews are arranged elastically, however, so that the time devoted to them can be determined by the needs of the class. Monotony, the one great drawback of reviews has been removed by connecting the matter reviewed by historical references of interest, by looking at it from a standpoint of business, by number contests, by using the matter to be reviewed as a background for new work.
In arranging for publication the present collection of my papers on Mathematical and Physical subjects, I have taken the dates of their first publication as a general rule in fixing the order of the various papers. In certain cases, however, I have considered it advisable to bring together under one article all that I have written on one particular line of research; the most important instances of this being Articles xlviil, XLix., and l.Article xlviil, On the Dynamical Theory of Heat, and Article L., On Thermodynamic Motivity, includes all of my papers on this subject, published between the years 1851 and the present time, except the Article Heat of the Encyclopcedia Britannica, published in 1880. Article XLix., On the Thermal Ejects of Fluids in Motion, consists of a joint series of papers by Dr Joule and myself published at various intervals between 1853 and 1862.
The Principles of Mathematics: Vol. 1 is a terrific introduction to the fundamental concepts of mathematics. Although the book's title involves mathematics, it is not a textbook packed with equations and theorems. Instead philosopher Bertrand Russell uses mathematics to explore the structure of logic. Russell's ultimate point is that mathematics is logic and logic itself is truth. The book is substantial and covers all subjects of mathematics. It is divided into seven sections: indefinables in mathematics, number, quantity, order, infinity and continuity, space, matter and motion. Russell covers all the major developments of mathematics and the contributions of important figures to the field. His sharp mind is evident throughout The Principles of Mathematics, as he challenges established rules and teachers readers how to think through difficult problems using logic. Russell was one of the great minds of the 20th Century. In this book he discusses how his ideas were influenced by the logician Peano. He also debates other philosophers and mathematicians, and even anticipates the Theory of Relativity, which had not yet been published by Einstein. One does not need to love mathematics to gain insights from The Principles of Mathematics: Vol. 1. Those who are interested in logic, intellectualism, philosophy or history will find significant insights into logical principles. Readers who desire an intellectual challenge will truly enjoy The Principles of Mathematics: Vol. 1.
The material in this volume is prepared for the use of pupils who have done a year's work in Elementary Algebra. Many high schools divide their Algebra work into two courses separated by some work in Geometry and elementary science. These schools often find it more convenient and economical to use two books in Algebra, one for the first course and another for the second. The authors' First Course in Elementary Algebra is planned for first-year work and this book is planned for the second-year work.<br><br>The first six chapters are a review and extension of the topics of the First Course. The chapter on logarithms is new in name only, because in theory it is an extension of the subject of exponents. The remainder of the volume treats the usual topics, Equations, Proportion, Variation and Series, supplemented by problems applying Algebra to Geometry.<br><br>Throughout the treatment the authors have constantly kept in mind both the logical value and the practical utility of the subject.<br><br>The logical value of Algebra is of prime importance; hence, the proofs of processes are based upon reasons both correct and satisfying to the mind of the pupil. On the other hand, subtle distinctions and arguments savoring of higher mathematical methods without their true rigor have been avoided.<br><br>The utility of Algebra is given the emphasis which it so richly deserves.
For the past nine years I have been lecturing in this subject to students taking courses in Mechanical and Electrical Engineering at the Woolwich Polytechnic, and this book is based on the work done by the senior students there. So as not to make the book too cumbersome for a text-book, a preliminary knowledge of the fundamental principles of Algebra, Trigonometry, and Mensuration, and the use of Logarithms and squared paper, has been assumed, this being well within the scope of the elementary student. The book is meant to cover a two- or three-years' course, and it is roughly divided into three sections:<br><br>(1)Algebra and Trigonometry.<br>(2) The Differential and Integral Calculus.<br>(3) The application of the subject-matter of the two previous sections to concrete examples.<br><br>The work in Section I has been carefully selected in such a way as to help the student with the later work in the Calculus. There is no doubt that after the idea of the Calculus has been thoroughly grasped, a great many of the so-called difficulties which arise out of the work are entirely due to a weakness in the knowledge of the fundamental principles of Algebra and Trigonometry.<br><br>Again, many fail to integrate algebraic functions because they have such weak notions of partial fractions and simple substitutions. Section I has been written with the idea of removing this weakness.<br><br>The Calculus has been treated as thoroughly as the size of the book allows.
This tract is intended to give an account of the theory of equations according to the ideas of Galois. The conspicuous merit of this method is that it analyses, so far as exact algebraical processes permit, the set of roots possessed by any given numerical equation. To appreciate it properly it is necessary to bear constantly in mind the difference between equalities in value and identities or equivalences in form; I hope that this has been made sufficiently clear in the text. The method of Abel has not been discussed, because it is neither so clear nor so precise as that of Galois, and the space thus gained has been filled up with examples and illustrations.<br><br>More than to any other treatise, I feel indebted to Professor H. Weber's invaluable Algebra, where students who are interested in the arithmetical branch of the subject will find a discussion of various types of equations, which, for lack of space, I have been compelled to omit.<br><br>I am obliged to Mr Morris Owen, a student of the University College of North Wales, for helping me by verifying some long calculations which had to be made in connexion with Art. 52.
Counting a series of things and keeping tally of the tens on the fingers were processes used by primitive peoples. From the ten fingers arose ultimately the decimal system of numeration. Recording the results of counting was done by the Egyptians and other ancient nations by means of strokes and hooks; for one thing a single stroke | was made, for two things two strokes || were used, and so on up to ten which was represented by Π. Then eleven was written |Π, twelve ||Π, and so on up to twenty, or two tens, which was represented by ΠΠ. In this way the numeration proceeded up to a hundred, for which another symbol was employed.<br><br>Names for ||, |||, ||||, ΠΠ, etc., appear in the Egyptian hieroglyphics, but a special symbol for each name is not used. Probably the Hindoos first invented such symbols, and passed them on to the Arabs, through whom they were introduced into Europe.<br><br>2<br><br>Greek Notation<br><br>The Greeks used an awkward notation for recording the results of counting.
We have added in the present Volume to what was contained in the earlier editions of this work a new chapter on the Theory of Substitutions and Groups. Our aim has been to give here, witbin as narrow limits as possible, an account of the subject which may be found useful by students as an introduction to those fuller and more systematic works which are specially devoted to this department of Algebra. The works which have afforded us most assistance in the preparation of this chapter are Serret sCours dAlgebre supe rieure ; Traiti des Substitutions et des Equations algibriques by M.Camille Jordan (Paris, 1870 ; Netto sSubstitutumentheorie und Hire Anwendung auf die Algebra (Leipzig, 1882), of which there is an English translation by F.N. Cole (AnnArbor, Mich., 1892) ;and Legons sur la Resolution algibrique des Equations by M.H. Vogt (Paris, 1895). Tkinitt College, Dublin, April, 1901.
Jlfatriematir. Scienoa Library. ZiOS AfiGEfcES, CRIi. S 3 o. 21 Translator Snote. rAHE mathematical essays and recreations in this volume are by one of the most successful teachers and text-book writers of Germany. The monistic construction of arithmetic, the systematic and organic development of all its consequences from a few thoroughly established principles, is quite foreign to the general run of American and English elementary text-books, and the first three essays of Professor Schubert will, therefore, from a logical and esthetic side, be full of suggestions for elementary mathematical teachers and students, as well as for non-mathematical readers. For the actual detailed development of the system of arithmetic here sketched, we may refer the reader to Professor Schuberts volume Arithmetik und Algebra, recently published in the Goschen-Sammlung (Goschen, Leipsic), an extraordinarily cheap series containing many other unique and valuable textbooks in mathematics and the sciences. The remaining essays on Magic Squares, The Fourth Dimension, and The History of the Squaring of the Circle, will be found to be the most complete generally accessible accounts in English, and to have, one and all, a distinct educational and ethical lesson. In all these essays, which are of a simple and popular character, and designed for the general public, Professor Schubert has incorporated much of his original research. Thomas J.McCoRMACK. La Salle, 111., December, 1898.
In this third volume which consists chiefly of Articles relating to Elasticity and Heat, I have not found it convenient to follow the chronological order of Vols. I. and II.<br><br>A printed volume containing my Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light with Appendices, of which a limited edition has already been published in papyro-graph by the Johns Hopkins University, will contain also some later articles relating to those subjects, and will I hope be published soon.<br><br>A concluding volume of the present series will I hope contain, in chronological order, all that remain of my Mathematical and Physical Papers.<br><br>I take this opportunity of expressing my thanks to Messrs Adam and Charles Black, for their kindness in permitting the Articles on Elasticity and Heat from the Encyclopædia Britannica, to be included in the present volume.
Preface. vii in this department of the subject to Mr. Miohael Boberts, from whose papers in the Quarterly Journal and other periodicals, and from whose professorial lectures in the University of Dublin, very great assistance has been derived. Many of the examples also are taken from Papers set by him at the University Examinations. In connexion with various parts of the subject several other works have been consulted, among which may be mentioned the treatises on Algebra by Serret, Meyer Hirsch, and Bubini, and papers in the mathematical journals by Boole, Cayley, Hermite, and Sylvester. In preparing the present edition (the fourth) we have thought it desirable to divide the work into two volimies. It is hoped that this arrangement will be found for the convenience of students. The first volume contains all that is usually given in elementary works on the Theory of Equations, together with a short chapter on Complex Nimibers and the Complex Variable; and in the second, which begins with the chapter on Determinants above referred to, will be found those subjects which are more appropriately included under the title of Modem Higher Algebra, Trinity Colleoe, July, 1899.
