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A stimulating and rigorous approach to Mathematics that goes beyond the requirements of the National Curriculum for Year 6 pupils (aged 10 and above) and lays the foundation for success at Common Entrance and other independent entrance exams at 11+. - Plenty of worked examples to demonstrate method. - Develops key skills with clear explanations and... more...
Laplace Transforms for Electronic Engineers, Second (Revised) Edition details the theoretical concepts and practical application of Laplace transformation in the context of electrical engineering. The title is comprised of 10 chapters that cover the whole spectrum of Laplace transform theory that includes advancement, concepts, methods, logic, and... more...
Popular Lectures in Mathematics, Volume 12: Mathematical Problems and Puzzles: From the Polish Mathematical Olympiads contains sample problems from various fields of mathematics, including arithmetic, algebra, geometry, and trigonometry. The contest for secondary school pupils known as the Mathematical Olympiad has been held in Poland every year since... more...
Functional Equations in Probability Theory deals with functional equations in probability theory and covers topics ranging from the integrated Cauchy functional equation (ICFE) to stable and semistable laws. The problem of identical distribution of two linear forms in independent and identically distributed random variables is also considered, with... more...
Linear Integral Equations: Theory and Technique is an 11-chapter text that covers the theoretical and methodological aspects of linear integral equations. After a brief overview of the fundamentals of the equations, this book goes on dealing with specific integral equations with separable kernels and a method of successive approximations. The next... more...
On Applications and Theory of Functional Equations focuses on the principles and advancement of numerical approaches used in functional equations. The publication first offers information on the history of functional equations, noting that the research on functional equations originated in problems related to applied mathematics. The text also highlights... more...
Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems,... more...
Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight... more...... more... | 677.169 | 1 |
Mathematics
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Mathematics
Mathematics is the study and application of arithmetic, algebra, geometry, and analysis. Mathematical methods and tools, such as MATLAB® and Mathematica®, are used to model, analyze, and solve diverse problems in a range of fields, including biology, computer science, engineering, finance, medicine, physics, and the social sciences. Important subareas of mathematics include combinatorics, differential equations, game theory, operations research, probability, and set theory and logic.
Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuse e...
An Entertaining and Enlightening Guide to the Who, What, and Why of String Theory
During the last 50 years, numerous physicists have tried to unravel the secrets of string theory. Yet why do these scientists work on a theory lacking experimental confirmation?
Why String Theory? provides the......
Exact sampling, specifically coupling from the past (CFTP), allows users to sample exactly from the stationary distribution of a Markov chain. During its nearly 20 years of existence, exact sampling has evolved into perfect simulation, which enables high-dimensional simulation from interacting...
Since a major source of income for many countries comes from exporting commodities, price discovery and information transmission between commodity futures markets are key issues for continued economic development.This book covers the fundamental theory of and derivatives pricing for major commodity...
Today's graduates should be grounded in the basics of personal finance and possess the skills and knowledge necessary to make informed decisions and take responsibility for their own financial well-being. Faced with an array of complex financial services and sophisticated products, many graduates...
Computational Mathematics: Models, Methods, and Analysis with MATLAB® and MPI is a unique book covering the concepts and techniques at the core of computational science. The author delivers a hands-on introduction to nonlinear, 2D, and 3D models; nonrectangular domains; systems of partial...
Highly Regarded, Accessible Approach to Image Processing Using Open-Source and Commercial Software
A Computational Introduction to Digital Image Processing, Second Edition explores the nature and use of digital images and shows how they can be obtained, stored, and displayed. Taking a strictly...
Functions of a Complex Variable provides all the material for a course on the theory of functions of a complex variable at the senior undergraduate and beginning graduate level. Also suitable for self-study, the book covers every topic essential to training students in complex analysis. It also...
Mathematics in Games, Sports, and Gambling: The Games People Play, Second Edition demonstrates how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. With emphasis on mathematical thinking and problem solving, the text draws on...
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Algebraic geometry
It can be seen as the study of solution sets of systems of polynomials.
When there is more than one variable, geometric considerations enter and are important to understand the phenomenon.
One can say that the subject starts where equation solving leaves off, and it becomes at least as important to understand the totality of solutions of a system of equations as to find some solution; this does lead into some of the deepest waters in the whole of mathematics, both conceptually and in terms of technique.
June 11, 2009 — Hirzebruch's problem at the interface of topology and algebraic geometry has occupied mathematicians for more than 50 years. A professor of mathematics at the Ludwig-Maximilians-Universitaet in ... read more
Sep. 16, 2013 — Researchers have found high school students in the United States achieve higher scores on a standardized mathematics test if they study from a curriculum known as integrated ... read more
Aug. 3, 2009 — As mathematics continues to become an increasingly important component in undergraduate biology programs, a more comprehensive understanding of the use of algebraic models is needed by the next ... read more
Aug. 16, 2006 — Studying complex systems, such as the movement of robots on a factory floor, the motion of air over a wing, or the effectiveness of a security network, can present huge challenges. Mathematician ... read more
June 20, 2011 — A new study finds important differences in math curricula across US states and school districts. The findings suggest that many students across the country are placed at a disadvantage by less ... read more
Mar. 4, 2009 — Greek mathematics is considered one of the great intellectual achievements of antiquity. It has been decisive to the academic and cultural development of Western civilization. The three Roman authors ... read more
Apr. 29, 2014 — Mathematicians have found a framework for the celebrated Rogers-Ramanujan identities and their arithmetic properties, solving another long-standing mystery stemming from the work of Indian math | 677.169 | 1 |
books.google.ca - Wide... Algebra
Abstract Algebra
Wide results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. * The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.
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A Descriptive, Survey Research Study Of The Student Characteristics Influencing The Four Theoretical Sources Of Mathematical Self-Efficacy Of College Freshmen, Tonja Motley Locklear
The Sources of Middle School Mathematics Self-Efficacy Scale (Usher & Pajares, 2009) was adapted for use in this study investigating the impact that gender, race, sexual orientation, hometown location (rural, suburban, or urban), high school GPA, college GPA and letter grade of a mathematics course in the previous semester had on the four sources of mathematical self-efficacy of 102 college freshmen attending three small, private, liberal arts institutions. Even though this study found no interaction effects between the student characteristics, the four sources of mathematical self-efficacy, or the three subcategories of the vicarious experience construct, this study did find statistically significant ...
Theses: Doctorates and Masters
This study investigated and described the status and quality of secondary science teaching and learning in Lagos State, Nigeria. Quantitative and qualitative methods were used for gathering research data. Quantitative data were obtained from the surveys of 78 junior secondary science teachers and 500 junior secondary students from three Local Education Districts of Lagos State. Qualitative data on the other hand, were gathered from analysis of national and state curriculum documents and from focus groups of science teachers, school principals, parent association representatives, education officers, teacher educators, representatives of the professional association for science teachers and representatives of examination bodies ...
How To Graphically Interpret The Complex Roots Of A Quadratic Equation, Carmen Melliger
MAT Exam Expository Papers
As a secondary math teacher I have taught my students to find the roots of a quadratic equation in several ways. One of these ways is to graphically look at the quadratic and see were it crosses the x-axis. For example, the equation of y = x2 – x – 2, as shown in Figure 1, has roots at x = -1 and x = 2. These are the two places in which the sketched graph crosses the x-axis.
Exploring The Use Of Mathematics Manipulative Materials: Is It What We Think It Is?, Linda Marshall, Paul Swan
EDU-COM International Conference
The use of mathematics manipulative materials such as counters and Base Ten Blocks is common in many Australian classrooms. Seemingly there is an unchallenged assumption that the use of manipulative materials in the teaching of mathematics is a key to learning about mathematics concepts, and this is supported by the mathematics manipulatives industry. Teachers who are time poor and under pressure are either looking for a miracle manipulative to solve all their problems with teaching a particular topic such as fractions, or have abandoned the use of manipulatives in favour of textbooks. This paper reports on a survey and follow-up ...
Senior Honors Theses
Math anxiety is a real problem facing students and teachers today. The mathematics teacher especially needs to understand the causes and effects of math anxiety as well as ways to help students overcome it. There are many symptoms of math anxiety including an unwillingness to attempt mathematics problems, a fear of taking advanced mathematics classes, and being unusually nervous when in mathematics class. Math anxiety hinders students' working memory (Perina, 2002). It occurs at different ages in different people for different reasons. The main cause of math anxiety is the teacher himself It has been shown that students tend to ...
Grade 6-8 Living Things, Theresa Gomez
Science
Abstract: This unit explores the characteristics of living things. Students must evaluate and classify various specimens to determine if they meet agreed upon criteria for life. The unit emphasizes the ways in which different organisms perform the same life functions, and reveals that non-living things may appear to perform some functions but do not perform all functions. The unit culminates in the relation that all living things are made of cells.
Grades 3-5 Pollution, Amy Silviotti
Science
This is a science lesson for grades third through five on pollution. Through this lesson students will be able to describe the relationships among air, water, land on Earth, characteristics of living and non living things, survival behaviors of common living specimens, the factors that help promote good health. Students will also be able to identify how plants and animals depend on each other and in what ways humans have changed the environment. The lesson is tiered in three levels based on ability. Within each tier the student will complete a shape contract where they choose tasks based on interest ...
Theses: Doctorates and Masters
This study focused on the intended learning outcomes, curriculum and assessment in the science curriculum offered at a regional independent Middle School in the state of Victoria, Australia. In-school assessment has indicated that the current science curriculum of this Middle School may not develop students' skills in scientific literacy as effectively as intended. One hypothesis to explain this deficit is that there is a misalignment of intended outcomes, curriculum materials and assessment. This study aimed to determine the extent to which the intended curriculum and assessment in this Victorian middle years' science program is aligned to its stated goals and ...
Master of Education Theses & Projects
This quantitative study provides information obtained through the use of inquiry-based mathematics instruction verses traditional mathematics instruction. The use of each curriculum was implemented into two classrooms of eighth grade pre-algebra students. The study was based on data collected before and after each of the two units of study. Fifty-two suburban eighth grade students represented the sample population. Results of the SPSS analysis showed that both classes made improvement from their pre-test to their post-test for both units but students receiving instruction through inquiry-based instruction showed significantly more improvement on the second unit. These results can be useful for educators ...
Undergraduate Theses and Professional Papers
Research on pre-service elementary school teachers' understanding of the multiplicative structure of the natural numbers demonstrates an under-utilization of unique prime factorization in the identification of a number's factors. For example, Zazkis and Campbell (1996b) found that a majority of teacher candidates employed trial division to analyze factor-candidates of a number, even when both were presented in prime-factored-form. Recent studies (i.e. Roscoe & Feldman, 2015) have shown that teachers' understanding of factor can be strengthened by engaging in a sequence of instructional tasks that explore the relationship between a number's prime factorization and its factors. This study seeks ...
Identities And Motives Of Naturalist Development Program Attendees And Their Relation To Professional Careers, Jennifer A. Mraz
Dissertations
In recent years, there has been much concern over the decline of biologists who actually identify themselves to be naturalists, which negatively impacts the field of conservation and the study of biology as a whole. This could result in a decrease in individuals who participate in naturalist-like activities, such as informal environmental education and environmental volunteerism. The purpose of my study was to determine what discourse identities were held by naturalist development program participants, how these discourse identities related to their volunteer motives in environmental settings, and how discourse identity related to professional careers. I defined identity through the lens ...
Education Dissertations
Grounded in metacognitive theory (Flavell, 1976) and historical foundations that reach back as far as the writings of Plato (1973), the last few decades have seen an increase in research regarding the impact of metacognitive practice on student learning, often through the use of reflective writing. Studies have focused on a range of aspects, from how to measure metacognition to the effect metacognitive practice has on the academic achievement of students in a variety of subject areas. Specifically with regard to mathematics, researchers have studied the impact of reflective strategies on primary, secondary, and university level students.
Ecology, Evolution and Organismal Biology Publications
Misconceptions about biological evolution specifically and the nature of science in general are pervasive in our society and culture. The view that biological evolution explains life's origin(s) and that hypotheses become theories, which then become laws are just two examples of commonly held misconceptions. These misconceptions are reinforced in the media, in people's personal lives, and in some unfortunate cases in the science classroom. Misconceptions regarding the nature of science (NOS) have been shown to be related to understanding and acceptance of biological evolution. Previous work has looked at several factors that are related to an individual ...
Derivation Of The Volume Of Tetrahedron/Pyramid Bounded By A Given Plane & The Co-Ordinate Planes, Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
The article here deals with the derivation of a general expression to calculate the volume of tetrahedron/pyramid bounded by a given plane & the co-rdinate planes (i.e. XY-plane, YZ-plane & ZX-plane) using intercept form of equation of a plane in 3-D space. All the derivations are based on simple geometry. These are very useful to directly calculate the volume of the bounded tetrahedron/pyramid.
Journal of Pre-College Engineering Education Research (J-PEER)
Students' knowledge about a profession influences their future decisions about careers. Research indicates that students tend to hold stereotypical views of engineers, which would hinder engineering as a career choice. The purpose of this study was to measure how participating in a week long engineering summer camp affected middle school students' (N519) attitudes towards engineering and their conceptions of engineering and technology. Results indicate that participation in the programs had a positive impact on the students' understandings of what technology is and the work engineers do. Although the results indicate a positive impact on participants, it is not clear which ...