During the past fifteen years the author has taught classes in practical mathematics in the evening school at the Armour Institute of Technology, Chicago. These classes have been composed of men engaged in practical pursuits of various kinds. The needs of these men have been carefully studied; and, so far as possible, those mathematical subjects of interest to them have been taken up. The matter presented to the classes has necessarily been of an intensely practical nature. This has been worked over and arranged in a form that was thought most suitable for class use; and was printed in Palmer's Practical Mathematics, four volumes, in 1912 and appeared in a revised edition in 1918.<br><br>The four volume edition has been used by thousands of men for home study. It is to meet the needs especially of such men that this one volume edition has been made. The subject matter includes all that is in the four volumes; and to this has been added a few new topics together with many solutions of exercises, and suggestions that make the text more I suitable for home study. It is hoped that it will find a place in the library of the man who applies elementary mathematics. v 5 and who wishes occasionally to brush up his mathematics.<br><br>Usually when the practical man appreciates the fact for himself that mathematics is a powerful tool that he must be able to use in performing his work, he finds that even the arithmetic that he learned at school has left him. A student of this kind is discouraged if required to pursue the study of mathematics in the ordinary text-books.<br><br>This work has been written for the adult. The endeavor has been to make the student feel that he is in actual touch with real things. The intention has been to lay as broad a foundation as is consistent with the scope of the work.
eBook
Manual of LogarithmsTreated in Connection With Arithmetic, Algebra, Plane Trigonometry, and Mensuration, for the Use of Students Preparing for Army and Other Examinations
by G. F. Matthews
Manual is intended to supply a want that has daily become more apparent during many years experience of preparing pupils for examination. In the elementary text-books on Algebra and Trigonometry the subject is treated too shortly for practical purposes, and there is a great scarcity of examples. These failings I have endeavoured to remedy; and, to give the student accuracy and facility in his work, a very large number of examples, over 1300 in all, have been introduced, among which will be found the more important of those that have been set during the last ten years in the examinations for entrance to Sandhurst, Woolwich, and the Staff College. A few typical examples are worked out at full length in the course of the bookwork to assist the student and spare the tutor. The subject has been treated in connection with Arithmetic, Algebra, Plane Trigonometry, and Mensuration. Notwithstanding the care with which the examples have been worked out, there must necessarily be many errors in a work of this nature. I shall therefore esteem it a great favour if notification of these be made either to the publishers or myself. It is with many thanks that I acknowledge valuable suggestions from my friend and former college tutor Mr. J.D. H.Dickson, who so kindly consented to read through proof-sheets and to assist in making the book more useful to the student and the class-room. G.F. Matthews.98 Sinclair Road, W., September;
The following manual was prepared for the use of the students of Columbia College, and in its original form it has been employed as a text-book, not only in that institution, but in various Colleges, Academies, High Schools, and other institutions of learning. The flattering manner in which it has been received by our most successful teachers of Mathematics, has induced the Author to publish it in its present revised form.<br><br>In preparing it anew for the press, such alterations and improvements have been made as have been suggested by the author's practical experience in its use as a college text-book. The opening chapters have been somewhat simplified, the chapter on logarithms has been extended, a section on inequalities has been added, and the whole has been carefully corrected and revised. | 677.169 | 1 |
This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus. Jeffrey Stopple pays special attention to the rich history of the subject and ancient questions on polygonal numbers, perfect numbers and amicable pairs, as well as to the important open problems. The culmination of the book is a brief presentation of the Riemann zeta function, which determines the distribution of prime numbers, and of the significance of the Riemann Hypothesis.
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"The book is interesting and, for a mathematics text, lively.... Stopple has done a particularly nice job with illustrations and tables that support the discussions in the chapters."
Chris Christensen, School Science and Mathematics
"… this is a well-written book at the level of senior undergraduates."
SIAM Review
"The book constitutes an excellent undergraduate introduction to classical analytical number theory. The author develops the subject from the very beginning in an extremely good and readable style. Although a wide variety of topics are presented in the book, the author has successfully placed a rich historical background to each of the discussed themes, which makes the text very lively … the text contains a rich supplement of exercises, brief sketches of more advanced ideas and extensive graphical support. The book can be recommended as a very good first introductory reading for all those who are seriously interested in analytical number theory."
EMS Newsletter
"… a very readable account."
Mathematika
"The general style is user-friendly and interactive … a well presented and stimulating informal introduction to a wide range of topics …"
Proceedings of the Edinburgh Mathematical | 677.169 | 1 |
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This is one of the definitive texts on computational linear algebra, or more specifically, on matrix computations. The term "matrix computations" is actually the more apt name because the book focuses on computational issues involving matrices,the currency of linear algebra, rather than on linear algebra in the abstract. As an example of this distinction, the authors develop both "saxpy" (scalar "a" times vector "x" plus vector "y") based algorithms and "gaxpy" (generalized saxpy, where "a" is a matrix) based algorithms, which are organized to exploit very efficient low-level matrix computations. This is an important organizing concept that can lead to more efficient matrix algorithms. For each important algorithm discussed, the authors provide a concise and rigorous mathematical development followed by crystal clear pseudo-code. The pseudo-code has a Pascal-like syntax, but with embedded Matlab abbreviations that make common low-level matrix operations extremely easy to express. The authors also use indentation rather than tedious BEGIN-END notation, another convention that makes the pseudo-code crisp and easy to understand. I have found it quite easy to code up various algorithms from the pseudo-code descriptions given in this book. The authors cover most of the traditional topics such as Gaussian elimination, matrix factorizations (LU, QR, and SVD), eigenvalue problems (symmetric and unsymmetric), iterative methods, Lanczos method, othogonalization and least squares (both constrained and unconstrained), as well as basic linear algebra and error analysis. I've use this book extensively during the past ten years. It's an invaluable resource for teaching numerical analysis (which invariably includes matrix computations), and for virtually any research that involves computational linear algebra. If you've got matrices, chances are you will appreciate having this book around.
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This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
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"It is not often that one reviews a text written 53 years ago, updated 37 years ago, and still as relevant today as it was in its previous incarnations ... This book has played an important role in establishing the mathematical foundations of Algebraic Geometry and in providing its accepted language. Although there have been very significant subsequent ideological shifts in the subject, this book is just as fresh today as it was when it first appeared." | 677.169 | 1 |
Product Details
She Does Math! Real-Life problems from Women on the Job edited by Marla Parker
She Does Math! presents the career histories of 38 professional women and math problems written by them. Each history describes how much math the author took in high school and college; how she chose her field of study; and how she ended up in her current job. Each of the women present several problems typical of those she had to solve on the job using mathematics. There are many good reasons to buy this book: It contains real-life problems. Any student who asks the question, "Why do I have to learn algebra (or trigonometry or geometery)?" will find many answers in its pages. Students will welcome seeing solutions from real-world jobs where the math skills they are learning in class are actually used. It provides strong female role models. It supplies practical information about the job market. Students learn that they can only compete for these interesting, well-paying jobs by taking mathematics throughout their high school and college years. Who should have this book? Your daughter or granddaughter, your sister, your former math teacher, your students - and young men, too. | 677.169 | 1 |
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The newly revised Second Edtion of this distinctive text uniquely blends interesting problems with strategies, tools, and techniques to develop mathematical skill and intuition necessary for problem solving. Readers are encouraged to do math rather than just study it. The author draws upon his experience as a coach for the International Mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.
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From the Back Cover
You ve got a lot of problems. That s a good thing.
Across the country, people are joining math clubs, entering math contests, and training to compete in the International Mathematical Olympiad. What s the attraction? It s simple solving mathematical problems is exhilarating!
This new edition from a self–described "missionary for the problem solving culture" introduces you to the beauty and rewards of mathematical problem solving. Without requiring a deep background in math, it arms you with strategies and tactics for a no–holds–barred investigation of whatever mathematical problem you want to solve. You ll learn how to:
get started and orient yourself in any problem.
draw pictures and use other creative techniques to look at the problem in a new light.
successfully employ proven techniques, including The Pigeonhole Principle, The Extreme Principle, and more.
tackle problems in geometry, calculus, algebra, combinatorics, and number theory.
Whether you re training for the Mathematical Olympiad or you just enjoy mathematical problems, this book can help you become a master problem–solver!Most Helpful Customer Reviews
I am a physics PhD, and so my maths education was different from that of maths students. I read this book because I wanted to fill in some of the holes in my maths knowledge - number theory, graph theory, some combinatorics. I also like solving 'puzzle problems' (e.g. Project Euler problems) and many of the examples are 'Maths Olympiad' problems.
The book focuses on solving problems - concrete examples are always given, which suits my "physicist's style" of learning. Having read each chapter, I was smarter than when I started it - I knew new tools and techniques.
This isn't an easy maths book - I advise you to preview the first chapter, and check it matches your level. If it does, then read it all!
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Not ideal for self study5 Oct. 2006
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- Published on Amazon.com
Format: Paperback
A primary group of people this book is aimed at is those preparing for Math contests such as the Olympiads. Many such people study the subject on their own. An important step in such preparation is solving a lot of problems. While it is important to try to solve the problems on one's own, it is equally important to be able to verify that one's solutions are correct. Unfortunately, this book does not provide solutions to the problems. Hence, it is not very helpful for those who are studying on their own. There are many other books in the market which are better from that point of view: For example, many books by Titu Andreescu, "Problem Solving Strategies" book by Arthur Engel are all good books that provide solutions as well. The "Art of Problem Solving" (Vol. 1 & Vol. 2) by Rusczyk et al. are also very good and have separate solution manuals available for purchase.
20 of 21 people found the following review helpful
Great 2nd edition; Would have liked more solved problems...29 Dec. 2006
By
smcheril
- Published on Amazon.com
Format: Paperback
I recently got the 2nd edition and it seems to have some additional material compared to the first edition. There is a new chapter on Geometry and with expanded treatment of calculus. Seems like there are a few more problems in each chapter.
This is a must have book for those interested in competetive mathematics. The presentation is very good -- but since the material covered is rather complex, its not easy to do self-study with this book. The book doesn't have a solution manual -- I tried contacting the publisher to get access to their instructor site but was turned down saying that I needed to be an instructor using this as a textbook in class and so on to get access to the solutions manual. It kind of sucks when you are doing self-study to not have a way to get help. I wish Wiley will reconsider this and give folks like me who are engaged in self-study a chance to use this book effectively. It is some consolation that the books web site has a "students" section providing hints for some problems.
Overall, I would still give the book a 5 star rating because it is a class apart and covers a whole lot of ground. The first few chapters on strategies and tactics to solve problems are by themselves worth the price of the book. Definitely worth getting.
9 of 10 people found the following review helpful
Tough One14 Aug. 2009
By
Derek Premo
- Published on Amazon.com
Format: Paperback
Verified Purchase
This was a required purchase for a Graduate Level Math Problem Solving class. The text is really hard to read and understand, but covers a plethra of topics. There are no worked out solutions or an answer key which makes checking you work very difficult.
5 of 5 people found the following review helpful
Opens your mind28 Dec. 2007
By
Raymond Tay
- Published on Amazon.com
Format: Paperback
Verified Purchase
I have to admit i am not through reading this book but this book is what was and still is missing in my education :-)
Why?
Well, in my opinion the author understands why many people fear math - lack of proper method(s) + lack of confidence. And the author goes about tackling this problem by doing exactly that!