Nutrition and Food Science Faculty Research Publications
MinorHow Science Teachers Balance Religion And Evolution In The Science Classroom: A Case Study Of Science Classes In A Florida Public School District, Pierre Willems
Doctoral Dissertations and Projects
...
Examining Differences In Middle School Student Achievement On A State Mandated Examination: Does A Full Year Of Agriscience Really Make A Difference?, Sarah Hicks, Dennis W. Duncan, Myra Womble, Robert Branch
Online Journal for Workforce Education and Development
Early agricultural education programs in the United States existed to promote new methods and techniques to further agricultural production. Today, extending integration, general knowledge, appreciation, and literacy about agriculture is the goal, especially at the middle school level. Not only is agricultural education designed to encompass academics, but science and technology, literacy, and career preparedness are parts of the total agricultural education program. Since the passage of No Child Left Behind Act (NCLB), more pressure has been put on teachers to generate increased student academic performance and improvement of test scores. The purpose of this research study was to determine ...
Publications & Research
What started as planning for the next generation of inquiry-based learning led to an entirely new center for innovation and entrepreneurship! Hear how this innovative idea moved to the design of a physical innovation hub and see how IMSA has transformed a former computer lab IN2 a working prototype of their future space.
Dive into the many aspects of creating innovation spaces: design process, STEM foundation and entrepreneurship cornerstone, Makerspace development through a student leadership and service initiative, collaboration potential with community partners and local/regional business entities, student inquiry and research potential and the ability to showcase area emerging ...
Publications & Research
The day will begin with six stories from innovative school districts, told in a short, engaging, "TED" talk format. After each story, David Chan and Henry Thiele will lead a time of reflection, sharing ideas, thoughts and connections. School professionals will share their stories about themes including: Inspiring Innovation and Inquiry.
DBER Speaker Series
Systems thinking, computational modeling, and simulating systems are examples of important skills stressed in life sciences education by Vision and Change. In response to these calls, we have designed a computational modeling and simulation‐driven intervention to supplement current instruction in the life sciences curriculum. As part of our pre‐intervention assessment we evaluated students on their systems thinking in the context of cellular respiration. For this assessment, we had students create conceptual models. We found that students with lecture instruction are able to recall more components associated with the cellular respiration process but are not better able to integrate ...
Faculty Scholarship
The objective of this article is to make explicit some concrete ways in which an accurate perspective of what science is contributes significantly to improving science teaching. Effective science teaching begins with the recognition that for both practising scientists and students the desire to find answers to personally meaningful questions about natural phenomena is the strongest incentive to study science. Instructional methods that nurture and draw upon the curiosity of students have the best chance to motivate students to learn science. Teaching in this way entails helping students 1) to see the conceptual relevance, utility, and aesthetic dimension of what ... | 677.169 | 1 |
Foundational Studies Math
Foundational Studies courses at Brookdale are courses specifically developed to prepare adult learners for college level course work. The Foundational Studies math courses are pre-requisites for math, science, business, culinary, automotive, and other college level courses. Math skills, as well as technical and critical thinking and writing skills, are addressed in our Foundational Studies courses.
About ACCUPLACER:
The Accuplacer is the placement tool that all New Jersey Community Colleges use to determine if students require remediation in Math, Reading or Writing. | 677.169 | 1 |
...
Show More studies and self-assessment begin each chapter. Incentives are built in to encourage students to move forward with a positive attitude. Now includes the interview process with advice and prescriptive direction from top level, experienced recruiters from different businesses and industries. Educates students on the world of social media (benefits, problems, and use of) for effective applications to the educational environment. Also illustrates how math affects every aspect of our lives recognizing that students are often intimidated by math despite its impact on every aspect of our success. Chapters are the right length to present specific concepts, provide affective exercises, activities, and threaded features thatwill enhance the college experience. There is no "busywork" - all charts, tables, and exercises are meaningful | 677.169 | 1 |
Linear Algebra. Ideas and Applications. 3rd Edition
This expanded new edition presents a thorough and up-to-date introduction to the study of linear algebra
Linear Algebra, Third Edition provides a unified introduction to linear algebra while reinforcing and emphasizing a conceptual and hands-on understanding of the essential ideas. Promoting the development of intuition rather than the simple application of methods, the book successfully helps readers to understand not only how to implement a technique, but why its use is important.
The book outlines an analytical, algebraic, and geometric discussion of the provided definitions, theorems, and proofs. For each concept, an abstract foundation is presented together with its computational output, and this parallel structure clearly and immediately illustrates the relationship between the theory and its appropriate applications. The Third Edition also features: - A new chapter on generalized eigenvectors and chain bases with coverage of the Jordan form and the Cayley-Hamilton theorem - A new chapter on numerical techniques, including a discussion of the condition number - A new section on Hermitian symmetric and unitary matrices - An exploration of computational
approaches to finding eigenvalues, such as the forward iteration, reverse iteration, and the QR method - Additional exercises that consist of application, numerical, and conceptual questions as well as true-false questions
Illuminating applications of linear algebra are provided throughout most parts of the book along with self-study questions that allow the reader to replicate the treatments independently of the book. Each chapter concludes with a summary of key points, and most topics are accompanied by a "Computer Projects" section, which contains worked-out exercises that utilize the most up-to-date version of MATLAB(r). A related Web site features Maple translations of these exercises as well as additional supplemental material.
Linear Algebra, Third Edition is an excellent undergraduate-level textbook for courses in linear algebra. It is also a valuable self-study guide for professionals and researchers who would like a basic introduction to linear algebra with applications in science, engineering, and computer science.
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"Linear Algebra (third edition) is an excellent undergraduate-level textbook for courses in linear algebra. It is also valuable self-study guide for professionals and researches who would like a basic introduction to linear algebra with applications in science, engineering, and computer science." (Mathematical Review, Issue 2009e)
"This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications." (Electric Review, November 2008)
"This book should make a good text for introductory courses." (Computing Reviews, September 30, 2008 146USD 155GBP 100
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Mathematica 9 features the Wolfram Predictive Interface, a suite of features that intelligently suggests what to try next based on sophisticated heuristics and data from millions of Wolfram|Alpha queries. Analysis and visualization of statistical data and social networks (e.g. for Facebook, Twitter) is fully integrated with existing capabilities, such as instant interactivity, computable documents and symbolic computation. Additional features include highly integrated units support, including free-form linguistic entry, conversions and dimensional consistency checking across graphics and numeric and symbolic calculations; data science, probability and statistics functionality, including survival and reliability analysis, Markov chains, queueing theory, time series and stochastic differential equations; R language fully integrated into workflow for seamless data and code exchange; 3-D volumetric image processing and out-of-core technology that scales up performance to very large 2-D and 3-D images and video; and integrated analog and digital signal processing. | 677.169 | 1 |
booklet containing 31 problem sets that involve a variety of math skills, including scientific notation, simple algebra, and calculus. Each set of problems is contained on one page. Learners will use mathematics to explore varied space...(View More) science topics including black holes, ice on Mercury, a mathematical model of the Sun's interior, sunspots, the heliopause, and coronal mass ejections, among many others.(View Less)
This is a booklet containing 87 problem sets that involve a variety of math skills, including scale, geometry, graph analysis, fractions, unit conversions, scientific notation, simple algebra, and calculus. Each set of problems is contained on one...(View More) page. Learners will use mathematics to explore varied space science topics in the areas of Earth science, planetary science, and astrophysics, among many others. This booklet can be found on the Space Math@NASA website | 677.169 | 1 |
books.google.com - This book categorizes, identifies and explains the various techniques that are used repeatedly in all proofs and explains how to read proofs that arise in mathematical literature by understanding which techniques are used and how they are applied.... to read and do proofs
How to read and do proofs: an introduction to mathematical thought processes
This book categorizes, identifies and explains the various techniques that are used repeatedly in all proofs and explains how to read proofs that arise in mathematical literature by understanding which techniques are used and how they are applied.
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Synopsis
This DVD-ROM for PC and Mac contains hundreds of friendly, step-by-step video tutorials that clearly explain Higher Level GCSE Maths (for the AQA, Edexcel, OCR and WJEC exam boards). It also includes printable exam-style questions, with fully-worked answers on video. There's grading information to show which topics are the most challenging, plus a full search function that makes it easy to find what you're looking for | 677.169 | 1 |
books.google.fr - The... Arithmetic of Elliptic Curves
The Arithmetic of Elliptic Curves
The begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and global fields. The last two chapters deal with integral and rational points, including Siegel's theorem and explicit computations for the curve Y^2 = X^3 + DX. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics. | 677.169 | 1 |
Recommended with confidence" by The Times Literary Supplement, this lively survey starts with simple arithmetic and algebra and proceeds by gradual steps through graphs, logarithms, and trigonometry to calculus and the world of numbers. Generations of readers have found it the ideal introduction to mathematics, offering accessible explanations of how theory arises from real-life applications. "The main object of this book is to dispel the fear of mathematics," declares author W. W. Sawyer, adding that "Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject." Now retired, Sawyer won international renown for his innovative teaching methods, which he used at colleges in England and Scotland as well as Africa, New Zealand, and North America. His insights into the pleasures and practicalities of mathematics will appeal to readers of all backgroundsW. W. Sawyer was one of the greatest teachers of mathematics within the past century. The continuing popularity (to the extent that books on math can be popular) of his other books -- *Prelude to Mathematics* (which deals with advanced math) and *Vision in Elementary Mathematics* (which deals with arithmetic and basic algebra) -- serve as evidence for the wonderful ability he had to make math seem useful and interesting to everyone from the math-phobic to the dedicated mathematician. Contrary to some other reviews, Sawyer's prose was NOT dull or dry. We have to keep in mind the fact that *Mathematician's Delight* was written for an audience in the 1940's to 1950's Britain and Canada. Obviously, the style and tone won't be consistent with the way that we 21st century Americans are used to. But even giving him that benefit of the doubt, Sawyer's prose is always lively, entertaining, and full of insights into his chosen subject of mathematics as well as insight into why many people struggle with aspects of that subject. I definitely agree with the positive aspects of the other reviews. This indeed is an excellent book to take you from the basics of algebra all the way up to and beyond calculus. I sincerely hope that someone brings this book back in print.
Why read fiction when you can learn how to do something. That has been my philosophy since I started reading. While I've read my share of fiction, it is the instructional non-fiction books that have always gotten my attention and I have read innumerable volumes. The reason for this introduction is to impress upon you the weight of my next statement:
This is the best book I have ever read!
I am not an educator, nor am I a mathematician, but there is not a sentence in this book that hasn't found its way into my personal philosophy of learning and education. I first read this book when I was in college, not as part of a course, but to "read around the subject" to paraphrase W.W. Sawyer. This was over 20 years ago, and recently I was reading through this book again and was astonished at how much of his advice and ideas had become part of who I am.
Just some fragments of his ideas:
1.) First study books that contain material you know 90% of, and then learn the remaining 10%. 2.) Read around a subject 3.) To learn a language, start with little children's books in that language. 4.) To learn to draw, sit on a bus and draw everything you see. 5.) Learn by doing. 6.) Develop an interest in the subject you want to learn.
And there are countless others. These sound obvious, and I am certainly not doing him justice. Read for yourself and you will be amazed at how all of this is woven into an inspiring and easy to read book that, by the way, contains some discussion of mathematics! How many authors do you know that not only teach you their subject, but teach you how to learn any subject!
This is a book that should be read by every teacher and by every student.
One of the best books on maths - ever. I first read it in 1966 and then, again, recently. It "explains" maths in the most simple, enjoyable and humorous way covering arithmetic, algebra, geometry, graphs, calculus, trig and, of course how to study this subject. If you have ever had difficulty with maths - read this book. If you teach maths then this approach should be your route map if true learning by your students is important to you. An excellent book which has stood the test of time - first published in 1947!
This is a great book. Highly recommended by me to be read by everyone especially students who fear mathemtics. "So long as a subject seems dull, you can be sure that you are approcahing it form the wrong angle" - W.W.Sawyer
Written nearly 70 years ago, but reprinted many times since then (my used copy dates from 1995), this is a perfect book for those aged 15 to 85 who find Mathematics intimidating or downright incomprehensible. W.W.Sawyer starts with basic principles, and takes the reader by the hand and leads him/her through the world of maths, showing how really it is essentially a kind of shorthand which enables us to work out and understand how the world works. Algebra, geometry, trigonometry, calculus,it's all there. Fascinating and fun - makes up for all the years of lousy maths teaching endured by so many of us at school! | 677.169 | 1 |
9th grade math english ninth 9
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If you practice hard, you can excel !! QVprep for grade 9 provides you hundreds of math and english problems with detailed answer explanations so that you can create a strong learning foundation. | 677.169 | 1 |
This is Volume 2 of the 4th revised and expanded edition of this standard work on numerical approaches to ordinary differential equations. It describes processes for numerically solving basic and boundary value problems for ordinary differential equations. The text guides the reader through tried and true practical methods, and includes... more...
The volume contains carefully selected papers presented at the International Conference on Differential & Difference Equations and Applications held in Ponta Delgada ? Azores, from July 4-8, 2011 in honor of Professor Ravi P. Agarwal. The objective of the gathering was to bring together researchers in the fields of differential & difference... more...
The proofs presented in this volume include complete mathematical details as well as extensive use of the implicit function theorem as a unifying approach to perturbative analysis. A wealth of end-of-chapter exercises enables its use as a textbook. more...
Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution... more...
"Krantz is a very prolific writer. He?creates excellent examples and problem sets." ?Albert Boggess, Professor and Director of the School of Mathematics and Statistical Sciences, Arizona State University, Tempe, USA more...
ORDINARY DIFFERENTIAL EQUATIONS Welcome! Introduction This Book Is a Field Guide. What Does That Mean for YOU? Mired in Jargon - A Quick Language Lesson! Introducing MATLAB A First Look at Some Elementary Mathematical Models
A Basic Analysis Toolbox Some Basic Mathematical Shorthand Set Algebra Functions The Space (R; j_j) A... more...
This book provides a complete and exhaustive study of the Green?s functions. Professor Cabada first proves the basic properties of Green's functions and discusses the study of nonlinear boundary value problems. Classic methods of lower and upper solutions are explored, with a particular focus on monotone iterative techniques that flow from them. In... more...
Deepen students? understanding of biological phenomena Suitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental... more... | 677.169 | 1 |
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Tag: Math
VEX Robots can be more competitive when they have addressed several drive motor control challenges:
Stopping a motor completely when the joystick is released. Joysticks often do not output a value of "zero" when released, which can cause motors to continue turning slowly instead of stopping.
Starting to move gradually, not suddenly, after being stopped. When a robot is carrying game objects more than 12 inches or so above the playing field, a sudden start can cause the robot to tip over.
Having motor speeds be less sensitive to small joystick movements at slow speeds. Divers seeking to position the robot precisely during competition need "finer" control over slow motor speeds than fast motor speeds.
These challenges can be solved using one or more "if" statements in the code controlling the robot, however using a single polynomial function can often solve all of these challenges in one step. A graph can help illustrate the challenges and their solution:
Once a set of learning objectives have been settled on for an activity, problem, or project, what should the problem's context be? Since linear equations model situations where there is a constant rate of change, common contexts for linear equation projects often include the following:
Steepness, height, angle
Examples: road grade, hillside, roof, skateboard park element, tide height over the two weeks before (or after) a full moon, sun angle at noon over a six month period
Estimating time to complete a task (setup plus completion)
Examples: mowing a lawn, painting a wall, writing a research paper | 677.169 | 1 |
Math Help Online for All Levels at Educator.com
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Educator.com has released several new math courses. These courses are in addition to 80+ subjects already available for high school, college, test prep, and professional subjects.
Educator.com pairs students with the best university professors and educators in the country.
Los Angeles, CA (PRWEB)February 11, 2014
Learning math is like building a staircase and each branch of math is a new block that requires a sturdy foundation in order to stand strong. Educator.com strives to foster growth in learning and knowledge, and that is why they offer a large variety of comprehensive Math courses taught by the best respective instructors.
Math can be a challenging subject at times, but this art of numbers and calculations is an essential everyday tool used by everyone from toddlers to students, to businesspeople and even rocket scientists. Educator.com offers everything mathematical from Basic Math to Differential Equations to support and guide students in their studies, and provide great review for helpful tutoring parents or professionals.
Each handpicked professor is a passionate and experienced educator. Their goal is to make each subject simpler, easier to digest with in-depth explanations and plenty of examples and worked out problems. Please feel free to click on any of the course links below--Meet the professors and explore the full syllabi and free sample lessons:
All of these math courses and more are available at one of three subscription plans--none of which exceed $1.50/day. A subscription grants you complete access to 100+ courses! Students can learn Math, Science, Computer Science, Software Training, Language, and AP/SAT Test Prep for the initial price of $45/month the first month ($35/month thereafter), $180/6 months, or $300/12 months.
Educator.com is proud to provide today's scholars with advanced digital study materials that meet both their academic and financial needs. New and exciting courses are frequently added. At this time, Educator's various Math lessons | 677.169 | 1 |
This online book examines the evolution of the principle of relativity in its classical, special, and general incarnations. It includes both technical and historical perspectives of the topic. Conceptual and mathematical aspects of the theory are covered. This text is part of a larg collection of essays on math and physics at
This site includes materials on a variety of topics relating to general number theory. Each link provides a short example that would provide helpful supplemental materials in mathematics education. The lessons vary from simple algebra to more advanced topics.
This site includes a number of mathematical lessons that help to illustrate historical math concepts.
Each link provides a short example that would provide helpful supplemental materials in mathematics education. The lessons cover a variety of topics like negative numbers, square roots, and interdisciplinary science topics.
This site includes a number of mathematical lessons that relate directly to physics topics.
Each link provides a short example that would provide helpful supplemental materials in mathematics or science education (particularly in physics or astronomy curriculum). The lessons cover a variety of topics like gravity, motion, waves and astronomy.
About 90 "informal notes" by Kevin Brown on set theory and foundations: what is fuzzy logic, fractal logic, Cantor's diagonal proof, are all triangles isosceles, on Gauss's mountains, problems with the luminiferous aether, and many more. | 677.169 | 1 |
Number Power is the first choice for those who want to develop and improve their math skills. Every Number Power book targets a particular set of math skills with straightforward explanations, easy-to-follow, step-by-step instruction, real-life examples, and extensive reinforcement exercises. Use these texts across the full scope of the basic math curriculum, from whole numbers to pre-algebra and geometry. Number Power 3: Algebra covers algebra from signed numbers to equation solving and working with polynomials.
Most helpful customer reviews
I've used other Number Power books and found them amazing. This one however, lacks dept. The author gives examples of only the simple equations so when you get to the complicated ones, you're left to fend for yourself. Also, the answers at the back give you only that, the final answers. So if you get something wrong, you don't know why. There are lots of practice exercises and reviews/tests, but you'll need YouTube or supplementary books to grasp the concepts.
Most Helpful Customer Reviews on Amazon.com (beta)
This is a a excellent book for a person that is studing at home and has no help. It help me get pass the pre-algebra exam placement test for collage and I have been out of school 30 years.
9 of 10 people found the following review helpful
school teacherSept. 21 2007
By
Richard K. Mulder
- Published on Amazon.com
Verified Purchase
This materials is excellant for older students to up-grade their math skills with pride. It is geared for older students. RKM
2 of 2 people found the following review helpful
great for all agesMarch 4 2011
By
jensch
- Published on Amazon.com
As a 30 year old going back to school, remembering all this is hard... My 12 year old loves it also, Fl new math books for her grade level even confuse the teacher. Her and I are understanding at a better pace and easier explanation of how to do the problems are great. If your looking to beef up your math skills or going back for the GED, or just trying to keep up with your kids in math this book is great...
2 of 2 people found the following review helpful
One of math's little gemsFeb. 1 2010
By
D. Welles
- Published on Amazon.com
Verified Purchase
If you are in need of assistance with baisc algebra, this is the book for you! The explainations are always detailed and in a step by step fashion. If you are a visual learner and need a little help, try these book. Each book also contains a pre-test, many problelms for each type of problem, problems using everyday situations and a post test. don't for get the key to math is to practice the proper methods.
2 of 2 people found the following review helpful
Great seriesNov. 27 2009
By
Annell Wayman
- Published on Amazon.com
Verified Purchase
Number Power books are really well organized - sequential, small steps, good examples, and sufficient practice for most people. The answers in back allow users to be sure that they understand how to do the problems. I highly recommend all the books in this series. | 677.169 | 1 |
Beginning And Intermediate Algebra An Integrated Approach
9780495117933
ISBN:
0495117935
Edition: 5 Pub Date: 2007 Publisher: Thomson Learning
Summary: Easy to understand, filled with relevant applications, and focused on helping students develop problem-solving skills, BEGINNING AND INTERMEDIATE ALGEBRA is unparalleled in its ability to engage students in mathematics and prepare them for higher-level courses. Gustafson and Frisk's accessible style combines with drill problems, detailed examples, and careful explanations to help students overcome any mathematics anx...iety. Their proven five-step problem-solving strategy helps break each problem down into manageable segments: analyze the problem, form an equation, solve the equation, state the conclusion, and check the result. Examples and problems use real-life data to make the text more relevant to students and to show how mathematics is used in a wide variety of vocations. Plus, the text features plentiful real-world application problems that help build the strong mathematical foundation necessary for students to feel confident in applying their newly acquired skills in further mathematics courses, at home or on the job.
Gustafson, R. David is the author of Beginning And Intermediate Algebra An Integrated Approach, published 2007 under ISBN 9780495117933 and 0495117935. Fifteen Beginning And Intermediate Algebra An Integrated Approach textbooks are available for sale on ValoreBooks.com, and fifteen used from the cheapest price of $2 | 677.169 | 1 |
Well, if it's a book for your students, you might try something like "In the present book we're going to treat stuff you better know 100% or else you'll flunk my class!" I bet this will really hook them in! If it is a general book you might try to open with some nice problems (linear systems/linear programation, some easy probability stuff with some easy stochastic matrix, etc.) and show how can these problems be attacked with methods of lin. alg.
– DonAntonioMay 31 '12 at 14:29
2 Answers
2
I would start with the physical interpretation of vectors first, since it's the easiest to grasp, and easy to see the use of. Go through a physically motivated example, emphasize important points (like a basis, or linearity), and present a different example that might motivate you to generalize the definition (like the basis of a function space). Beginner linear algebra students can sometimes balk at the abstraction, since they're often used to more concrete ideas and an emphasis on calculation. In general I would do
The major thing is that the students see a need for linear algebra. If they're happy with their knowledge of vectors so far, why would they care about abstracting and looking at certain properties of them? You should be giving the idea of a bridge that lets you carry tools from one area (vectors here) into all sorts of other applications that don't look at all like the original, and that you need to know your bridge is sturdy before you start carrying things across.
My particular favourite example is the fourier transform and signal processing. You don't have to get into the calculus specifics, but it was a great moment for me when I realized the underlying idea of basis functions, and that not all vectors look like vectors. | 677.169 | 1 |
Drawing examples from science, engineering, health, finance, and the arts, this textbook explains the algebraic methods for solving linear equations and inequalities, factoring polynomials, adding rational expressions and radical expressions, solving a system of equations, and graphing quadratic functions. The closing chapters deal with exponential and logarithmic…
See more details below
Elementary and Intermediate Algebra, Books a la Carte Edition / Edition 3 available in
Other Format | 677.169 | 1 |
Subject: [mg109031] Re: if using Mathematica to solve an algebraic problem
From: "David Park" <djmpark at comcast.net>
Date: Sun, 11 Apr 2010 04:30:42 -0400 (EDT)
Factoring integers or factoring polynomials?
In any case, if you wanted to teach factoring methods why would you use
Factor or FactorInteger? You would use more primitive routines that did
various steps in the factoring process and students would practice with
these. If they did enough of that they might get to know the techniques. Why
would you deliberately use a routine that hides all the steps? You are
always throwing up instructional methods that are certain not to work and
ignoring approaches that could work.
If people want to do mathematics with Mathematica it is because they see
some advantage in it. The problem is that they don't know Mathematica well
enough (because it really does take time and practice to get good at it) and
Mathematica doesn't provide all the routines that might be necessary or
useful for some particular subject (which means they have to be provided by
the professor or the student himself) and it isn't totally tuned up for this
kind of study (but it keeps getting closer).
David Park
djmpark at comcast.net
From: Richard Fateman [mailto:fateman at cs.berkeley.edu]
Bill Rowe wrote:
<snip>
If one becomes very skilled at using Mathematica to
> solve problems correctly wouldn't there have to be some
> corresponding gain in understanding of how the same problems
> would be solved without Mathematica?
Not necessarily.
If you use programs like Factor[], regardless of how many times you use
them, why would you have the slightest idea of how you would factor
polynomials without Mathematica?
> It seems becoming highly
> skilled at getting correct results from Mathematica requires
> mastery of these details to a large degree. And it also seems
> understanding those details are exactly what is required to
> solve the problem without Mathematica.
Not necessarily. This newsgroup is filled with messages that look like
-- I want to solve problem X; I know how to solve it by hand; how do I
get Mathematica to do it? | 677.169 | 1 |
Product Description
By using all of the decks together, students become proficient at recognizing conic equation characteristics for circles, parabolas, ellipses, and hyperbolas. When decks are used separately, students can study equation and graph characteristics (foci, eccentricity, point pair, standard form notation) in depth. Each deck has three examples of conic equations with translated origins. Includes five card decks and a 68-page teacher's manual. Grade 10 and up.
Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States.
Orders from outside the United States may be charged additional distributor, customs, and shipping charges. | 677.169 | 1 |
Course Summary
Use these video lessons and quizzes to help you understand equations, formulas and types of numbers used in high school algebra. Learn to solve word problems, find an absolute value and graph parallel and perpendicular lines.