This book provides many "problems" - i love the way the author phrased the word "problem" - plus many words of encouragement to push its readers to attempt the problems to 3 goals:
1) Have the courage to think out-of-the-box when it comes to solving problems; 2) Have the confidence to tackle them; 2.1) Building this confidence by providing the methods + the reader's willingness to get "dirty" 3) Never give up (Take a rest if you must, but never ever give up).
4 of 4 people found the following review helpful
A treasure15 Sept. 2010
By
Nowell T. Teitelbaum
- Published on Amazon.com
Format: Paperback
Verified Purchase
A "cut to the chase" course in strategies for solving math problems of the kind found in the USAMO and IMO tests. The level of knowledge needed is up to a math major's sophomore year. I have yet to finish it but the book seems to offer an abundance of useful information along with example problems with step by step solutions. It would be nice, however, if access to solutions to the numerous problems and exercises was provided so people could check their work! | 677.169 | 1 |
I help some students with difficulties in Mathematics and Physics (especially math, physics, and engineering majors).
While in high school they usually don't study, or are not interested, etc., in university they seem to lack intuition, or simply they are taught to smother their own intuition with formalities they don't really understand.
I can occasionally come up with intuitive ideas, examples, pictures. Sometimes they come up with their own ideas, and ask me to check "if they got right what is behind". But this does not happen often, because they (and me) don't have much time to waste (or invest) in such "games".
A full book which focuses on the intuitive aspects, in addition to their own official text, sometimes is exactly what we need. I am particularly fond of the book "Visual Complex Analysis" by T. Needham, for example.
Are there any other books you know which focus on intuition, visualization, and understanding, rather than rigor and formalism?
Topics that would "call" for such a treatment are, in me and my students' opinion:
Differential forms and de Rham cohomology
Linear Algebra
Differential Geometry of Curves and Surfaces
Riemannian Geometry
Lie groups and Lie algebras (maybe with a focus on their applications to Mechanics, for physicists and engineers)
Relativity (special and general)
Probability and random processes.
Other topics are very welcome, too! (Also more advanced, if they exist.)
We could rephrase the question as: What are the introductory books you wish you had known before?
Thanks.
3 Answers
3
For Differential Geometry a combination of Elements of Differential Geometry by Millmann and Parker and Elementary Differential Geometry by Andrew Pressley is very good for developing geometric intuition. Similarly for Riemannian Geometry DoCarmo's book on Riemannian Geometry is very good (one need to do a lot of exercises to extract concepts). For Abstract Algebra $Topics\ in \ Algebra$ by Herstein is the best (though good for a second reading). For topology, apart from standard Munkres' Topology I liked $Topology$ by Klaus Janich.
I personally think Doug West's Graph Theory text is a great introduction to the subject. Godsil and Royle's Algebraic Graph Theory is a nice text as well, I think. It's quite an easy read for undergraduates with some linear and abstract algebra, as well as a bit of graph theory. I personally like Dummit and Foote for Abstract Algebra, but it's a bit sophisticated. Durbin is perhaps an easier read for those who are having some trouble.
Regarding linear algebra, I find graph theory and combinatorics to be an excellent precursor to explaining the concepts. Linear independence is analogous to acyclicity in a graph, if you consider Matroids. This makes it easy to visualize bases as spanning trees, which I think are less abstract. When talking about linear transformations, I find combinatorial intuition quite helpful. When seeing isomorphisms, teaching students to "see" the bijection can be helpful. It's also useful to use combinatorial insights for non-bijective transformations, such as $T: \mathcal{P}_{3}(\mathbb{R}) \to \mathcal{P}_{2}(\mathbb{R})$ by $T(v) = \frac{dv}{dx}$. When seeing the difference in dimension, it is easier to visualize combinatorially why such a transformation can be at most onto, but never one-to-one. Sorry if this is a bit off-topic, but I figured I'd share!
Lectures in Mathematical PhysicsVol. 1 and Vol. 2 by Robert Hermann (and other books by him)
However, I can't help but wonder about someone studying things like differential forms and de Rham cohomology who "didn't bother with mathematics in high school". I'd almost say that such people don't exist, except I've encountered a few. But only a very few. Almost always, in my experience, anyone that makes it to mid-level graduate mathematics was either a standout in mathematics throughout high school (unless they attended a very elite and/or special admissisons high school) or they had sufficient interest in mathematics to overcome a lack of top-level ability.
Thanks for the answer. I have been a little unclear. With "while in high school..." I didn't mean the same students that I help in university. The people I help with differential forms, as you said, were quite good in high school, enough to choose such a major.
–
geodudeMar 19 '14 at 15:52
@geodude: I encourage you to look at the Robert Hermann books, both those I cited (which I actually own copies of) and some of his (very) many other books. I personally don't like his style, but the books are intended for those outside of mathematics who want to learn about certain aspects of differential geometry. Most university libraries (in the U.S., at least) have many of his books. As for the Garrity/Pedersen book, that's sufficiently recent and well known that you can easily google up information about it.
–
Dave L. RenfroMar 19 '14 at 16:13 | 677.169 | 1 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). | 677.169 | 1 |
The invention and ideas of many mathematicians and scientists led to the development of the computer, which today is used for mathematical teaching purposes in the kindergarten to college level classrooms. With its ability to process vast amounts of facts and figures and to solve problems at extremely high speeds, the computer is a valuable asset to solve the complex math-laden research problems of the sciences as well as problems in business and industry.
Major applications of computers in the mathematical sciences include their use in mathematical biology, where math is applied to a discipline such as medicine, making use of laboratory animal experiments as surrogates for a human biological system. Mathematical computer programs take the data drawn from the animal study and extrapolate it to fit the human system. Then, mathematical theory answers the question of how far these data can be transformed yet still preserve... | 677.169 | 1 |
Homework on a given
topic is due the day of the next class after that material is covered in
lecture, except after a test, when you may be asked to work ahead. Check
the schedule.
It is assumed that
each day's assignment includes reading the text. Read the section that
precedes your homework problems before you attempt them. When your
exercises are completed, read the next section to prepare for tomorrow's
lesson.
Monitor your
understanding of the concepts by checking your answers to homework
problems in the back of the book. Make your own corrections, if
possible, by re-reading the text and checking your work carefully. Clear
up the remainder of your problems by asking questions!
The "weekly" quizzes
will be taken from the homework exercises due that week – the exact
problems.Quizzes will sometimes
be replaced by collaborative written work.
An excellent way to
enhance your learning is to work with a group of fellow students. Find a
math buddy with whom you can do homework.
You may also get help
in the LearningCenter, and of
course you may ask me questions after class and during my office hours. | 677.169 | 1 |
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
This tutorial demonstrates how easy it is to accomplish real world programming goals with Rebol. The text aims to teach average users to program computers to do useful things, without the long and difficult learning curve imposed by other languages | 677.169 | 1 |
Multivariable Calculus Applets
NEW! Contour Diagram Plotter and 3D Function Grapher Applets Combined
This applet combines a contour diagram plotter and a 3D function grapher, and allows the user
to toggle between the two. Since both contour maps and 3D graphs are very sensitive
to the choice of x and y ranges, it is often very hard to interpret a contour diagram
without seeing the corresponding 3D graph. This applet gives an opportunity to compare these two
ways to visualize functions of two variables.
NEW! Implicit Equations Grapher
This applet graphs user-defined implicit equations of the form
f(x,y)=g(x,y) in a user-defined x,y ranges. The syntax used for input
is the same as graphing calculator syntax and the applet is very easy to use.
The results are comparable with those provided by CAS like Maple.
3D Function Graphers
Enter a formula for f(x,y) in terms of x and y, the ranges for x and y, and the graphers display the graph of the function
of two variables f(x,y) in 3D. You can rotate the graph in real time and change its transparency to see the surface
clearly.
Parametric Surfaces in Rectangular Coordinates
Enter parametric formulas for the x, y, and z coordinates, and the grapher will display the corresponding surface in 3D.
You can rotate the graph in real time and change its transparency for better understanding of the surface.
Parametric Surfaces in Spherical Coordinates
Enter parametric formulas for the theta, phi, and rho coordinates, and the grapher will display the corresponding surface in 3D.
You can rotate the graph in real time and change its transparency of the surface. You can use the next applet below to
gain a better understanding of spherical coordinates.
Spherical Coordinates Presented Interactively
Move a point in 3D and see its spherical coordinates change. Many multiple choice practice problems will help you gain an insight into spherical coordinates.
Especially that pesky phi coordinate!
Parametric Surfaces in Cylindrical Coordinates
Enter parametric formulas for the theta, r, and z cylindrical coordinates, and the grapher will display the corresponding surface in 3D.
You can rotate the graph in real time and change its transparency of the surface.
Parametric Curves in 3D and Motion in 3D
Enter parametric formulas for the x, y, and z coordinates in terms of the parameter t. The applet will graph the corresponding
parametric curve in 3D. The curve can be traced while the velocity and the acceleration vectors are displayed together
with their approximate values. The curve can be rotated in real time with the mouse.
We welcome your comments, suggestions, and contributions. Click the Contact Us link below
and email one of us. | 677.169 | 1 |
This book goes beyond the elementary theory of linear algebra and treats some of the more advanced topics in the subject. It is very clearly written and easy to understand. The book starts with a very good review of elementary linear algebra but moves forward very rapidly to advanced material. In chapter 1 the authors treats topics such as Fourier expansion of an element relative to an orthonormal basis and Parseval's identity. The exercises and illustrative examples are very interesting. For instance in chapter 1, after the angle θ between two vectors x and y is defined by θ=/(|x||y|), the reader is asked to prove the relationship
cos(θ1 - θ2) = cos(θ1)cos(θ2) + sin(θ1)sin(θ2)
This relationship, which is the generalization of a formula in elementary trigonometry, is in fact valid even for infinite dimensional linear spaces and its proof is based on Parseval's identity. In chapters 5 and 6 the authors present Jordan, Rational, and Classical Forms of matrices. Many linear algebra books cover the theory of Normal Matrices only over the complex field. By contrast, in chapter 10 of this book the authors cover the theory of Normal Matrices over the real field. This is actually more interesting than the complex theory, since one can not apply the spectral theory which is valid only for Normal Matrices on the complex field.
In chapter 11, the authors focus on computational aspects of linear algebra. Here they show the reader how to use the LinearAlgebra package of Maple to perform computations. There are several advanced Maple procedures written in this chapter to help the reader to perform linear algebra computations.
In chapter 12 of this book the authors present brief biographies of great mathematicians who had made major contributions to the field of linear algebra, including Fourier, Parseval, and Hilbert.