About the Course
The lessons in the Algebra I course offer a supplement to help you better understand what you learn in the classroom. Algebra plays some major and minor roles in work, play and life in general. Knowing how to figure out a 30% off sale price, how to get the best tax return, or how to measure the stats of your favorite ball players all require the use of algebra skills. This course provides easy-to-follow video lessons that explain how to use algebra in clear and simple terms. Check out the fun, instructional videos in this algebra course and quiz yourself on the following topics:
Basic arithmetic and word problems
Decimals and fractions
Real and imaginary numbers
Exponents, graphing and geometry
Exponential and radical expressions
Absolute values and inequalities
Ratios, percentages, statistics and probability
Linear, polynomial, binomial and quadratic equations
Our algebra instructors not only understand the importance of algebra but also realize that it's not always easy to follow or interesting to learn about. The video lessons break down chapters into bite-sized and engaging components, making learning fun and appealing. After each short video lesson, you can take the corresponding quiz to see how well you understand the information.
Course Topics
Course Chapters
Objective
Basic Arithmetic
These lessons review addition, subtraction, multiplication and division as well as covering associative property, greatest common factors, least common multiples, the use of parentheses in math, the order of operations and algebra vocabulary terms.
Solving Math Word Problems
Learn how to break down math story problems into smaller steps, personalizing problems to make them easier to understand, and restating problems using words or images.
Discover how to convert percent, decimal and fractional notations and test your skills.
Real Numbers
Use these lessons to help you understand the different types of numbers, how to graph rational numbers, and how to find the absolute value of a real number.
Exponents and Exponential Expression
This chapter helps you comprehend exponents, scientific notations, the power of zero, and how to multiply and divide exponential expressions.
Radical Expressions
The lessons in this chapter cover square roots of quotients, radicands, radical equations, computing problems using radical notations, and multiplying radical expressions with two or more terms.
Algebraic Expressions and Equations
Learn how to write arithmetic expressions, evaluate and simplify math formulas, write equations with inequalities and other common algebraic equations, solve one-step equations, use the addition and multiplication principles, and solve single-step and multi-step equations in word problems.
Properties of Functions
This chapter discusses the basics and key terms of functions as well as how to compute functions, graph a plane, compose functions and work with inverse functions.
Matrices and Absolute Value
These lessons teach you what a matrix is and how to take a determinant of a matrix. Other lessons discuss evaluating, solving, and graphing absolute value equations.
Working With Inequalities
Examples and practice problems in this chapter explain how to graph 1- and 2-variable inequalities, set notations, compound inequalities, and systems of inequalities as well as how to solve and graph absolute value inequalities.
Properties of Exponents
Discover the five main exponent properties in this chapter. Also learn how to define a zero and negative exponent and how to simplify expressions with rational exponents.
Complex and Imaginary Numbers
This chapter teaches you what an imaginary number is as well as how to add, subtract, multiply and divide complex numbers. Learn to graph a complex number on the complex plane and solve a quadratics problem with a complex number solution.
Algebraic Distribution
In this chapter, you can learn why we distribute in algebra and the difference between distributing first and adding first. Review distributing signs, how to distribute algebraic expressions with numbers and variables, how to change negative exponents to fractions, how to distribute more than one term and how to work with fractional powers.
Linear Equations
This chapter defines linear equations and covers distributive property application to linear equations. You can also learn about intercepts, standard form, graphing an undefined and zero slope, parallel and perpendicular lines and how to write and use a system of linear equations.
Factoring
Learn why we factor in this chapter as well as how to find the prime factorization of a number and use it to find least common multiples. Other lessons cover using fraction notation, factoring out variables, combining numbers and variables when factoring, transforming factors into a division problem and factoring by grouping.
Graphing and Factoring Quadratic Equations
These lessons explore tables and graphs, scatterplots, line graphs, parabola, binomials and trinomials, squares, and solving quadratic equations by factoring.
Properties of Polynomial Functions
This chapter shows you how to graph cubics, quartics and quintics; how to add, subtract, multiply and divide polynomials; and how to use synthetic division with polynomials.
This chapter teaches you how to solve perfectly and imperfectly cubed equations, how to use the greatest common factor, grouping, and integers in cubic equations, how to change radical equations into linear or quadratic equations, how to square both sides of an equation twice, and how to use synthetic division.
Quadratic Equations
These lessons teach you how to square up quadratics, solve quadratics by assigning the greatest common factor and multiplication property of zero, use the quadratic formula to solve equations, and solve quadratic inequalities using two binomials.
Measurement and Geometry
This chapter discusses the metric system and standard units of measure, how to perform basic operations and convert measurements, and how to read and interpret scales and meters. Lessons also cover points, types of lines and angles, properties of shapes, and how to find the perimeter, area, circumference and volume of a shape.
Calculations, Ratios, Percent & Proportions
Lessons define and provide examples of problems that include money and time, proportion and percent, compound interest, taxes and discounts, combinations and permutations, and distance formulas.
Data, Statistics, and Probability
Learn the probability of independent and dependent events, how to calculate for a mean, median, mode and range, and organization of data with tables and schedules, as well as bar graphs and pie charts.
Well-Known Equations
This chapter goes over some well-known theories and equations, such as the theory of relativity, Pythagorean theorem, the value of e, Isaac Newton's formula for the force of gravity, Fermat's Last Theorem, the Absolute-Value Inequality, and the quadratic formula.
Earning College Credit
Did you know… We have over 49 college courses that prepare you to earn
credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save
thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. | 677.169 | 1 |
Using the complex numbers calculator the answers to algebra problems covering this topic is only as far as your mobile phone. All the basic operations for complex are provided: addition, subtraction, multiplication, division, square root, modulus.
Graphical function plotting software. Use this software to represent any function of one variable, f(x). Our 2D function plotter provides an easy to use interface allowing you to see the graph of a chosen function in a very short time.Virtual and Mobile Art gallery, will allow you to discover Wabyanko 2007 Artworks, Hiroshima painting. Slideshow of painting and scrolling text with famous expressions to read and help you thinking...sort of meditation..may be ! | 677.169 | 1 |
Math 8
Doug Ingamells, Periods 2 & 5
Unlike years past these classes are entirely populated with 8th graders. The two classes are usually on
the same page and assignment, except that they have different "block"
days so assignment and due dates can differ. There are two other
sections of Math 8, both taught by Kerry Bayne.
PPS has decided that the first six (of twelve total) chapters in the
algebra text will be part of the Math 8 curriculum. This means that
Algebra 1-2 next year will start at Chapter 7, and students must complete the
first six chapters before enrolling in Algebra 1-2. The district
calendar has us working with a few
pre-algebra topics in addition. All students in Math 8 should
be in Algebra 1-2 the following year.
PPS uses standard A-F grades. In this class grades are weighted so
that tests count 60% and homework/classwork counts 40%. We use the
standard 90%(A), 80%(B), 70%(C), 60%(D) breakpoints.
A copy of the general information letter for this class can be found here:
Please click on the link below for a list of the planned assignments.
Note that homework is not always assigned on the exact date listed.
NOTE 2/4/14: Due to widespread failure during chapters 4 & 5 27 people are repeating this material and 10 people are working through alternate material. Check with your child to find which list they should use | 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 |
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. Five hundred nineteen Linear Algebra textbooks are available for sale on ValoreBooks.com, thirteen used from the cheapest price of $44.98, or buy new starting at $158.46 | 677.169 | 1 |
Algebra 2, Course Syllabus
1.
Welcome to Algebra 2
2.
Algebra 2 is a high school mathematics course designed for students who have successfully acquired and mastered, basic Algebraic skills. In this course, we will consider the properties of real numbers, linear and quadratic equations (and their graphs), functions, systems of equations, polynomials, rational expressions, and basic data analysis. This is relatively the same as Algebra 1, but at a slightly different level. We will go on to discuss such topics as exponential and logarithmic relations, sequences and series, and then finish with basic trigonometric functions.
3.
<ul><li>Have demonstrated mastery of Algebra 1 material with a final grade of ____________. </li></ul>STUDENT REQUIREMENTS You are expected to:
4.
<ul><li>Have demonstrated mastery of Algebra 1 material with a final grade of ____________. </li></ul>STUDENT REQUIREMENTS C (or better) You are expected to:
8.
<ul><li>Have demonstrated mastery of Algebra 1 material with a final grade of ____________. </li></ul><ul><li>Attend class daily, participating in class discussions and activities. </li></ul><ul><li>Complete homework assignments. </li></ul><ul><li>Study materials presented in class, online, and from the textbook. </li></ul><ul><li>Show a high level of maturity and determination! </li></ul>STUDENT REQUIREMENTS C (or better) You are expected to:
20.
SOME TECHNOLOGIES : At least these, probably more. Email - All students are required to have an email account! I suggest Google's gmail.
21
22
23 Voki – A site that allows anyone to create an account, and animated characters with a voice . They are then easily placed in the wiki page.
25>
26>
27>
28><ul><li>Parents are welcome and encouraged to contact me or visit our classroom at any time. </li></ul> | 677.169 | 1 |
books.google.be - With IntellisimTM, a powerful interactive math engine developed by Intellipro, Inc., you can use the CD-ROM to quickly perform dynamic calculations and analysis on over 100 of the most popular equations in this book. If you're a designer, project engineer, plant engineer or engineering student, you will... Formulas Interactive | 677.169 | 1 |
Getting started
You don't have to install Sage to try it out! In this article, we will use the notebook interface to showcase some of the basics of Sage so that you can follow along using a public notebook server. These examples can also be run from an interactive session if you have installed Sage. Go to and sign up for a free account. You can also browse worksheets created and shared by others. The notebook interface should look like this:
Create a new worksheet by clicking on the link called New Worksheet:
Type in a name when prompted, and click Rename. The new worksheet will look like this:
Enter an expression by clicking in an input cell and typing or pasting in an expression:
Click the evaluate link or press Shift-Enter to evaluate the contents of the cell.
A new input cell will automatically open below the results of the calculation. You can also create a new input cell by clicking in the blank space just above an existing input cell.
Using Sage as a powerful calculator
Sage has all the features of a scientific calculator—and more. If you have been trying to perform mathematical calculations with a spreadsheet or the built-in calculator in your operating system, it's time to upgrade. Sage offers all the built-in functions you would expect. Here are a few examples:
If you have to make a calculation repeatedly, you can define a function and variables to make your life easier. For example, let's say that you need to calculate the Reynolds number, which is used in fluid mechanics:
When you type the code into an input cell and evaluate the cell, your screen will look like this:
Now, you can change the value of one or more variables and re-run the calculation:
Sage can also perform exact calculations with integers and rational numbers. Using the pre-defined constant pi will result in exact values from trigonometric operations. Sage will even utilize complex numbers when needed. Here are some examples:
Symbolic mathematics
Much of the difficulty of higher mathematics actually lies in the extensive algebraic manipulations that are required to obtain a result. Sage can save you many hours, and many sheets of paper, by automating some tedious tasks in mathematics. We'll start with basic calculus. For example, let's compute the derivative of the following equation:
The following code defines the equation and computes the derivative:
var('x') f(x) = (x^2 - 1) / (x^4 + 1) show(f) show(derivative(f, x))
The results will look like this:
The first line defines a symbolic variable x (Sage automatically assumes that x is always a symbolic variable, but we will define it in each example for clarity). We then defined a function as a quotient of polynomials. Taking the derivative of f(x) would normally require the use of the quotient rule, which can be very tedious to calculate. Sage computes the derivative effortlessly.
Now, we'll move on to integration, which can be one of the most daunting tasks in calculus. Let's compute the following indefinite integral symbolically:
The code to compute the integral is very simple:
f(x) = e^x * cos(x) f_int(x) = integrate(f, x) show(f_int)
The result is as follows:
To perform this integration by hand, integration by parts would have to be done twice, which could be quite time consuming. If we want to better understand the function we just defined, we can graph it with the following code:
f(x) = e^x * cos(x) plot(f, (x, -2, 8))
Sage will produce the following plot:
Sage can also compute definite integrals symbolically:
To compute a definite integral, we simply have to tell Sage the limits of integration:
This would have required the use of a substitution if computed by hand.
Have a go hero
There is actually a clever way to evaluate the integral from the previous problem without doing any calculus. If it isn't immediately apparent, plot the function f(x) from 0 to 1 and see if you recognize it. Note that the aspect ratio of the plot may not be square.
The partial fraction decomposition is another technique that Sage can do a lot faster than you. The solution to the following example covers two full pages in a calculus textbook —assuming that you don't make any mistakes in the algebra!
We'll use partial fractions again when we talk about solving ordinary differential equations symbolically.
Linear algebra
Linear algebra is one of the most fundamental tasks in numerical computing. Sage has many facilities for performing linear algebra, both numerical and symbolic. One fundamental operation is solving a system of linear equations:
Although this is a tedious problem to solve by hand, it only requires a few lines of code in Sage:
Notice that Sage provided an exact answer with integer values. When we created matrix A, the argument QQ specified that the matrix was to contain rational values. Therefore, the result contains only rational values (which all happen to be integers for this problem).
Solving an ordinary differential equation
Solving ordinary differential equations by hand can be time consuming. Although many differential equations can be handled with standard techniques such as the Laplace transform, other equations require special methods of solution. For example, let's try to solve the following equation:
It turns out that the equation we solved is known as Bessel's equation. This example illustrates that Sage knows about special functions, such as Bessel and Legendre functions. It also shows that you can use the assume function to tell Sage to make specific assumptions when solving problems.