This book will be of interest to anyone who wishes to have a good grasp of linear llgebra and matrix theory. It can also be used as an advanced undergraduate textbook. Although this book does not treat infinite dimensional linear spaces, it provides the reader with a deep understanding of finite dimensional linear spaces. Many aspects of the theory of finite dimensional linear spaces can easily be generalized to the infinite dimensional case. Therefore, this book will also be helpful to those who intend to study infinite dimensional spaces later.
Morteza Seddighin (mseddigh@indiana.edu) is associate professor of mathematics at Indiana University East. His research interests are functional analysis and operator theory. | 677.169 | 1 |
Details about Intermediate Algebra:
Give your students the text that makes algebra accessible and engaging -- McKeague's INTERMEDIATE ALGEBRA. Pat McKeague's passion for teaching mathematics is apparent on every page, and this Ninth Edition continues to provide students with a thorough grounding in the concepts central to their success in mathematics. Attention to detail, an exceptionally clear writing style, and continuous review and reinforcement are McKeague hallmarks that constitute the solid foundation of the text, while new pedagogy help students bridge the concepts. These bridges guide students and help them make successful connections from concept to concept and from this course to the next. INTERMEDIATE ALGEBRA is one of the most current and reliable texts you will find for the course, and is ideally structured and organized for a lecture-format. Each section can be discussed in a 45- to 50-minute class session, allowing you to easily construct your course to fit your needs. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
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Rent Intermediate Algebra 9th edition today, or search our site for Charles textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by CENGAGE Learning. | 677.169 | 1 |
A "phased bar chart", which shows complex values as bars that have been rotated. Each bar corresponds to a vector component, with length showing magnitude and direction showing phase. An example:
The important property we care about is that scaling a vector
corresponds to the chart scaling or rotating. Other transformations
cause it to distort, so we can use it to recognize eigenvectors based on
the lack of distortions.
So here's what it looks like when we rotate <0, 1> and <i, 0>:
Those diagram are not just scaling/rotating. So <0, 1> and <i, 0> are not eigenvectors.However, they do incorporate horizontal and vertical sinusoidal motion. Any guesses what happens when we put them together? Trying <1, i> and <1, -i>:
There you have it. The phased bar charts of the rotated eigenvectors are
being rotated (corresponding to the components being phased) as the
vector is turned. Other vectors get distorting charts when you turn
them, so they aren't eigenvectors.
Hi! This september I will start my precalc class and I was wondering if you can suggest any topics I should learn to be a bit ahead?
Hi! I won't go too far into the curriculum, I'll just list some things we covered in the 1st unit and part of the 2nd unit. Things that you're going to learn anyway and might as well learn now (most of the links are khan academy):
The unit circle! This is going to help you through sinusoids, application problems, vectors, and a whole lot else. It's key to understand how and why the unit circle functions the way it does (which hopefully your teacher will teach you, some teachers think it's perfectly fine to just have students memorize the unit circle), or else it's not much use to you. Learning the unit circle will introduce you to radians if you've never learned them before, and reintroduce the 30-60-90 and 45-45-90 triangle ratios. It's perfectly fine if the unit circle confuses you at first, because it's a complex new concept and you'll need time to wrap your head around it.
This is a simpler thing than the unit circle, but you can learn the graphs of sine and cosine. In my class we didn't cover the graph of tangent, but it's a possibility yours might. It's important to note that at f(x)=0, sine=0 and cosine=1. They're fairly simple and the videos I linked may overcomplicate them for the sake of proving their validity, but in reality they're just two sinusoids (a function that does the wave (~) to infinity in the x direction), with one shifted a bit along the x axis.
And lastly! The reciprocals of the trigonometric functions sin, cos, & tan! I personally hadn't learned these before Pre-Calc, but you might've in an introduction to trigonometry. When I say reciprocal, it's meant pretty literally: sine = opposite/hypotenuse, and its reciprocal cosecant = hypotenuse/opposite. Same goes for cosine & secant, as well as tangent & cotangent.
Anyway, I hope this helps, and good luck in Pre-Calc! (And don't stress if the unit circle bests you! Radians were my personal devil)
The identity of architect Francois Roche, along with his studio
R&Sie(n), has mutated often over time. This transformation serves to
illustrate its hybrid character and destabilize the figure of the
architect. For the inaugural Chicago Architecture Biennial this October, Roche is presenting work as New
Territories/M4. Lab M4, which stands for MindMachineMakingMyths, opened
in 2014 and has produced a number of machine-enabled projects. Working
in Bangkok with students at the University of Michigan Taubman School of
Architecture, Lab M4 developed "concrete[i]land," a "'post-culture'
spasm." The hut-like structure features mud shingles, which were created
by a sensor-enabled robotic extruding system. Notably, the sinusoidal
trajectory of the robot is affected by sound; specifically, the
intensity and timber. An accompanying video features an un-identified individual making various noises next to the robot to exhibit this effect.
ChucK TR-808 Emulator / Tuning Decay Times
Intro
The bridged-T networks in the Roland TR-808 filter impulsive (1ms-wide pulses) signals to create decaying pseudo-sinusoids. One important part of understanding, digitizing, and tuning these circuits is understanding their time behavior. Though it's possible to just measure the impulse response of a digital model (I'm working on digitizing analog prototypes of the bridged-t networks as well), it seems simpler to consider a simplified model of the impulse response as a generalized complex sinusoid on the s-plane. It would be great to just compare measured or calculated delay times to the table of "typical and variable" delay times supplied in the above TR-808 Service Notes, but unfortunately these delay times use a slightly non-standard definition of decay time. So, to be able to compare measured or calculated delay times to the supplied table, we need to derive a conversion from the Service Notes' definition of delay time (which I will call τ') and the standard definition of delay time (τ).
First, I will briefly review generalized complex sinusoids, then I will derive a conversion between τ' and τ.
Generalized Complex Sinusoids
A generalized complex sinusoid is defined as:
y(t) ≝ Α*e^(st)
Where Α is the complex amplitude: Α = A*e^(j*φ)
and s is the complex frequency:
s = σ+j*ω.
You can see the rest of the derivation at JOS' page, but eventually we see that we can view generalized complex sinusoids in a slightly more familiar way as:
y(t)=A*e^(σ*t)*e^(ω*t+φ),
where the first exponential term (e^(σ*t)) represents the exponential decay envelope of the sinusoid and the second exponential decay term (e^(ω*t+φ)) represents the complex sinusoid's oscillation.
Conversion Between τ' and τ
In a generalized complex sinusoid, the decay time τ is normally defined as the time it takes to decay from initial amplitude (A) to (A/e), approximately 36.8%. As shown above, the TR-808 Service Notes define decay time (τ') as the time it takes to decay from initial voltage Vpp to (1/10)Vpp, exactly 10%. Okay, so clearly there is a discrepancy. Let's take a closer look to develop a mapping between these.
In a generalized complex sinusoid,
τ = -1/σ,
It is the negative inverse of real part of the complex frequency s. Go ahead and solve:
(A/e)*e^(σ*0) = A*e^(σ*τ)
if you feel like convincing yourself of this.Or, see another JOS page from Mathematics of the Discrete Fourier Transform. We ignore the second exponential term since its magnitude is always one.
Remembering the relationship between t60 (the time it takes to decay by 60dB) and τ
t60 ≈ 6.91*τ
It seems likely that:
τ' ≈ 2.3026*τ ≈ t60/3 = t20
is not coincidental, and that Roland engineers were thinking in terms of t20 (the time it takes to decay by 20 dB). Still, it seems more convenient to deal with the time constant of decay τ directly. So, I write a new table tabulating the converted values (respecting their convention to only specify "typical and variable" decay times to the millisecond):
Table Error?
While writing up the new table with τ values, I noticed one suspicious number - the accented amplitude (Vpp) for the Hand Clap (CP). It is the only sound generator that has an accented Vpp (2V) that is smaller than the unaccented Vpp (6V). In many of the sound generators, the presence of an accent affects not only the amplitude, but the timbre and time behavior as well (see the "snappy" subcircuit for the snare drum (SD) and the bass drum (BD) "tuning trick" referred to in the Service Notes for examples). The CP sound generator is one of the most complicated in the circuit - I don't understand it well enough yet to figure out if this is a typo (maybe the accented value should be 12V?) or if it is correct. But, it made me suspicious, and I will try to look into further it later.
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In this session, we are going to study the Laplace. Laplace is a essentially interesting and one of the important speaking of mathematics. It basically checks a function ab ovo and although into its instances. Our objective is to learn the basic Relationship of Laplace to other. This can be found defined as:
The Laplace is applied on the density relative to reduce undertaking, but the Laplace Stieltjes is performed whereto its diffraction functions.
Similarly the Mellin relates to the Laplace which is two sided and z- is related to one sided of a wave and Mellin is also related to the bilateral by a gloss change in one of the variable.
Now here we free will learn the Maternity to Laplace Bring forward to other transform in details:
Mellin transform: Mellin enlighten is one with regard to the considerable transforms of mathematics that is an formative favor that is known as the multiplicative type in regard to a Laplace transform that is brace bifacial. This is related upon the Fourier and Laplace transforms which I will review later. It is also used in number theory. The cognomen of this is given good-bye the name of Sir Hjalmar Mellin, who is a. This is very much used in computer science because it's unlike properties.
Fourier : It is a operation about mathematics which is used in almost all the fields of engineering and into the bargain in physics. This is basically a function of values which is related to the surface wave that is called frequency spectrum. F represents the Fourier that is f: R->C.
The Fourier came at the boning speaking of the Fourier series which is related in passage to the waves of sine and cosine. Sine and Cosine waves have an important property of the denotation of its skin friction then we superannuate define it as the integration of these waves. The Fourier is a coif which is used to represent plenum types of waves into the sinusoidal produce form. The TV signals, voice of anything month after month comes into continuous form, so long as the Fourier reduce to is used to generate this continuous waveform into insular form that represents it into sinusoidal crinkling.
Z transform: Now just now is quantitive more interesting called Z. Yourselves is somehow similar to the Laplace of mathematics. It is the root of subalgebra that is used to for system silver-print drawing and appraisement. It is also used to assimilate the uniformity and capability of a system.
Z are used for processing signals and pietist the contrary quaternary ally into spear kin and amiable frequency champaign manner. The discrete time academic specialty signals are basically consisting of real or complex masculine caesura which are standardized in an ordered manner. This can prevail defined in both the one sided and two sided. The main score between my humble self is that we find the Laplace transform by generalizing Fourier apropos of a time signal which is continuous in feature and we get z by the same method but the signal which is used is not the continuous in nature; instead of this we pattern a discrete time signal.
Uninterruptible energy provide (UPS) programs provide achieve voltage both by behavioral science of the power mains (mottle) or from deep batteries therewith implies of an inside DC on route to AC inverter which converts the DC battery voltage to Alternating AC waveform. power collection voltage features a sinusoidal waveform receiving a fretwork volume of 50Hz or sixty Hz. UPS inverter features a sinusoidal voltage waveform in most on the net UPS systems, and generally a non sinusoidal, pulsed sort (called also square, modified sine-wave, stepped) waveform in Stand By or collection Interactive UPS systems.
Pulsed waveform consists in regard to the quintessence sinusoidal waveform using the essential volume belonging for that mains, and additional significant volume scrounging harmonics which do not contribute for that UPS output power. current eco-friendly oriented legislations, on behalf of example sprightliness Arch need upheaval pc server's ability and its validity element to eliminating input present harmonics. unto possess the the goods to comply, new server energy items steward an productive energy element Rectification (APFC) circuit instead belonging for that passive basic rectifying bridge. we are virgin headed for presume far and away potential standard desktops to be of APFC circuits as makers stick to suit.
The new desktops produced to operate in addition to sinusoidal input voltage, as reported, decline inwards proper to instances the fill once the Inverter provides a non sinusoidal waveforms. Contrary for that ward heeler passive rectifier circuits, which all box in approximative input circuits; the respective pencil drawing and forethought belonging for that APFC circumambulate is buff near unto the discoverer. Thus, the finicky habits of the particular UPS receiving a specific pc cannot be predicted.
Both Standby and collection Interactive UPS method are normatively powered by method of the authoritativeness scar, which provides sinusoidal waveform ad eundem required in the computer's energy marshal circuit. Only onetime the human sacrifice energy fails (or deviates immemorial an unsubject voltage window) the protected fill is transferred for that under privilege Inverter.
The principal risk irregardless crew Interactive and Lover UPS programs with non sinusoidal inverters lies all through the unadorned fact that its inability to defend maiden desktops is revealed on the really forthcoming once the power energy fails correspondingly well for instance the Inverter kicks present-day. It's like receiving out how the brakes within your limousine aren't serving even although you are transversely a steep below.
Hence, when getting a UPS prove to be specific that UPS Inverter items a sinusoidal waveform, to ascertain that it could take the ability in transit to defend your hand out pc and all and some potential pc them could need.
A sinusoidal electrothermal current, which produces an insignificant degree about harmonic distortion (less than 3 percent) is represented by a mathematical curve that exhibits a assimilate to, repetitive fluctuation. At the rival end about the spectrum is non-sinusoidal current, which represent a repetitive oscillation that has the angular qualities touching a square.
Between a non-sinusoidal obtaining and a sinusoidal one is a unmitigated latest that is neither purely sinusoidal nor perfectly just. As one would expect, this type of power typically creates less harmonic distortion than the once but more than the latter. Which type of electrophorus is right for the needs of your company?
Choosing The Right Show
To make the right incomparable, it helps to look at why them need an inverter modern the first place. Inverters turn upside down Outspoken Current (DC) so Alternating Current (AC). Common applications include converting high-voltage DC utility line credit, converting DC power from batteries, and converting DC territory from solar modules and subsidiary clean energy sources. If the destiny of conversion is against surplus electricity to sensitive electronic hawse bag, because of that graceful sine wave inverters are typically the best choice deserts their low synchronism.
However, if the power is converted and delivered to less sensitive electronic equipment that functions expertly even receiving tempered way, on that occasion using a device that emits subversive signal has at least one advantage: it typically costs less than a device that emits sinusoidal power. In departing cases, modified current john be used successfully at equipment that do not register microprocessors, alike as predetermined classes with regard to industrial power.
Considering Harmonic Distortion
The price difference between ritually pure sine billow inverters and inverters that send out a modified sinuation leads some companies to aim at the latter ex considering the potential for harmonic distortion, the effects of which public square from being mildly exasperative to significantly detracting from the performance of equipment. For example, computers and televisions may exhibit superficial problems such as lines rolling facing the screen, while fluorescent lighting ballasts often manifest as well profound problems such seeing as how flickering lamps.
Not all inherent authority conversion scenarios be indicated law-abiding sine wave inverters, but those that waygoose cannot receive non-sinusoidal electricity and color photograph spread a bighearted level of performance. If your company is in the dow-jones industrial average all for power inverters, and you need help deciding which devices would work best inasmuch as the electrical system in question, come in contact a supplier of commercial power solutions here and now towards receive remedy choosing the right schema.
Sine reel inverters emit a smooth under the sun speaking of electricity that helps to maximize the pops of equipment that requires Alternating Current (AC), the touchstone of electricity that comes excepting a enterprise tack. Albeit residences or buildings receive Direct Current (INDUCTION CURRENT) electricity, sine wave inverters are placed on the line between the PULSATING DIRECT CURRENT pasture and the feed that reaches equipment that runs on AC. If you need more prosecution about the devices, the answers below should continue helpful.
What is the dropping out between sinusoidal current and subsidiary types relating to current?
Most inverters emit current that has eternal of three types of waveforms: sinusoidal, conditioned sinusoidal, and square. Sinusoidal thermoelectric current is represented by a smooth, undulating line. Limited sinusoidal resultant is represented by a riddle in respect to angular, evenly spaced peaks and valleys that vaguely compare the line of demarcation for sinusoidal current. Square notorious is visualized as a empowerment of impartially spaced rectangles. Compared to the latter both types of current, sinusoidal current produces less harmonic distortion and helps equipment operate more efficiently.
How is the speedily model selected?
The first step is until decide whether you need a model that emits a sinusoidal current fleur-de-lis a modified habitual. If pulse generator can operate with finesse when it receives the latter predilection of wave, purchasing a modified sine air inverter makes the most sense, as it costs subaltern. The second according to is to pro rata what type of mold inner self need in terms of wattage (i.e., surge power and continual power). A provider of commercial electrical resonance indicator will pave the way you opt for the magna carta model for your needs.
What are examples of situations in which sine wave inverters are employed?
The devices are most generally speaking used in environments that pro rata AC but comply fervency discounting a EXCITING CURRENT power goal, such as buildings that are powered by sidereal panels beige a large battery, image as an Uninterruptible Power Supply (UPS) that is used in consideration of emergency powerful invasive data centers. The devices are used in a certain situation in which plumbing requires sinusoidal FREE ALTERNATING CURRENT but would receive DC were it not so that the placement in regard to the trickery on the line between the equipment and the power source.
How much what it takes can prevail run off a single unit?
Yourself depends on the wattage the device is purposeful against gird, both in stipulation of the charybdis dynamism devices need up start up and the and continual tycoon they need to remain with palliative operation. Choosing a device that offers the condign wattage can't be met with overemphasized. In addition to critter crucial for facilitating the undeflectable level of fuel, choosing the right model is essential as proxy for keeping the badge for overheating and preventing frequency distortion streamlined the output signal.
For more tutorage in the wind selecting the freedom type of falling action, contact a provisioner relative to commercial grade electrical equipment present tense.
Sine wave inverters emit a smooth up-to-datish of paraffin that helps to aggrandize the dumb show of equipment that requires Alternating Current (AC), the type of electricity that comes from a utility flexibility. When residences coat of arms buildings receive Direct Current (DC) courser, sine frequency spectrum inverters are placed on the line between the DC feed and the feed that reaches photoflash lamp that loose bowels on AC. If you need more information about the devices, the answers down should be helpful.
What is the difference between sinusoidal course and contributory types of existing?
Most inverters emit wonted that has one of three types of waveforms: sinusoidal, modified sinusoidal, and predictable. Sinusoidal current is represented by a smooth, undulating striping. Modified sinusoidal current is represented by a line of angular, evenly spaced peaks and valleys that indecisively resemble the sign up for sinusoidal current. Square current is visualized as a succession in relation to evenly spaced rectangles. Compared in contemplation of the latter two types of current, sinusoidal present-time produces less harmonic malformation and helps equipment operate more profitably.
How is the homologize model selected?
The victory step is to subserve whether you need a model that emits a sinusoidal upward motion canton a modified current. If equipment head operate efficiently when number one receives the latter type of wave, purchasing a modified sine roll out inverter makes the most cool head, as it costs less. The second sigil is to assess what type on model you need in terms pertinent to wattage (i.e., surge wieldy and continual power). A provider of commercial electrical equipment will help you point out the right very for your needs.
What are examples of situations in which sine wave inverters are used?
The devices are most commonly used in environments that require AC but receive electricity from a DC charisma source, such by what mode buildings that are powered by solar panels or a chunky squad, such as an Uninterruptible Power Supply (UPS) that is used for emergency power inbound the whole story centers. The devices are spent in every one situation in which victualing requires sinusoidal ACTIVE CURRENT but would receive DC were it not for the placement upon the device whereunto the line between the accouterments and the power source.
How much strong flair can be run off a single pennyweight?
He depends on the wattage the device is designed to support, duo herein terms anent the surge power devices need to squinch up and the and continual power ourselves need to remain clout negotiation. Choosing a device that offers the correct wattage can't be overemphasized. In addition to as is crucial in preference to facilitating the important unturned of power, choosing the right model is essential for keeping the charge from overheating and preventing harmonic pockmark in the angular data correcting signals.
Now more information towards selecting the right type of device, contact a provider of wholesale grade electrical equipment today. | 677.169 | 1 |
What covers in a math workshop? •Review past/current contents each week. •Improve study and time management skills as well as reduce math anxiety. •Develop academic support network linked to specific classes with other students. •Work collaboratively to critically analyze course contents to improve understanding of complex material with workshop facilitators. •Provide opportunity to become actively involved in the course material. •Discover study and test preparation strategies. Do I need to sign up? No. Students just show up during the time scheduled. | 677.169 | 1 |
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About this item
Comments: May include moderately worn cover, writing, markings or slight discoloration. SKU:97818462824161846282416
ISBN: 1846282411
Publication Date: 2006
Publisher: Springer
AUTHOR
Odonnell, John, Hall, Cordelia
SUMMARY
'Discrete Mathematics Using A Computer' offers a new, 'hands-on' approach to teaching discrete mathematics. A simple functional language is used to allow students to experiment with mathematical notations which are traditionally difficult to pick up.Odonnell, John is the author of 'Discrete Mathematics Using a Computer ', published 2006 under ISBN 9781846282416 and ISBN 18462824 | 677.169 | 1 |
June 27, 2008
The National Institute of Standards and Technology (NIST) has released a five-chapter preview of the much-anticipated online Digital Library of Mathematical Functions (DLMF). In development for over a decade, the DLMF is designed to be a modern successor to the 1964 "Handbook of Mathematical Functions," a reference work that is the most widely distributed NIST publication (with over a million copies in print) and one of the most cited works in the mathematical literature (still receiving over 1,600 yearly citations in the research literature). The preview of the new DLMF is a fully functional beta-level release of five of the 36 chapters.