More advanced graphics
Sage has sophisticated plotting capabilities. By combining the power of the Python programming language with Sage's graphics functions, we can construct detailed illustrations. To demonstrate a few of Sage's advanced plotting features, we will solve a simple system of equations algebraically:
var('x') f(x) = x^2 g(x) = x^3 - 2 * x^2 + 2
solutions=solve(f == g, x, solution_dict=True)
for s in solutions: show(s)
The result is as follows:
We used the keyword argument solution_dict=True to tell the solve function to return the solutions in the form of a Python list of Python dictionaries. We then used a for loop to iterate over the list and display the three solution dictionaries. Let's illustrate our answers with a detailed plot:
We created a plot of each function in a different colour, and labelled the axes. We then used another for loop to iterate through the list of solutions and annotate each one.
Visualising a three-dimensional surface
Sage does not restrict you to making plots in two dimensions. To demonstrate the 3D capabilities of Sage, we will create a parametric plot of a mathematical surface known as the "figure 8" immersion of the Klein bottle. You will need to have Java enabled in your web browser to see the 3D plot.
In the Sage notebook interface, the 3D plot is fully interactive. Clicking and dragging with the mouse over the image changes the viewpoint. The scroll wheel zooms in and out, and right-clicking on the image brings up a menu with further options.
Typesetting mathematical expressions
Sage can be used in conjunction with the LaTeX typesetting system to create publication-quality typeset mathematical expressions. In fact, all of the mathematical expressions in this article were typeset using Sage and exported as graphics.
A practical example: analysing experimental data
One of the most common tasks for an engineer or scientist is analysing data from an experiment. Sage provides a set of tools for loading, exploring, and plotting data. The following series of examples shows how a scientist might analyse data from a population of bacteria that are growing in a fermentation tank. Someone has measured the optical density (abbreviated OD) of the liquid in the tank over time as the bacteria are multiplying. We want to analyse the data to see how the size of the population of bacteria varies over time. Please note that the examples in this section must be run in order, since the later examples depend upon results from the earlier ones.
Time for action – fitting the standard curve
The optical density is correlated to the concentration of bacteria in the liquid. To quantify this correlation, someone has measured the optical density of a number of calibration standards of known concentration. In this example, we will fit a "standard curve" to the calibration data that we can use to determine the concentration of bacteria from optical density readings:
What just happened?
We introduced some new concepts in this example. On the first line, the statement import numpy allows us to access functions and classes from a module called NumPy. NumPy is based upon a fast, efficient array class, which we will use to store our data. We created a NumPy array and hard-coded the data values for OD, and created another array to store values of concentration (in practice, we would read these values from a file) We then defined a Python function called standard_curve, which we will use to convert optical density values to concentrations. We used the find_fit function to fit the slope and intercept parameters to the experimental data points. Finally, we plotted the data points with the scatter_plot function and the plotted the fitted line with the plot function. Note that we had to use a function called zip to combine the two NumPy arrays into a single list of points before we could plot them with scatter_plot.
Time for action – plotting experimental data
Now that we've defined the relationship between the optical density and the concentration of bacteria, let's look at a series of data points taken over the span of an hour. We will convert from optical density to concentration units, and plot the data.
What just happened?
We defined one NumPy array of sample times, and another NumPy array of optical density values. As in the previous example, these values could easily be read from a file. We used the standard_curve function and the fitted parameter values from the previous example to convert the optical density to concentration. We then plotted the data points using the scatter_plot function.
Time for action – fitting a growth model
Now, let's fit a growth model to this data. The model we will use is based on the Gompertz function, and it has four parameters:
What just happened?
We defined another Python function called gompertz to model the growth of bacteria in the presence of limited resources. Based on the data plot from the previous example, we estimated values for the parameters of the model to use an initial guess for the fitting routine. We used the find_fit function again to fit the model to the experimental data, and displayed the fitted values. Finally, we plotted the fitted model and the experimental data on the same axes.
Summary
This article has given you a quick, high-level overview of some of the many things that Sage can do for you.
Specifically, we looked at:
Using Sage as a sophisticated scientific and graphing calculator
Speeding up tedious tasks in symbolic mathematics
Solving a system of linear equations, a system of algebraic equations, and an ordinary differential equation | 677.169 | 1 |
Learning Matlab
A Tutorial for Getting Started in MatLab by Thomas M. Green
Natural & Applied Sciences Division (NAS)
Mathematics Department
Matlab is a computer program for doing numerical computation. It began
as a "MATrix LABoratory" program in the late 1970s, intended to provide
interactive access to the FORTRAN libraries Linpack and Eispack. These are
carefully tested, high-quality programming packages for solving linear
equations and eigenvalue problems.
The goal of MatLab is to enable scientists to use matrix-based techniques to
solve problems, using state-of-the-art code, without having to write programs
in traditional languages like C and Fortran.
More capabilities have been added as time has passed -- many more commands,
a programming environment, and very fine graphics capabilities.
Matlab is available from The MathWorks, Inc. Natick, MA.
Information can be found at "
The following sessions will introduce you to MatLab and how you can use it
to do calculations, solve problems, create plots and write your own functions.
Use each session as a guided tour as you work through the examples presented
therein while using MatLab. These sessions are designed to introduce the
features of MatLab to a Pre-Calculus student so that MatLab can be used in
the study of the Calculus and higher mathematics.
Note:
(Also, we offer a short-term, 6 week course,
Math 175 - Intro. to MatLab, beginning in the Fall '98 semester and
in subsequent semesters covering this material essentially
at the pre-calculus level.)
Look at
Outline
(If you are viewing a printed copy of this document, then be advised that
these sessions are available on-line over the Internet. When one visits
the Contra Costa College Home Page ( it's found
via a link from the the Math Dept. Home Page. )
This document last modified: May 15, 2004.
By Thomas M. Green Contra Costa College
San Pablo, CA 94806
Permission to use this document is granted so long as
the author is acknowledged.
Please send comments and suggestions to:
Thomas M. Green c/o CCC Math Dept.
hwalters@contracosta.edu
First Session
________________________________
MatLab Demos
MatLab Commands, Functions, Operations covered in this Session:
COMMANDS:
helpwin
helpdesk
demo
quit
Note:
In these sessions, rather than continually switching back and forth
between this window and MatLab's window, it might be easier to print
these sessions and use the printout to follow along while working in
MatLab.
MatLab is installed in the NAS Computer Lab, or check with the Natural
and Applied Science Division.
To start the program choose Math and then
MatLab from the Start menu of Windows 95.
The system should respond with the MatLab logo and then with the MatLab
workspace as follows:
This version is for educational classroom use only.
To get started, type one of these commands: helpwin, helpdesk, or demo
>>
The ">>" is Matlab's prompt. You type your commands for MatLab
following this prompt.
To quit MatLab type quit at the prompt.
>> quit
Before we quit, however, our first session will be to explore some demos to see
examples of MatLab at work. Type:
>> demo
The MatLab Demos window will display three dialog boxes and two buttons.
(You may want to expand the window to the full screen.)
In the first box select the Visualization option.
Read the text in the second box.
In the third box select the 2-D Plots option, then
click the Run the "Demo" button.
Follow the directions in the MiniCommand window that appears.
Close the demo and select Klein Bottle Example from the
third box for your next demo. Check out the Info
button before closing this demo.
Next try the Vibration Movie.
Now, back at the MatLab Demos window select Gallery
in the first box. Again read the second box and then select
Knot in the third box and click the Run the "Demo
button. Close that and try another selection or two before
proceeding.
Back at the MatLab Demos window select Games
in the first box. Again read the second box and then select
one of the game demos in the third box and try it out.
Next, select Numerics in the first box of the MatLab
Demos window, read the second box, and select
2-D Visual Solutions in the
third box. Now click the Run the "Demo" button.
After viewing the demo, answer the following question? Which is larger, e^pi or pi^e ?
Which is larger, e^pi or pi^e ?
Ans. __________
Write your answer on the printed copy.
Close the demo, close the MatLab Demos window, and enter the "quit"
command at the prompt to terminate this MatLab session.
Finally, during the next week visit the MathWorks website several times
for more information.
Matlab is available from The MathWorks, Inc.
Natick, MA.
Information can be found at "
If you have the Student Edition of MatLab or your own copy, you can make a
record of your sessions. The "diary" command saves your work in a file
named "session2" as shown below:
Type:
>> diary session2
To stop recording the session, use
>> diary off
More than one command may be
entered on a single line, if they are seperated by commas.
Type in each expression:
>> 2+3
>> 3*4, 2-4
As is the convention, powers are performed before division and
multiplication, which are done before subtraction and addition.
>> 2+3*4^2
The arrow keys
allow "command-line editing," which cuts down on the amount of
typing required, and allows easy error correction. Press the "up" arrow, and
add "/5." What will this produce?
>> 2+3*4^2/5
Note:
Repeated pressing of the arrow key
scrolls back through prior commands.
Similarly, pressing the arrow key
scrolls forward through the commands.
At any time pressing the arrow keys moves the cursor within
the current command at the prompt.
To correct an error in a previous command, use the arrow keys to place the
cursor at the proper location, press "Delete" to remove a character, or
enter a character to insert it, or both if necessary. Press "Enter" to
tell MatLab to reevaluate the expression.
Parentheses may be used to group terms, or to make them more readable.
>> (2 + 3*4^2)/5
Variable names consist of a letter, followed by any number of letters,
digits, or underscores. MATLAB uses only the first 31 characters of a
variable name. Names are case sensitive; MatLab distinguishes between
uppercase and lowercase letters. A and a are
not the same variable.
The "=" sign is used to assign values to variables and the "==" sign
is used to compare variables.
>> x = 4
>> y = x^3
>> y/x
>> X = 1;
>> X == x
>> Area = x*y
(A semicolon placed at the end of a MatLab statement suppresses the printing
of the results.)
If no other name is given, an answer is saved in a variable named
ans.
>> 4 + 6
>> ans, z=ans^2, ans
Here z was defined in terms of ans. The result was called
z, so ans was unchanged.
To get a list of your variables, use
>> who
To evaluate your variables, just enter their names.
>> x, y, ans, X, Area
Note:
More than one command may be
entered on a single line, if they are seperated by commas.
A semicolon placed at the end of a MatLab statement suppresses the printing
of the results.
If no other name is given, an answer is saved in a variable named
ans.
To save your workspace variables you can use the save command.
This will save all workspace variables in a file named matlab.mat.
The data can be retrieved with the load command.
(These commands are also available as options in the MatLab File
menu.)
To save all workspace variables in a file named myvars.mat, in reloadable
format, use
>> save myvars
To restore the workspace, use
>> load myvars
There are other variations of the save command and you can
either look these up in the text, the reference manuals, use the
help save command, or use the helpdesk command.
There's also a "lookfor" command, so that you don't have to guess the topic
name precisely (more on this in Session 3).
>> help
>> help save
>> help sqrt
>> helpdesk
>> dir
All arithmetic is done to double precision
[about 16 decimal digits], even though results are normally
displayed in a shorter form.
MATLAB uses conventional decimal notation for numbers, with an optional
decimal point and leading plus or minus sign. Scientific notation
uses the letter e to specify a power-of-ten scale factor.
Imaginarynumbers use either i or
j as a suffix. Some examples of legal numbers are
3 -99 0.0001
9.6397238 1.60210e-20 6.02252e23
1i -3.14159j 3e5i
All numbers are stored internally using the long format
specified by the IEEE floating-point standard. Floating-point numbers
have a finite precision of roughly 16 significant decimal
digits and a finite range of roughly 10-308 to
10+308.
Suppose we want to solve the quadratic equation ax2 + bx + c = 0.
(In Session 4 we will learn about a special built-in function called
roots for solving polynomial equations in general. For now we will
use the quadratic formula.)
The roots are given by
Matlab statements, like the above, can be prepared with any editor, and
stored in a file for later use. The file is referred to as a script,
or an M-File (since they must have names of the form
filename.m). We can also use the MatLab special editor.
From the File menu choose New and select M-File.
This brings up the text editor window where we can enter our statements.
Save the file with the extension .m, for example, quadrat.m.
Then in the MatLab workspace just enter the prefix file name to have
MatLab load and execute the statements.
>> quadrat
This approach is convenient for longer sequences of statements or when
data is entered into large arrays or matrices. The files can be re-edited
to make changes if desired, and then re-executed. The what
command returns a listing of all M-Files in the current directory or
folder:
>> what
The command edit calls up the special editor, so changes
can be made if necessary:
>> edit quadrat.m
Finally, to stop a Matlab session and return to the operating system, use
MatLab Commands, Functions, Operations covered in this Session:
COMMANDS:
lookfor
help
format
clear
FUNCTIONS:
sqrt
round
ceil
floor
real
imag
conj
abs
exp
log
log10
cosh
acosh
sin
cos
tan
asin
fzero
fmin
CONSTANTS:
realmax
realmin
pi
i, j
eps
inf
nan
MATLAB provides a large number of standard elementary mathematical
functions, including abs, sqrt, exp,
and sin.
Taking the square root or logarithm of a negative number is not an error;
the appropriate complex result is produced automatically.