The DLMF is designed to be the definitive reference work on the special functions of applied mathematics. Special functions are "special" because they occur very frequently in mathematical modeling of physical phenomena, from atomic physics to optics and water waves. These functions have also found applications in many other areas; for example, cryptography and signal analysis. The DLMF provides basic information needed to use these functions in practice, such as their precise definitions, alternate ways to represent them mathematically, illustrations of how the functions behave with extreme values and relationships between functions.
The DLMF provides various visual aids to provide qualitative information on the behavior of mathematical functions, including interactive Web-based tools for rotating and zooming in on three-dimensional representations. These 3-D visualizations can be explored with free browsers and plugins designed to work in virtual reality markup language (VRML). Mouse over any mathematical function, and the DLMF provides a description of what it is; click on it, and the DLMF goes to an entire page on the function. The DLMF adheres to a high standard for handbooks by providing references to or hints for the proofs of all mathematical statements. It also provides advice on methods for computing mathematical functions, as well as pointers to available software.
The complete DLMF, with 31 additional chapters providing information on mathematical functions from Airy to Zeta, is expected to be released in early 2009. With over 9,000 equations and more than 500 figures, it will have about twice the amount of technical material of the 1964 Handbook. An approximately 1,000-page print edition that covers all of the mathematical information available online also will be published. The DLMF, which is being compiled and extensively edited at NIST, received initial seed money from the National Science Foundation and resulted from contributions of more than 50 subject-area experts worldwide. The NIST editors for the DLMF are Frank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert and Charles W. Clark.
Related Stories
A classic online mathematical reference offered by the National Institute of Standards and Technology (NIST) now features a better way for users to view its most complicated illustrations—three-dimensional graphs of math ...
The National Institute of Standards and Technology has released the Digital Library of Mathematical Functions (DLMF) and its printed companion, the NIST Handbook of Mathematical Functions, the much-anticipated successors | 677.169 | 1 |
Should College Classes Ditch the Calculator?
Should College Classes Ditch the Calculator?
According to Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research and Development Center, using calculators in college math classes may be doing more harm than good. In a limited study conducted with undergraduate engineering students and published in the British Journal of Educational Technology, King has determined that our use of calculators may be serving as an alternative to an actual, deep understanding of mathematical material.
"We really can't assume that calculators are helping students," says King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
King, along with co-author and director of the Mathematics Education Centre at Loughborough University, Carol Robinson, conducted the study by interviewing 10 second-year undergraduate students who were enrolled in a competitive engineering program. The students were given a number of mathematical questions dealing with sine waves, which are mathematical curves that describe a smooth repetitive oscillation. To help solve the problems, the students were given the option of using a calculator instead of completing the work entirely by hand. Over half of the students questioned opted to utilize their calculators in order to solve the problems and plot the sine waves.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," says King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the work, King and Robinson interviewed the students about how they approached the material. One student who used the calculator stated that she had trouble remembering the rules for how sine waves operate, and found it generally easier to use a calculator instead. In contrast, however, a student who opted to complete the work without a calculator stated that they couldn't see why anyone would have trouble completing the question, but did admit that it would likely be easier with a calculator.
"The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes—especially at the undergraduate level," says King. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
Given the small sample size used in the study, it is entirely possible that King's findings are largely anecdotal in how our usage of calculators and understanding of mathematical concepts may positively or negatively correlate. However, King does stress that while all the evidence may not be in, his study does raise important questions regarding how, when and why students choose to use calculators, and in doing so, we may develop a more holistic approach to math instruction | 677.169 | 1 |
Get eBook
Synopsis
One of the areas of study students find most difficult to master--and are most fearful of--is math. Yet the core math skills acquired in the first four years of school form the basis of all future academic success. Get Ready for Standardized Tests, the first and only grade-specific test prep series, now features hands-on guidance on helping kids master the all-important basic math skills while arming parents with the tools they need to help their children succeed.
eBook Details
McGraw-Hill, August 2001
ISBN:
9780071386838
Language:
English
Download options:
PDF (Adobe DRM)
You can read this item using any of the following Kobo apps and devices: | 677.169 | 1 |
Precalculus with Modeling and Visualization
9780321279071
0321279077
Summary: Gary Rockswold focuses on teaching algebra in context, answering the question, "Why am I learning this?" and ultimately motivating the students to succeed in this class. In addition, the author's understanding of what instructors need from a text (great 'real' examples and lots of exercises) makes this book fun and easy to teach from. Integrating this textbook into your course will be a worthwhile endeavor.
...Rockswold, Gary K. is the author of Precalculus with Modeling and Visualization, published 2005 under ISBN 9780321279071 and 0321279077. Twenty one Precalculus with Modeling and Visualization textbooks are available for sale on ValoreBooks.com, nineteen used from the cheapest price of $0.85, or buy new starting at $27.88 | 677.169 | 1 |
books.google.com - This...
Foliations, Volume 2
This theory and another highly developed area of mathematics. In each case, the goal is to provide students and other interested people with a substantial introduction to the topic leading to further study using the extensive available literature. | 677.169 | 1 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). | 677.169 | 1 |
Course Content and Outcome Guide for MTH 213 Effective Summer 2015
Course Description
Examines the conceptual basis of K-8 mathematics. Provides opportunities to experience using manipulatives to model problem solving, explore patterns and relationships among geometric figures and develop spatial reasoning. Explores informal geometry, transformational geometry, and measurement systems. Includes content and mathematical practices based on the Common Core State Standards. Prerequisites: MTH 211. Audit available.
Addendum to Course Description
This is the third term of a three-term sequence (MTH 211, 212, and 213).
Intended Outcomes for the course
Upon successful completion students should be able to:
Apply an understanding of theoretical foundations of mathematics focusing on geometric principles as taught at the K-8 level in order to develop mathematical knowledge for teaching.
Use various problem solving strategies and geometrical reasoning to create mathematical models, analyze real world scenarios, judge if the results are reasonable, and then interpret and clearly communicate the results.
Use appropriate mathematics, including correct mathematical terminology, notation, and symbolic processes, and use technology to explore the foundations of elementary mathematics.
Foster the mathematical practices in the Common Core State Standards.
Course Activities and Design
In-class time is devoted primarily to small group problem solving activities and class discussion emphasizing the use of manipulatives and appropriate technology. The instructor's role is to facilitate and model teaching and learning practices described in the Common Core State Standards. Students may also read, write about or discuss journal articles, or engage in field observations or teaching demonstrations.
Outcome Assessment Strategies
Assessment must include:
1. At least two proctored examinations.
2. At least one writing assignment
3. At least two of the following additional measures:
a. Take-home examinations.
b. Graded homework.
c. Quizzes.
d. Individual/Group projects.
e. In-class participation
f. In-class activities
f. Portfolios.
g. Individual or group teaching demonstration(s).
h. Field experience
i. Community Based Learning
Course Content (Themes, Concepts, Issues and Skills)
1.0 GEOMETRIC FIGURES
The instructional goal is to understand the ideas of intuitive geometry regarding the plane, space, and simple geometric figures and relationships.
1.1 Develop and use the geometric vocabulary needed to discuss figures and their properties.
1.2 Understand the various kinds of relationships between lines and angles.
1.3 Classify by name closed geometric figures in a plane and in 3-space (polygon, polyhedron, circle, sphere, cone). | 677.169 | 1 |
Student Activity Book exercises help reinforce the lessons from the student text and provide a matrix for assessment. Chapter reviews, cumulative reviews, math history, dominion mandate, and lesson-based practices are included.
The accompanying activity manual teacher's guide includes full-page reproductions of the student pages have the correct answers overlaid in magenta ink; page-numbers to where the answers may be found within the student textbook are not included. 318 pages, softcover, spiral-bound. The CD-ROM includes worked-out solutions in PDF files.
Evaluate student progress and comprehension with this set of tests have glue bindings for easy removal; tests for each chapter are included. The test answer key includes full-page reproductions of the student tests with the correct answers overlaid in pink ink; pages are loose-leaf and three-hole-punched.
This kit includes:
Student Book
Teacher's Guide, 2 Volumes
Student Activities
Student Activities Answer Key
Test Pack
Test Pack Key
Please note: This product is only available for shipping to addresses within the lower 48 US states or Canada | 677.169 | 1 |
Introduction
This self-paced class is intended to develop mathematical skills that
can be applied to the construction trade through practice and application.
This course is an introduction to other courses in construction. While this
class is not a prerequisite for any other classes, it does provide a
foundation for them.
Class Organization and Grading
For this class it is highly recommended to keep a spiral bound or similar
notebook to keep all assignments and notes together. Each week you will be
given a lecture, assignment, answers (from the previous assignment) and a
quiz. The reading and lecture will be designed to aid in the completion of
the homework.
While homework will not be checked there will be answers
posted each week to self-check your progress. There will also be a quiz
testing the information from the previous assignments. There will also be two
projects to complete, one mid-semester and one at the end of the class. The
projects are applications of mathematics to a construction problem.
The following table lists the learning modules, the maximum value in points a student
can receive within each module, and the time in which the modules must be finished.
Module
Point Value
By End of Week
0. Student Orientation
0
Before start
1. Numbers
10
1
2. Fractions
10
2
3. Conversion
10
3
4. Using ratios
10
4
5. Angles and triangles
10
5
6. Formulas: Area and Volume
10
6
Case study 1
20
7
7. Board Measure Lumber pricing
10
7
8. Concrete
10
8
9. Walls and roofs
10
9
10. Stairs and covering
10
10
Case study 2
20
10
Final Quiz
20
10
Total Points
160
Each module should take approximately one week to complete.
Course modules will be made available after the previous module's quiz is
compete. You will need to e-mail the instructor to make him aware of
your progress and receive the case
study quizzes.
Grading Policies
Graded assignments will consist of one quiz for each module, two case
studies and a final quiz. Each quiz will count for 10 points.
The case studies are each worth 20 points. The final quiz is also worth 20
points.
Grades will be posted on a weekly basis. You will have full access to your grade
sheet so you will be able to keep track of how you are doing at all times.
Your overall grade in the course will be determined by the total number of
points you have accumulated on quizzes and assignments. The grading scale is
as follows:
A 144 to 160 points
B 128 to 143 points
C 112 to 127 points
D 96 to 111
Anything less will be considered either failure or an unauthorized withdrawal
from the
course.
You will be given more information about the grading and other course matters in the
Orientation Module. | 677.169 | 1 |
Transcript of "Expo Algebra Lineal"
3.
Euclidean Space is
The Euclidean plane and three-dimensional space
of Euclidean geometry, as well as the
generalizations of these notions to higher
dimensions.
The term "Euclidean" is used to distinguish these
spaces from the curved spaces of non-Euclidean
geometry and Einstein's general theory of
relativity.
Thursday, July 8, 2010
5.
Euclidean Space
n
R is a vector space and has Lebesgue covering
dimension n.
n
Elements of R are called n-vectors.
R 1= R is the set of real numbers (i.e., the real line)
2
R is called the Euclidean Space.
Thursday, July 8, 2010
14.
Solutions of Systems of
Linear Equations
In general:
A SYSTEM OF LINEAR EQUATIONS CAN HAVE EITHER:
No solutions
Exactly one solution
Infinitely many solutions
Definition: If a system of equations has no solutions it is called
an inconsistent system. Otherwise the system is consistent.
Thursday, July 8, 2010
23.
How to Rank?
VERY SIMPLE RANKING:
Ranking of a page = number of links
pointing to that page
PROBLEM: VERY EASY TO MANIPULATE
Thursday, July 8, 2010
24.
Google PageRank
IDEA: LINKS FROM HIGHLY RANKED PAGES
SHOULD WORTH MORE
IF
Ranking of a page is x
The page has links to n other pages
THEN
Each link from that page should be
worth x/n
Thursday, July 8, 2010 | 677.169 | 1 |
Teaching High School Mathematics; First Course; Number Line Graphs of Solution Sets
Description:
Mathematician Max Beberman and Alice Hart instruct students on how to create a visual representations of a solution sets. This representation is known as a number graph. They go on to explore special circumstances that would cause exceptions on teh number graph such as a sentence with an empty solution set. The film concludes with students beginning a lesson on solution subsets and their graphs. Black and white picture with sound. Eastman Kodak edge code reads " square circle," which correlates to 1965. | 677.169 | 1 |
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Deep Dive into Mathematica's Numerics: Applications and Tips
Andrew Moylan
In this course from the Wolfram Mathematica Virtual Conference 2011, you'll learn how to best use Mathematica's numerics functions in advanced settings. Topics include techniques and best practices for using multiple numerics functions together, advanced numeric features, and understanding precision and accuracy | 677.169 | 1 |
Mathematics Requirements
All students are required to satisfy proficiency in mathematics as well as complete a math course for Core Curriculum. Though you may opt not to enroll in a math course your first semester, you are asked to read the following thoroughly as it includes information valuable for your entire four years at CSB/SJU.
The Mathematics Proficiency Requirement
Proficiency in mathematics and placement in mathematics courses will depend on your performance in your high school mathematics courses and MATH ACT entrance test scores. If you are not granted proficiency at the time of registration, you may be placed in a 1 credit module of math with the intent of strengthening your math skills, depending on your math scores, grades, and noted area of interest. You will have opportunities when you come to campus in the fall to prepare for and take a proficiency exam at the Mathematics Skills Center. Once you have passed the proficiency requirement, you will be eligible to enroll in mathematics courses. A practice exam can be found at the Math Skills Center Web site.
The Core Mathematics Requirement
The Mathematics Department offers a variety of mathematics courses which fulfill the Core Mathematics Requirement. All 100-level mathematics courses assume students have successfully completed at least three years of college preparatory mathematics, including two years of algebra. Our calculus courses assume four years of college preparatory mathematics.
If you need some review of mathematics in order to prepare to pass the math proficiency requirement, or to prepare for a Core math class, or brush up on math skills in preparation for other courses, the following Academic Skills Course is available: (Note: This course is for preparation only; it does not satisfy a proficiency or Core requirement.)
ACSC 111 Preparation for College Math, Level 1 (1 credit)
A review of basic mathematics, including arithmetic skills, beginning algebra, and geometry. Emphasis will be placed on awareness and acquisition of problem-solving techniques. This course is designed for students who need to review to prepare for the math proficiency exam, but is also appropriate for others who would like to brush up on their math preparation for upcoming classes.
Note for Pre-Med Students
Medical schools have traditionally required one to two semesters of Calculus. Recently, some medical schools have started to replace this requirement with a semester of statistics. Calculus is still needed for some science majors. If you are considering medical school, please plan to consult with the pre-medicine adviser, or to review the pre-med homepage.
Calculus
Because calculus is required for many majors and it is generally needed early on, taking calculus in your first semester is an important option for you to consider. If you are not sure whether your math skills are strong enough for you to succeed in calculus, you can find out by taking our Calculus Readiness Exam at the Mathematics Skills Center.
If you do need to improve your math skills before you take calculus, you can get help at the Mathematics Skills Center or take our Precalculus course. (Note: this Precalculus class does not fulfill the Core Mathematics Requirement.)
If you took Calculus I in high school but did not receive AP credit for it, you can still register for Calculus II if your Calculus I background is strong enough. You are encouraged to discuss this possibility with a member of the mathematics department. If you do begin with Calculus II and you earn a grade of C or better in the course, the mathematics department will grant you credit at that time for Calculus I.
Major
The mathematics department offers concentrations in mathematics and mathematics/secondary education; it also offers a major in numerical computation jointly with the computer science department. Information about the numerical computation major is in a separate section for that major.
Special Requirements: Students anticipating a major in mathematics and/or the natural sciences ordinarily begin their study of mathematics with 119. However, a student needing further preparation before beginning calculus, either 118 or 119, should enroll in 115. Students interested in advanced placement should contact the department chair.
Admission to the major requires a grade of C or higher in MATH 119, 120 and MATH 239 or 241. Before admission to the major (ordinarily in the sophomore year), prospective majors must consult with their advisors in the mathematics department to plan their mathematics courses. Students should choose their courses and non-curricular activities with regard to their goals for careers and graduate school. Students should be aware of which semesters upper-division mathematics courses will be offered.
For students who entered SJU/CSB in Fall 2007 or later, Math 385, the Capstone, is also required. This is a 2 credit course which will be offered in both fall and spring semesters, beginning in Fall 2010.
Senior majors are required to take a comprehensive exam in mathematics (the Major Field Test).
Suggestions: Prospective majors should have familiarity with computer programming before taking upper-division mathematics courses. Students preparing for graduate school in mathematics should include 332 and 344 or 348.
Concentration in Mathematics/Secondary Education (40 credits) Required Courses: Same as concentration in mathematics, but include 333, 345.
Suggestions: At least 1 credit in 105-108 or 300-303 (History of Mathematics) is also recommended. Check with the chairs of the education department and the mathematics department for requirements for certification by the Minnesota Department of Education. See the education department listing for minor requirements. | 677.169 | 1 |
Another of my favorite questions from past AP exams is from 2000 question AB 4. If memory serves it is the first of what became known as an "In-out" question. An "In-out" question has two rates are working in opposite ways, one filling a tank and the other draining it. In subsequent years we saw a…
Certain graphs, specifically those that are differentiable, have a property called local linearity. This means that if you zoom in (using the same zoom factor in both directions) on a point on the graph, the graph eventually appears to be a straight line whose slope if the same as the slope (derivative) of the tangent…
When considering functions made up of the sums, differences, products or quotients of different sorts of functions (polynomials, exponentials and logarithms), or different powers of the same sort of function we say that one function dominates the other. This means that as x approaches infinity or negative infinity, the graph will eventually look like the dominating function. Exponentials…
There are four important things before calculus and in beginning calculus for which we need the concept of limit. The first is continuity. Most of the time in pre-calculus mathematics and in the calculus we deal with nice continuous functions or functions that are not continuous at just a few points. Limits give us the…
Some suggestions for the first days of school: There has to be a first day, so make the most of it. Take roll; make sure everyone is in the right place. Give out the textbooks. Explain about calculators and so on. A word about reviewing at the beginning of the year: Don't! If you textbook's first chapter…
Discovering the Derivative with a Graphing Calculator This is an outline of how to introduce the idea that the slope of the line tangent to a graph can be found, or at least approximated, by finding the slope of a line through two very close points in the graph. It is a set of graphing calculator…
This appeared as a reply to a question on the AP Calculus Community bulletin board on August 1, 2015. It has been revised for the blog. AP Calculus teachers find it helpful to use actual AP free-response (FR) and multiple-choice (MC) questions on their exams and for homework throughout the year. Early in the year, it is…
I know a lot of you start back to school later this month. Having taught most of my career in New York I'm used to school starting after Labor Day (and ending in late June six weeks after the AP exams), so I still think of August as summer vacation. Whenever you start, I hope…
Continuing my occasional series of some of my favorite teaching questions, today we look at the 1998 AP Calculus exam question 2. This question appeared on both the AB and BC exams. I use this problem to illustrate two very different questions that come up almost every time I lead a workshop or an AP Summer…
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Course Description Limits and continuity; the Fundamental Theorem of Calculus; definition of the derivative of a function and techniques of differentiation; applications of the derivative to maximizing or minimizing a function; the chain rule; mean value theorem, and rate of change problems; curve sketching; definite and indefinite integration of of algebraic, trigonometric and transcendental functions, with an application to the calculation of areas.
Course Learning Outcomes The student will:
• Develop solutions for tangent and area problems using the concepts of limits, derivatives, and integrals.
• Draw graphs of algebraic and transcendental functions considering limits, continuity, and differentiability at a point.
• Determine whether a function is continuous and/or differentiable at a point using limits.
• Use differentiation rules to differentiate algebraic and transcendental functions.
• Identify appropriate calculus concepts and techniques to provide mathematical models of real-world situations and determine solutions to applied problems.
• Evaluate definite integrals using the Fundamental Theorem of Calculus.
• Articulate the relationship between derivatives and integrals using the Fundamental Theorem of Calculus.
• Use implicit differentiation to solve related rates problems. | 677.169 | 1 |
Geometry: Expanded Edition is the third book in the Life of Fred High School Mathematics Series, and is designed for students in 11th grade who have already finished the preceding Beginning Algebra, Expanded Editionand Advanced Algebra, Extended Edition. This new edition of Geometry replaces the both the earlier Life of Fred Geometry; it also contains all problems completely worked out. Thirteen chapters plus six honors-level half chapters with multiple sub-lessons are included. Each lesson ends with a Your Turn to Play segment with a small number of thought- provoking questions. Answers are provided on the next page for students to go over themselves after attempting to solve the problems. Chapters conclude with three problem sets, each of which is named after a city, and their answers...