>> a=sqrt(-1)
>> b=sqrt(a)
>> c=b^2
>> b/a
>> b\a
>> a/b
In MatLab no special handling of complex numbers is required. Operations
on complex numbers are written the same as for real numbers and the results
are handled by MatLab automatically. Solve the following quadratic
equation ax2 + bx + c = 0 if a, b, and c each equal 1.
MATLAB also provides many more advanced mathematical functions, including
Bessel and gamma functions. Most of these functions accept complex arguments.
For a list of the elementary mathematical functions, type
>> help elfun
Some of the functions, like sqrt and sin,
are built-in. They are part of the MATLAB core so they are
very efficient, but the computational details are not readily accessible.
Other functions, like gamma and sinh, are
implemented in M-files (We'll examine M-files further in Session 4).
You can see the code and even modify it if you want.
Try the following to determine the effect of the functions round,
ceil and floor.
Infinity is generated by dividing a nonzero value by zero, or by evaluating
well defined mathematical expressions that overflow, i.e.,
exceed realmax. Not-a-number is generated by trying to evaluate
expressions like 0/0 or inf-inf that do not
have well defined mathematical values.
Note: The function names are not reserved. It is possible to overwrite any of them with a new variable, such as
eps = 1.e-6
and then use that value in subsequent calculations. The original function
can be restored with
Examine the last four results and draw a conclusion from what you observe.
In standard mathematical notation write your conclusions in the table below:
_________________________________
_________________________________
_________________________________
_________________________________
Write your answers on the printed copy.
MatLab also provides a set of function functions. By that, we
mean functions that work with arguments which are themselves functions.
As an example, we will examine the function fzero:
>> x = fzero( 'sin', 3)
This returns the value of pi since the sine of pi is
zero. The function fzero takes two arguments, the first is
the name of the function presented as a string in single quotes, the second
is an arbitrary value chosen near the value of the "zero of the function".
The function fzero will use numerical methods to try to find
the point where the input function crosses the x-axis closest to the input
value.
For functions with no valid zeros, fzero may execute until
you terminate it (with control-C) or return an erroneous result.
Try the following (and record your results on the printed copy):
A limitation of fzero is that zeros of functions that touch,
but do not cross the x-axis are not found by fzero since it's
looking for a sign change in the evaluation of the input function. For
polynomial functions we can use another function called roots
that works for polynomials. We will cover polynomials in the next session.
Another function function is fmin which returns one of
the x-values in the domain specified where the minimum value of the input
function can be found. The next example finds the x-value where the sine
function has a minimum value over the interval from 0 to 2*pi.
>> x = fmin( 'sin', 0, 2*pi)
What did you find? ____________________________________
Then to get the minimum value of the function we need:
Session 4
MatLab Commands, Functions, Operations covered in this Session:
COMMANDS:
function
(function functions)
(M-files)
FUNCTIONS:
roots
poly
real
polyval
linspace
conv
deconv
function
prod
OPERATORS:
:
.*
./
.\
.^
.'
[ ]
Polynomials & Vectors
Interestingly, in MatLab a polynomial is represented by a
vector! The elements of the vector are the coefficients of the
polynomial in descending order.
For example, the polynomial x2 + 8x + 12 is entered as
>> p = [1 8 12]
The polynomial x4 - 12x3 + 25x + 116 is entered as
>> q = [1 -12 0 25 116]
Note:
Vectors in MatLab are arrays (ordered lists) of elements, numbers
in this case.
The elements are separated from one another by a space (or spaces)
and not commas.
The elements are enclosed in brackets, [ ]. (The same is true of
matrices in MatLab, but matrices will be discussed at another time.)
Terms with zero coefficents must be included.
One of the most useful functions for polynomials, and a very powerful
function, is roots for finding the roots of a
polynomial.
>> roots_of_p = roots(p)
>> roots_of_q = roots(q)
The roots of a polynomial also form a vector in MatLab. This vector,
however, is organized as a column vector, as opposed to the polynomial
vector representation which is organized as a row vector.
Thus, in MatLab you will see a column display of the roots.
Given the roots of a polynomial, it is also possible to construct the
associated polynomial by using the poly function.
>> original_p = poly(roots_of_p)
>> original_q = poly(roots_of_q)
Occasionally, when complex roots are involved, you may get complex
forms for the coefficients. If the imaginary parts of these expressions
are zeros, they can be discarded as follows:
A polynomial can be evaluated at a value of the independent variable
using polyval. The polynomial p, given above
for instance would be evaluated at, say -6, one of its roots, as
follows:
>> value_of_p = polyval( p, -6)
(Of course, if -6 is a root, the value of p should be ____________)
Try the following:
>> value_of_q = polyval( q, -1-i)
>> value_of_q = polyval( q, [2 3])
Here, we see that a polynomial can be evaluated at complex values and
if the the second argument is a vector, then the polynomial is evaluated
at each of the elements, and value_of_q is itself a vector in
the latter case.
Also, in this example, the values of q
at 2 and at 3 are of opposite sign implying that one of the roots
of q is between 2 and 3. Check it out.
The function polyval is similar to a function function
(Session 3), however, the arguments for polyval are two
vectors. Most of MatLab's utility is based on using vectors or matrices
for input and output, making it a very powerful mathematical tool.
The built-in elementary functions, for instance, all accept a vector
input. Try the following:
>> x = [ 0 pi/6 pi/4 pi/3 pi/2 ] ;
>> y = sin(x)
The colon operator,:, in MatLab is used to create vectors. The expression
1:10 is the same as [1 2 3 4 5 6 7 8 9 10]. Suppose we wanted to
evaluate the polynomial q over the integers from -5 to 5.
In MatLab enter the following:
>> vector = -5:5
>> value_of_q = polyval( q, vector)
In this example, by viewing ans we can determine that q is a
decreasing function over the interval from -5 to 5.
To create a vector with arbitrary
real increments MatLab provides a two colon operator as follows:
>> vector = -5:0.1:5
>> value_of_q = polyval( q, vector)
This time q is evaluated at over one hundred values from
-5 to 5, incrementing the independent variable by 0.1.
If we wanted to evaluate q at exactly 100 points (values)
we would use MatLab's linspace function. linspace(-5, 5, 100) generates 100 evenly spaced points
starting with -5 and ending with 5. The space between points (or
increment) is controlled by MatLab.
In MatLab the multiplication of two polynomials is accomplished by
the convolution of two arrays. The conv
function is used and takes two arguments, the polynomials to be multiplied.
For example, to multiply the polynomial x2 + 8x + 12 and the
polynomial x4 - 12x3 + 25x + 116 enter the following:
>> p = [1 8 12]; q = [1 -12 0 25 116] ;
>> product = conv(p, q)
In this example, the degree of the product is 6, which can also be
determined by counting the terms in ans (starting at zero).
Multiplying more than two polynomials requires repeated use of
conv.
Using conv find the following powers of x + 1:
(x + 1)^2
_________________________________
(x + 1)^3
_________________________________
(x + 1)^4
_________________________________
(x + 1)^5
_________________________________
Write your answers on the printed copy.
Division is accomplished with the function deconv
which also takes two arguments, but this time the order of the arguments
matters. The first argument is the dividend and the second is the
divisor. Also, not all divisions come out exact, there can be a
nonzero remainder. The following examples will illustrate this (using
p and q from above):
Note that the results, quotient and remainder are collected
in an array of two vectors, each representing a polynomial. Consider this,
what are the degrees of the quotient and remainder in the two examples
above?
There are no functions in MatLab to add or subtract polynomials.
However, polynomials are represented by vectors and these can be
added, subtracted and multiplied by a scalar if desired. The difference
is that vectors must be of the same size in order to be added
or subtracted. Thus, if v1 = [1 2 3] and v2 = [3 -4 5], then
>> v1=[1 2 3]; v2=[3 -4 5];
>> Sum=v1 + v2
This works out ok. But that being the case, how would you add p
and q from the above examples? Write the MatLab statements
to add p and q in the boxes below: (Hint: Sum = p + q won't work
unless you redefine p.)
p =
_________________________________
q =
_________________________________
Sum =
_________________________________
Write your answers on the printed copy.
Note:
Although there are no functions in basic MatLab to add or subtract
polynomials, there are tools in the Symbolic Math Toolbox
(another MathWorks product) to enter symbolic expressions, symbolic
equations, etc., and to carry out all of the fundamental algebraic
operations (including addition and subtraction, and solving
equations symbolically), as well as those processes and operations
of the calculus, linear algebra, differential equations, and more.
The handling of symbolic expressions, which are character strings
or arrays of character strings, is the topic of another set of
tutorial lessons.
User Functions and M-Files
We will use the factorial function as an example of a user-defined
function.
Line 1: A function definition or header line. This line defines
the function name and the number and order of the input and output argumnents.
Line 2: A H1 line. H1 stands for "help 1" line. This line is
used by the online MatLab help system when help or
lookfor command are invoked. Line 2 starts with a % symbol
indicating that this line is a comment, not an executable statement.
Lines 3-5: Additional comments providing more of the "help" text, all
beginning with the % symbol.
Last Line(s): A function body. May consist of many lines.
This part of the function contains the statements to perform the
computations and assign values to any output arguments.
The function definition line, function f = fact(n),
has five parts:
the keyword, function.
the output argument, f.
the equal sign, =.
the function name, fact.
the input argument, n.
There can be more than one input argument as well as more than one
output argument. For example,
function [x,y] = polarconv(r, theta)
Use brackets for the output arguments and separate the arguments with
commas.
Now that we have seen a MatLab function, we need to put it in action.
User defined functions, such as the example above, are placed in
special MatLab files called M-Files. These files can be created
using a text editor or the MatLab special editor, just as was the
case with MatLab scripts discussed in Session 2.
From the File menu choose New and select M-File.
This brings up the text editor window where we can enter our functions.
When the file is saved it should be saved with a filename the same
as the function name, followed by .m . In the example above, the
fact function we would type in each of the lines indicated,
including the comment lines,
and then save the file with the name fact.m .
That is, fact is used just like any other MatLab function
might be used.
(Note, mathematically, the value of z given should be the number of
differnent groups of 10 one could select from a collection of 14 objects.)
Create the function y = f(x) where
f(x) = x2 - 1/x and evaluate the function at
x equal to the values -1, -0.5, 0, 0.5, and 1. (The function
should be undefined at x = 0.)
Now create the same function, f(x), so that it will accept a vector input.
In order to do this we need to learn more about vector operations.
MatLab Array Operations
Assume U and V are vectors of the same size and
s is a scalar.
Now to create the function, f(x), so that it will accept a vector input,
we just need to change the operations to the appropriate array operations.
For example, change x^2 to x.^2 and 1/x to
1./x.
Use this new version of f(x) to evaluate it at
x = [-1:0.5:1] and then find its zero(s) with fzero
(see Session 3).
New functions can be created in terms of existing functions in MatLab.
For additional practice, create a function called, cat
that takes one input argument, x, and returns a value equal to
(exp(x) + exp(-x))/2
Use the cat function to find the values of cat(-2)
through cat(2). Then find the values of the built-in
cosh function over the same domain. What did you
discover?
Try the function function fmin on the cat
function. (See Session 3)
The expression
fact(n)/(fact(r)*fact(n-r))
is called a combinatorial or a binomial coefficient (with
r less than or equal to n).
In the
case of the binomial coeficient, it is returned by this expression as the
coefficent of the term involving xr when the binomial,
(x + 1), is raised to the nth power and
expanded.
Write a function called comb that will return the value
of this expression when called with two input arguments, n
and r.
Use this function to find the values of
comb(4,4), comb(4,3), comb(4,2), comb(4,1), comb(4,0)
Compare your results to the 4th row of Pascal's Triangle.
Note:
MatLab also provides the common programming constructs, such as,
logical operators, if_then_else decision making, for_ loops, and while_
loops. These can be used in creating your own functions or directly
in the MatLab workspace. Here is an example, creating
a "program loop."
MatLab Commands, Functions, Operations covered in this Session:
COMMANDS:
figure
grid
hold
gtext
orient
print
clf
zoom
axis
gcf
pause
FUNCTIONS:
linspace
plot
figure
axis
title
xlabel
ylabel
text
polar
cart2pol
pol2cart
fplot
subplot
fill
The graphics capabilites of MatLab are extensive, including both 2 and 3
dimensional plots. Begin by trying the following:
>> x = linspace(-pi, pi, 40) ;
>> y = sin(x) ;
>> plot(x, y)
Press the enter key to return from the figure window to the
MatLab workspace.
The graph was generated by MatLab as a plot of y vs. x ( both x and y
are vectors (arrays)) by placing 40
points in the figure window and connecting them by straight lines.
In this example x is a vector of 40 entries evenly positioned
between -pi and pi. The plot function
can take two or more arguments, the first two of which are vectors.
(plot can also take just one vector argument, see the online
help system for more information.)
The following generates a graph of x vs. y and adds a grid system:
>> plot(y, x)
>> grid
>> figure(1)
The grid system is a feature of the current plot. Just entering
the grid command toggles the grid from 'off' to 'on' or
'on' to 'off' (if it was already on) in the current figure window.
We can also turn it on or off with the commands >> grid on
or >> grid off. Other features
include axis and graph annotations, such as, labels, legend,
and text. We will demonstrate these in the upcoming examples.