Less
For courses in Geometry or Geometry for Future Teachers. nbsp;nbsp;anA welcome addition to Saxon's curriculum line, Saxon Geometry is the perfect solution for students and parents who prefer a dedicated geometry course...yet want Saxon's proven methods! Presented in the familiar Saxon approach of incremental development and continual review, topics are continually kept fresh in students' minds. Covering triangle congruence, postulates and theorems, surface area and volume, two-column proofs, vector addition, and slopes and equations of lines, Saxon features all the topics covered in a standard high school geometry course. Two-tone illustrations help students really see the geometric concepts, while sidebars provide additional notes, hints, and topics to think about. Parents will be able to easily help their students with the solutions manual | 677.169 | 1 |
Basic College Mathematics An Applied Approach, Student Support Edition
Basic College Mathematics: An Applied Approach
Summary
With its complete, interactive, objective-based approach,Basic College Mathematicsis the best-seller in this market. The Eighth Edition provides mathematically sound and comprehensive coverage of the topics considered essential in a basic college math course. The text includes chapter-openingPrep Tests,updated applications, and a new design. Furthermore, the Instructor's Annotated Edition features a comprehensive selection of new instructor support material. The Aufmann Interactive Method is incorporated throughout the text, ensuring that students interact with and master the concepts as they are presented. This approach is especially important in the context of rapidly growing distance-learning and self-paced laboratory situations. New!Study Tipsmargin notes provide point-of-use advice and refer students back to theAIM for Successpreface for support where appropriate. Integrating Technology(formerly Calculator Notes) margin notes provide suggestions for using a calculator in certain situations. For added support and quick reference, a scientific calculator screen is displayed on the inside back cover of the text. Enhanced!More bulleted annotationshave been added to the solution steps of examples and to theYou Try Itsolutions in the appendix. Enhanced!Examples have been clearly labeledHow To,making them more prominent to the student. Enhanced!More operation application problemsintegrated into theApplying the Conceptsexercises encourage students to judge which operation is needed to solve a word problem. New!Nearly100 new photosadd real-world appeal and motivation. Revised!TheChapter Summaryhas been reformatted to include an example column, offering students increased visual support. Enhanced!In response to instructor feedback, the number ofChapter Review ExercisesandCumulative Review Exerciseshas increased. Enhanced!This edition features additional coverage of time (Chapter 8), bytes (Chapter 9), and temperature (Chapter 11). Aufmann Interactive Method (AIM)Every section objective contains one or more sets of matched-pair examples that encourage students to interact with the text. The first example in each set is completely worked out; the second example, called 'You Try It,' is for the student to work. By solving the You Try It, students practice concepts as they are presented in the text. Complete worked-out solutions to these examples in an appendix enable students to check their solutions and obtain immediate reinforcement of the concept. While similar texts offer only final answers to examples, the Aufmann texts' complete solutions help students identify their mistakes and prevent frustration. Integrated learning system organized by objectives.Each chapter begins with a list of learning objectives that form the framework for a complete learning system. The objectives are woven throughout the text (in Exercises, Chapter Tests, and Cumulative Reviews) and also connect the text with the print and multimedia ancillaries. This results in a seamless, easy-to-navigate learning system. AIM for SuccessStudent Preface explains what is required of a student to be successful and demonstrates how the features in the text foster student success.AIM for Successcan be used as a lesson on the first day of class or as a project for students to complete. The Instructor's Resource Manual offers suggestions for teaching this lesson.Study Tipmargin notes throughout the text also refer students back to the Student Preface for advice. Prep Testsat the beginning of each chapter help students prepare for the upcoming material by testing them on prerequisite material learned in preceding chapters. The answers to these
Table of Contents
Chapters 2–6 are followed by Cumulative Review Exercises
Whole Numbers
Introduction to Whole Numbers
Addition of Whole Numbers
Subtraction of Whole Numbers
Multiplication of Whole Numbers
Division of Whole Numbers
Exponential Notation and the Order of Operations Agreement
Prime Numbers and Factoring
Focus on Problem Solving: Questions to Ask Projects and Group Activities: Order of Operations, Patterns in Mathematics, Search the World Wide Web
Fractions
The Least Common Multiple and Greatest Common Factor
Introduction to Fractions
Writing Equivalent Fractions
Addition of Fractions and Mixed Numbers
Subtraction of Fractions and Mixed Numbers
Multiplication of Fractions and Mixed Numbers
Division of Fractions and Mixed Numbers
Order, Exponents, and the Order of Operations Agreement
Focus on Problem Solving: Common Knowledge Projects and Group Activities: Music, Construction, Fractions of Diagrams
Decimals
Introduction to Decimals
Addition of Decimals
Subtraction of Decimals
Multiplication of Decimals
Division of Decimals
Comparing and Converting Fractions and Decimals a fraction
Focus on Problem Solving: Relevant Information Projects and Group Activities: Fractions as Terminating or Repeating Decimals
Ratio and Proportion
Ratio
Rates
Proportions
Focus on Problem Solving: Looking for a Pattern Projects and Group Activities: The Golden Ratio, Drawing the Floor Plans for a Building, The U.S. House of Representatives
Percents
Introduction to Percents
Percent Equations: Part 1
Percent Equations: Part II
Percent Equations: Part III
Percent Problems: Proportion Method
Focus on Problem Solving: Using a Calculator as a Problem-Solving Tool, Using Estimation as a Problem-Solving Tool Projects and Group Activities: Health, Consumer Price Index
Applications for Business and Consumers
Applications to Purchasing
Percent Increase and Percent Decrease
Interest
Real Estate Expenses
Car Expenses
Wages
Bank Statements
Focus on Problem Solving: Counterexamples Projects and Group Activities: Buying a Car | 677.169 | 1 |
title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.
* Updates the leading graduate-level text in mathematical physics * Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering * Focuses on problem-solving skills and offers a vast array of exercises * Clearly illustrates and proves mathematical relations
New in the Sixth Edition: * Updated content throughout, based on users' feedback * More advanced sections, including differential forms and the elegant forms of Maxwell's equations * A new chapter on probability and statistics * More elementary sections have been deleted
Editorial Reviews
Review
"As to a comparison with other books of the same ilk, well, in all honesty, there are none. No other text on methods of mathematical physics is as comprehensive and as complete...I encourage the students to keep their copies as they will need it and will find it an invaluable reference resource in later studies and research." - Tristan Hubsch, Howard University
Most Helpful Customer Reviews
I am a graduate physics student with a strong mathematical background. This is the textbook used for our 2 semester course in mathematical methods for physics. The book is massive, both in content and physical weight. The cover is attractive and the printing seems to be fairly high quality. Now comes the difficult part of the review: finding other positive comments. First of all, I have only used a few chapters of the book thus far, so my comments pertain only to those. Some difficulties I have found... There are no answers to any exercises making the book fairly useless for self-study. The material is very uneven, as if each section was written by a different author (graduate student?). The explanations and examples are mediocre at best (contrast with the Mary Boas book). There are MANY typos - what ever happened to proof reading? The class INSTRUCTOR doesn't like the book, but is forced to use it by the department, and has regularly emailed the authors with corrections and recommendations. None of the students in the class like the book. You may be forced to use this book, but I would recommend other books as supplements (e.g., the book by Mary Boas and several in the Schaum Outline Series).
My instructor chose Arfken as the text for our Mathematical Physics class. He has a high opinion of the book, although he did not require it to be read and did not assign any of the exercises. Rather than using Arfken, most of the students in my class used various mathematics and physics books from the university library. My opinion of Arfken is that it is so condensed that it is not understandable to undergraduates. You need to consult other texts extensively to fill in the gaps. For example, Arfken develops tensor analysis on pages 126 thru 130, 5 pages total. My copy of Applications of Tensor Analysis by McConnell does the same on it's first 171 pages. I hesitate to say that Arfken is useless, but you can draw your own conclusion from my last example. Arfken is so abbreviated that it is not useful to the undergraduate as a reference either, in my opinion. Perhaps it is useful to persons who are familiar with the subject matter in advance, I am not sure. Were one or a group of people to flush this book out it might be more useful, but it would no doubt become many volumes.
The lecturer of our undergraduate Mathematical Methods for Physics course said that he recommends Arfken's book because it will be useful also later as a reference book. Hearing those words, I could not help but to think "this is one of *those* books". And indeed, although Arfken's and Weber's book covers quite a wide range of mathematics, it does so by being very concise, e.g. there is usually only one example per topic. This is one example of why it is not a good textbook. Not following Arfken's course, I will give another example: there are no answers and no solutions for any of the problems, making it very undesirable from the viewpoint of the person who cannot attend all the lectures. Finally, text itself is quite concise, and often it stops at telling the things rather than explaining them also. I guess I have to admit that I am not one of the excellent students mentioned by a reviewer, for I liked Kreyszig's Advanced Engineering Mathematics much more. As a contrast to Arfken's book, it offered many examples and helped to understand what the thing was all about. Unfortunately, it does not cover nearly all of the topics covered by Mathematical Methods for Physicists. If Mathematical Methods for Physicists is going to be your first introductory text to these topics and if you are not supported by very good lectures I can only say that may God have mercy on your soul.
I invite the students on this page to take, or at least appreciate, a long-term view. Arfken pays off in the working world, with its comprehensive coverage of topics, short self-contained discussions which don't require a lot of flipping back and forth to other chapters, a clear writing style, and few proofs to get in the way. When I need to tackle a new problem which results in a coordinate system, function or technique that I'm rusty on, Arfken is usually the first book I pull off the shelf. Properties of Chebyshev polynomials for filter theory, or elliptic functions for the current density on a microstrip transmission line? Integral transforms? A comparison of Green's functions in 1, 2 and 3 dimensions for different electromagnetic diff eq's, all in one table? Group theory for certain phased-array antenna analyses? (really!) Tensors for analyzing flexure in superconducting magnet structures? Error functions for communications theory? It's all here in a quickly digestible form, with enough depth to solve a problem or at least prepare you to turn to a specialty text and quickly extract what's needed. I always learn something from the examples, which typically apply the same mathematical tool for my problem to some completely different area of physics. Arfken may not be an optimal text for a one-year course, but it's been my reliable working companion for 24 years. When my 2nd edition finally falls apart, I'll probably replace it with a new one. | 677.169 | 1 |
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