After our first plot, we need to recall the figure window with
figure(1).
MatLab directs all graphics output to a figure window. When we add
a feature, we can redisplay the figure window in several ways, one of which
is to type the statement
>> figure(1)
We may have several figure windows available in any given session, and the
figure function returns the selected figure window to view.
The other way to view a figure window is to 'click' on its icon in the
status bar at the bottom of the workspace window, or the 'Window' pull-down
menu from the menu bar near the top of the workspace window. figure by itself opens a new figure window:
>> figure
The command gcf gets the current figure window handle.
We will use this frequently in our graphic scripts.
There are many more properties for the figure function that
we won't go into here. Also the set function can specify
properties, such as, background colors, axes colors, window resizing, and
more. See the online help system for more information.
When we generate a new plot, the old plot is cleared unless one of the
following conditions hold:
a new figure window is selected, for instance, >> figure(2),
or
the statement >> hold on is issued.
In the first case we end up with two figure windows; in the second case
we have only one figure window and subsequent plots (using hold)
and features are added to that figure window.
The following plots y vs. x and x vs. y in the same figure window:
>> plot(x, y)
>> hold on
>> plot(y, x)
>> hold off
>> figure(gcf)
We can get the same result with the 'extended' plot function:
>> plot(x, y, y, x)
>> figure(1)
Here two plots, y vs. x and x vs. y
are created in the same figure.
Sometimes we just want to start over with a figure window.
Use the command clf to clear the current figure window.
After we generate a plot, we add features, such as demonstrated in the
following: (this is a good place to create a script m-file!)
There are several features added to the figure window in the example
above: grid, axis, title, xlabel, ylabel, and text.
The axis function sets the scaling for the x- and y-axis
on the current plot, overriding MatLab's automatic scaling.
The general form is axis([ xmin, xmax, ymin, ymax ]).
To make the x- and y-axis data units to be equal, use axis
equal or axis equal tight. The latter
form causes the axes shape to conform to the plotted data.
We can return to automatic scaling with
>> axis auto
>> figure(1)
Here, axis is used more like a command than a function with
auto as a parameter, however, in MatLab commands and functions
are interchangeable to a certain extent. For instance, the command
given above could be written axis( 'auto' ). The parameter
'auto' is now the argument of the function expressed as a string.
There are many more properties for the axis function that
we won't go into here. See the online help system for more information.
The function text(x,y,S) adds the character string S to the
current plot at the coordinates (x,y).
Another command, gtext lets you place text on your plot
interactively using the mouse.
The plot function also has an optional string argument, called
linetype, where we can specify color, linestyle, and marker
for the given plot. For example:
>> plot(x, y, 'red : pentagram')
>> figure(gcf)
plots a red dotted line marked off at each point of the vectors x & y
with a five point star symbol (pentagram). Without this string argument
the default linetype is a solid line without markers and in the MatLab
automatic color choice.
LineType Symbols
Symbol
Color
c
cyan
m
magenta
y
yellow
r
red
g
green
b
blue
w
white
k
black
Symbol
Line Style
-
solid (default)
--
dashed
:
dotted
-.
dash-dot
none
no line
Symbol
Marker Description
+
plus signs
o
circle
*
asterisk
.
point
x
cross
square
square
^
upward pointing triangle
v
downward pointing triangle
>
right pointing triangle
<
left pointing triangle
pentagram
five-pointed star
hexagram
six-pointed star
none
no marker (default)
The following code plots the sine function twice, once with the default
linetype built into MatLab, the second with the data points marked with
green asterisks :
There are other options for the print command.
See the online help system for more information.
We can interactively zoom in or out at various points
of a 2-D plot in order to view a specific region in more detail.
The command zoom on turns on the zoom mode
and zoom off turns it off. While in zoom mode
we are prompted for the zoom center with the mouse.
We can zoom in by pressing the left mouse button and zoom out by
pressing the right mouse button. The command zoom out
zooms out fully, and just using the command zoom toggles
the zoom mode.
We can also create polar coordinate plots where the independent
variable, t in the following example, is measured in radians:
Here we created two different figure windows. The pause
command suspends execution until a key is pressed.
Like plot, the cart2pol function takes two
vector arguments representing the abscissae and ordinates of points
determined to be Cartesian, but cart2pol returns two column
vectors representing the corresponding polar coordinates which can then
be plotted using polar.
The function pol2cart works in a similar manner to reverse
the process.
The preceding example also illustrates the plotting of parametric
equations, with the parameter being t in this case for
plotting xy coordinates for a circle.
Using parametric equations, we can plot many possibilities. Here is
an example of an ellipse:
For the purposes of this example, there are only 5 points since 0 and
2*pi correspond to the same plotted point, and since we need
4 more points, we use 6 in the linspace function.
Another function function in MatLab that plots functions is
fplot. This is especially useful for plotting user defined
function (M-Files). For example, the function from Session 4,
f(x) = x2 - 1/x, called f could be plotted
as follows:
>> clf
>> fplot('f', [-1 1])
>> figure(gcf)
The first argument for fplot is a string naming the function,
the second argument is a vector specifying the x-axis limits for the plot.
Also, the string can include a variable x and a designation for
the y-axis limits if desired:
>> fplot('f(x)', [-1 1 -5 5])
>> figure(gcf)
Addtionally, a linetype can be added as a third argument (see
plot above).
For simple functions of x that can be expressed as a single
character string, we can plot the function without
creating a M-File using fplot. This makes it very convenient
for plotting user-defined simple functions. Here is an example:
Another use of fplot is the following: [x y] = fplot(...)
where the abscissae and ordinates for the function are returned in the
column vectors x and y. No plot is drawn on the screen.
The function can then be plotted with plot(x,y).
We will conclude this session with a discussion of the
subplot function.
Above we saw plots in multiple figure windows, and we saw plots
of several functions on one coordinate axes system in one figure window.
Now, subplot breaks the figure window into an m-by-n matrix
or array of small rectangular panes, each capable of containing its own
coordinate axes and plots. In the following example we will plot the
Cartesian and polar functions (demonstrated above) in the same figure
window, but on different coordinate systems:
In this case we created two plots side by side (one row, 2 columns).
In general, subplot( m, n, p) creates m-rows and n-columns
and makes the pth pane the current plotting focus.
These panes are indexed along the top row first, then the second row,
etc.
We can clear the figure window with either clf or we can
restore the default configuration with subplot(1, 1, 1).
Session 6
MatLab Commands, Functions, Operations covered in this Session:
FUNCTIONS:
det
inv
eye
OPERATORS:
\ matrix left div.
* matrix mult.
The underlying data structure for most of MatLab's operations and functions
is the matrix.
A matrix is a rectangular array of numbers: for example,
[ 1 2 3 ]
[ 4 5 6 ]
defines a matrix with 2 rows, 3 columns, 6 elements.
Every Matlab variable refers to a matrix, even a
number is a 1 row by 1 column matrix.
To enter a matrix in MatLab we use the brackets, [ ], and semi-colons, ;,
to separate the rows.
A matrix is entered in "row-major order", i.e., all of the first row, then
all of the second row, etc. The elements are separated from each other by
spaces or by commas. Here is a 2 row by 3 column matrix assigned to a:
>> a = [1,2,3; 4 5 6]
The element in the i'th row and j'th column of a is referred to by
naming the row-column pair in parentheses following the matrix variable:
>> a(1,2) %element in row 1 and column 2
It's very easy to modify matrices:
>> a(2,3) = 10
Without explaining everything about matrices at this time (you may
take a course in Linear Algebra at some point in your studies where
the study of matrices is rigorously examined) we will use matrices
in MatLab to solve systems of linear equations.
To illustrate consider the following example:
John works part time for an establishment that is open 24 hours
per day. Each week he may be asked to work days, swing shift,
or grave yard and he is paid different rates for each shift.
Last week he worked 10 hours on days, 5 hours
swing shift, and 5 hours grave yard and earned $152.50. The
week before he worked 12 hours on days, 6 hours swing shift,
and 2 hours grave yard and earned $147. The week before that
John worked 8 hours on days, 12 hours swing shift, no
grave yard hours, and earned $146. How much does John earn
per hour on days? on swing shift? on grave yard?
To solve this problem, write each statement as an equation. If we
let x1 be his hourly rate on days, x2 his
hourly rate on swing shift, and x3 his rate on grave yard,
then
represents the conditions stated in the problem.
One of the main uses of matrices is in representing such systems of linear
equations. The system of three equations given above could be represented
as follows:
where the 3 rows by 3 column matrix is the matrix of the coefficients
of the equations, the matrix of x's is a column matrix, and the
final matrix is also a column matrix of the "right-hand sides" of the
equations.
If A is a matrix containing the coefficients of a
system of linear equations, x is a column vector containing the "unknowns,"
and b is the column vector of "right-hand sides," the constant terms,
then the matrix equation
A * x =b
represents the system of equations. Matlab provides a matrix operation
for solving such a system of linear equations:
>> x = A \ b
This can be read "x = A divided into b", or in linear algebra
"x equals A-inverse times b."
Not all systems of equations have a solution and sometimes they have
more than one (unique) solution. Systems like the above have a unique
solution wherever the determinant of the coefficient matrix, A,
is nonzero. In MatLab we can test this with the det function
as follows:
>> det(A)
When det(A) is nonzero (as it is in the above example),
the inverse of A can be found and the system of equations can
be solved either by
>> x = inv(A)*b % inverse of A times b
or (the way we did it above)
>> x = A \ b % matrix left division
MatLab recommends the left divison operator over the inv
function for reasons that have to do with the way MatLab works.
It is interesting, however, to multiply the two matrices, A
and inv(A), together to get the identity matrix.
>> Identity = A * inv(A)
>> I = eye(3)
As you see, the multiplication operator is overloaded to handle matrices,
and the function eye also returns the identity matrix.
For more practice, you should solve the following problems:
1x1 + 2x2 + 3x3 = 12
4x1 + 5x2 + 6x3 = 36
7x1 + 8x2 + 0x3 = 33
Joanna works part time for an establishment that is open 24 hours
per day. Each week she may be asked to work days, swing shift,
or grave yard and she is paid different rates for each shift.
Last week she worked 14 hours on days, 4 hours
swing shift, and 2 hours grave yard and earned $150.50. The
week before she worked 8 hours on days, 6 hours swing shift,
and 6 hours grave yard and earned $157. The week before that
Joanna worked 10 hours on days, no hours swing shift, 10
grave yard hours, and earned $157.50. How much does Joanna earn
per hour on days? on swing shift? on grave yard?
A parabola given by the equation y = ax2 + bx + c
passes through the points (0, -3), (1, -2), and (-1, -6).
Find the exact equation of the parabola. (Hint: substitute the
coordinates of the points into the generic equation to get
a system of three equations in three unknowns, one for each
point; the unknowns will be a, b, and c which
you can then substitute in the generic equation to get your
answer.)
End of Session 6.
This document last modified: May 15, 2004.
By Thomas M. Green Contra Costa College
San Pablo, CA 94806
Permission to use this document is granted so long as
the author is acknowledged.
Teachers: Provide your students with a printed copy of these pages as they work
through the examples at a computer running MatLab. They can enter their results on
the printed pages for you to check and you can also ask for printouts of various graphs,
M-Files, and copies of their work sessions when they use the 'diary' command. | 677.169 | 1 |
What is taught in the Math 180 UIC class?
A:
Quick Answer
University of Illinois at Chicago's Math 180 class covers Calculus I. The course is a requirement to earn a Bachelor of Science degree in mathematics, the teaching of mathematics or mathematics and computer science. It is also required for minor degrees in mathematics or mathematics and computer science.
Keep Learning
The Math 180 Calculus I UIC course uses chapters 2 to 5 in the textbook "Calculus: Early Transcendentals" by William Briggs and Lyle Cochran. The second chapter covers the ideas, definitions and techniques for computing limits. The third chapter discusses differentiation, product and quotient rules, the chain rule, and derivatives of trigonometric functions, inverse trigonometric functions and logarithmic and exponential functions. The fourth chapter further discusses derivatives, as well as maxima and minima, graphing functions, optimization problems, linear approximation and differentials, the mean value theorem, L'Hopital's rule and anti-derivatives. The fifth chapter covers approximating areas under curves, definite integrals, the fundamental theorem of calculus, working with integrals and the substitution rule.
Students are expected to read chapters of the textbook before attending the class meetings. Both written and online homework is assigned. To access online homework, students need to create a MyMathLab account. Though basic calculators are required for some homework assignments, they are not allowed during exams. The final grade is a combination of points from homework, quizzes, hour-long exams and the final exam.
Related Questions
Newton was one of two people credited with the creation of calculus, but even though he developed his ideas first, he did not get them printed first. A German mathematician, by the name of Leibniz, released his findings almost 9 years before Newton did. Both men approached the concept of calculus differently and held different views, so often both men are credited with its creation.
A nonlinear function in math creates a graph that is not a straight line, according to Columbia University. Three nonlinear functions commonly used in business applications include exponential functions, parabolic functions and demand functions. Quadratic functions are common nonlinear equations that form parabolas on a two-dimensional graph.
Math is a field of study that attempts to describe and measure the physical world using models and numbers. Mathematics uses observation, simulation and experimentation as a means of discovering the truth behind natural phenomena, human behavior and social systems. | 677.169 | 1 |
This course provides an introduction to number theory, including topics such as prime numbers, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions and elliptic curves. The materials include lecture notes, exams and assignments with solutions. MIT presents OpenCourseWare as free educational material online. No registration or enrollment is required to...
This mathematical resource, provided by the OEIS Foundation and authored by Neil J.A. Sloane, contains a searchable database of integer sequences along with information about classic integer sequences and puzzles. The main table is a collection of number sequences arranged in lexicographic order of absolute values. Each sequence entry contains the beginning integers, name, description, formula,...
Written by Leo Moser and presented by the Trillia Group, this virtual text introduces visitors to the theory of numbers. After agreeing to the terms and conditions of use, users will be able to download the full document as an 87-page pdf file in either large or regular print. The chapters include: "Compositions and Partitions," "Irrational Numbers," "Diophantine Equations," and "Geometry of... | 677.169 | 1 |
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Mathematics is about number operations and algebra,
motion and change (calculus and differential equations), logical analysis,
scientific visualization, structure and geometry, the prediction of random
events (probability), the extraction of useful information from large sets of
data (statistics), the discovery of the best ways to do things (optimization).
It is abstract and theoretical, and intensely down-to-earth and practical, all
at the same time.
The mathematics major and minor prepare students for
exciting and rewarding work in industry, careers in teaching, and for advanced
post-baccalaureate study. Our calculus, differential equations, analysis, and
probability and statistics courses enable science students to analyze data and
predict outcomes in static and dynamic situations. Our foundations, discrete
math and algebra courses give students the tools they need for rigorous logical
and structural analysis and a deep conceptual understanding of quantitative
situations. Our mathematics education courses prepare students to be
outstanding teacher leaders with a deep knowledge of mathematics and the best
practices in teaching. Our general education courses give the general student
the mathematical background she or he needs to function in life as an educated
and informed citizen in an increasingly quantitative and data-driven world.
The Mathematics Department makes every effort to
attempt to offer its courses at times that are convenient for students. Courses
in the mathematics option of the major are generally offered in the morning.
Courses in the mathematics education option of the major and Master of Arts in
Teaching Mathematics are generally offered at night to accommodate the needs of
working students.
Students are welcome to see a math advisor at any
time when faculty are available. All full-time math faculty serve as advisors.
To schedule an appointment with an advisor, please call the math department
office (310) 243-3378 or drop by NSM A-122 during regular business hours. The
math department requires majors to meet with an advisor at least once each
semester.
Preparation
High School students should complete Algebra II, a
year of geometry and trigonometry. A mathematics course should be taken in the
senior year. Transfer students should complete three semesters of calculus and
one additional course if possible.
Career Opportunities
A degree in mathematics is a key that opens the door
to a world of opportunity. Students who major in mathematics are able to pursue
a diverse range of careers. They are sought out by profit and non-profit
institutions for their ability to use reasoning and logic and for their ability
to solve problems. Many are interested in passing their learning on to future
generations through teaching. Others seek advanced degrees in mathematics or
other sciences and pursue cutting-edge research. Some will pursue degrees in
business or economics, where the ability to work with numbers can be a great
advantage. Those with mathematical training have gone on to careers as business
executives at major software companies, as analysts for stock trading companies,
as actuaries and risk management experts for insurance companies and the
healthcare industry, as scientists and data analysts in engineering and biotech
firms, as software designers and programmers, and a whole host of other
careers.
Graduation With Honors
An undergraduate student may graduate with Honors in
Mathematics provided that the following criteria are met:
1.A minimum of 36 units in residence at CSU Dominguez Hills;
2.A minimum grade point
average of at least 3.5 in all courses used to satisfy the upper division
requirements in the major;
3.Recommendation by the
faculty of the Mathematics
Department.
Bachelor of Science in
Mathematics
Total Course Requirements
for the Bachelor's Degree
See the "Requirements for the Bachelor's Degree" in
the University Catalog for complete details on general degree requirements. A
minimum of 40 units, including those required for the major, must be upper
division.
Elective Requirements
Completion of elective courses (beyond the
requirements listed below) to reach a total of a minimum of 120 or a maximum of
132 units.
General Education Requirements (55-62 units)
See the "General Education" requirements in the
University Catalog or the Class Schedule for the most current information on
General Education requirements and course offerings.
Graduation Writing Assessment Requirement
See the "Graduation Writing Assessment Requirement"
in the University Catalog.
Minor Requirements
Single field major, no minor required.
Major Requirements (59-67 units)
Students must select one of the options listed
below. The following courses, or their approved transfer equivalents, are
required of all candidates for this degree. All courses used to satisfy this
major must be passed with a grade of "C" or better.
Mathematics Option - (59 -63 units)
Single field major - no minor required
A.Lower Division
Required Courses (32 units)
CSC 121.Introduction to Computer Science and Programming I
(4PHY 130.General
Physics I (5)
PHY 132.General
Physics II (5)
B.Recommended Course -
optional (0-4 units)
CSC 123.Introduction
to Computer Science
and Programming II (4)
C.Additional Required
Courses (27 units)
MAT 281.Discrete
Mathematics (3) or
MAT 367.Numerical
Analysis (3)
MAT 311.Differential
Equations (3) or
MAT 411.Mathematical
Modeling (3) or
PHY 306.Mathematical
Methods in Physics (3) or
PHY 310.Theoretical
Mechanics (3) or
PHY 380.An
Introduction to Nonlinear Phenomena (3)
MAT 321.Probability
and Statistics (3)
MAT 331.Linear
Algebra (3)
MAT 33.Abstract
Algebra (3)
MAT 361.Finite
Automata (3) or
MAT 347.Modern
Geometry (3) or
MAT 447.Number
Theory (3)
MAT 401.Advanced
Analysis I (3)
MAT 403.Advanced
Analysis II (3)
MAT 421.Complex
Analysis (3)
Mathematics Education
Option - (68 units)
Single field major - no minor required
Subject to approval by the California Commission on
Teacher Credentialing (CCTC), this option will satisfy the subject matter
preparation necessary for a secondary teaching credential in mathematics.
Students do not get Subject Matter Preparation on their diploma, the diploma
says Mathematics Education option.
Students not seeking a degree in mathematics, but
wishing to satisfy the requirements for the teaching credential in mathematics
must take at least nine (9) units of upper division mathematics at CSUDH,
including MAT 490.
A.Lower Division
Required Courses (40 units)
MAT 131.Elementary
Statistics and Probability (3)
MAT 143.Problem
Solving in Mathematics (3)
MAT 191.Calculus
I (5)
MAT 193.Calculus
II (5)
MAT 211.Calculus
III (5)
MAT 241.Programming
and Technology in Secondary School Mathematics Teaching (3) or
CSC 111.Introduction
to Computers and Basic Programming (3)
MAT 271.Foundations
of Higher Mathematics (3)
MAT 281.Discrete
Mathematics (3)
PHY 130.General
Physics I (5)
PHY 132.General
Physics II (5)
B.Upper Division Required
Courses (28 units)
MAT 331.Linear
Algebra (3)
MAT 333.Abstract
Algebra (3)
MAT 347.Modern
Geometry (3)
MAT 401.Advanced
Analysis I (3)
MAT 411.Mathematical
Modeling (3)
MAT 443.History
of Mathematics (3)
MAT 447.Number
Theory (3)
MAT 489.Fundamental
Mathematics and
Teaching in Secondary School (4)
MAT 490.Seminar
in Mathematics Education (3)
Minor in Mathematics (27 units)
All courses used to satisfy this minor must be
passed with a grade of "C" or better.
A.Required Courses (21
unitsMAT 331.Linear
Algebra (3)
B.Electives: Select two
courses from the following (6 units):
MAT 311.Differential
Equations (3)
MAT 321.Probability
and Statistics (3)
MAT 333.Abstract
Algebra (3)
MAT 347.Modern
Geometry (3)
MAT 361.Finite
Automata (3)
MAT 367.Numerical
Analysis I (3)
MAT 369.Numerical
Analysis II (3) [I]
MAT 401.Advanced
Analysis I (3)
MAT 403.Advanced
Analysis II (3)
MAT 411.Mathematical
Modeling (3)
MAT 413.Partial
Differential Equations (3)
MAT 421.Complex
Analysis (3)
MAT 447.Number
Theory (3)
Master of Arts in Teaching
of Mathematics
Admission Procedures
Students must submit an application to the
University for admission (or readmission) with graduate standing, and official
transcripts of all previous college work in accordance with the procedures
outlined in the Graduate Admissions section of the University Catalog. If the
student is currently enrolled as a post-baccalaureate student, he/she must
obtain a Request for Postbaccalaureate/Graduate Change of Objective form from
the department office and submit it to the program's Graduate Coordinator.
Admission Requirements
The student will qualify for admission to the program if he/she:
1.has a baccalaureate
degree from an accredited university. (See the University Catalog for
requirements of graduates of non-accredited institutions.);
2.has completed two
years of teaching and is currently teaching mathematics in a California school;
3.a)has
a California Single Subject Credential in Mathematics or
b)is eligible for a
California Single Subject Credential in Mathematics or
c)has completed a major
in mathematics or
d)has completed, with an average grade of "B" or
better, 20 semester units in college level mathematics and passed a department
administered entrance examination;
4.has submitted three
letters of recommendation, including one from the principal at the applicant's
school;
5.has completed a
successful interview with the program's Graduate Coordinator and
representatives from the department's mathematics education faculty;
6.has achieved a TOEFL
score of 550 (for those applicants who do not possess a bachelor's degree from
a postsecondary institution where English is the principal language of
instruction);
7.has a grade point
average of at least 2.5 (on a 4.0 scale) in his/her last 60 semester units of
upper division course work; lower division courses taken after obtaining the
bachelor's degree and extension courses, (except CSU Dominguez Hills upper division
resident extension courses or the equivalent on other campuses), will be
excluded from the calculation; and
8.is in good standing at
the last college attended.
Graduate Standing: Conditionally Classified
To qualify for admission with a graduate degree
objective, students must meet the admission requirements for postbaccalaureate
unclassified standing as well as any additional requirements of the particular
program. Students who apply to a graduate degree program but who do not satisfy
all program requirements may be admitted to conditionally classified status.
Program coordinators will outline all conditions for attainment of classified
status.
Graduate Standing: Classified
Students applying for master's degree programs will
be admitted in classified status if they meet all program admission requirements.
Classified standing as a graduate student is granted
by the academic unit to which the student is applying. Classified standing is
normally granted when all prerequisites have been satisfactorily completed for
admission to a master's degree program. Students must have classified standing
to qualify for Advancement to Candidacy.
Graduation Writing Assessment Requirement
All graduate students entering the University in the
Fall of 1983 or thereafter are required to satisfy the Graduation Writing Assessment
requirement (GWAR) in accordance with the established policies of the
university. Students must satisfy the requirements before being Advanced to
Candidacy. (See "Graduation Writing Assessment requirement" section of the
University Catalog.
Advancement to Candidacy
Advancement to candidacy recognizes that the student
has demonstrated the ability to sustain a level of scholarly competency
commensurate with successful completion of degree requirements. Upon
advancement to candidacy, the student is cleared for the final stages of the
graduate program which, in addition to any remaining course work, will include
the thesis, project, or comprehensive examination.
Following are the requirements for Advancement to
Candidacy:
1.A minimum of 15
resident units
2.Classified standing
3.An approved Program of
Study
4.Successful completion
of the GWAR
5.A cumulative GPA of 3.0
in all courses taken as a graduate student
6.No grade lower than a
"C" in the degree program
Advancement to Candidacy must be certified on the
appropriate form to the Graduate Dean by the department prior to the final
semester, prior to the semester of the comprehensive exams, and prior to
enrolling in thesis or project.
Acceptable Progress and Graduation Requirements
The following are specific graduation requirements
which must
be met to earn this graduate degree:
1.Completion of a
minimum of 32 semester units of approved graduate work within five years. An
extension of time may be granted if warranted by individual circumstances and
if the outdated work is validated by such means as examination, independent
study, continuing education, relevant additional course work, or by such other
demonstration of competence and/or currency as deemed acceptable by the
Graduate Coordinator and mathematics education faculty.
Distribution pattern of the 32 units:
a.at least 16 semester
units will be completed in residence after admission to graduate standing in
the program;
b.not more than 4
semester units of Graduate Seminar in Mathematics Education (MAT 590) can be
used to meet graduation requirements;
c.not more than 9
semester units may have been earned from approved extension and/or transfer
course credit; and
d.upon approval by the
Graduate coordinator and representatives from the mathematics education
faculty, courses taken previously may be used to meet the course content
requirements if they have been completed within the five years immediately
preceding the completion of the requirements of the degree. However, no courses
(with the exception of GED 500 - Research Methods in Education) previously used
to meet their requirements of another degree may apply toward the required
number of 32 semester units of approved graduate work.
2.achievement of a grade
point average of 3.0 or better in all courses taken to satisfy the requirements
for the degree, except that an approved course in which no letter grade is
assigned shall not be used in computing the grade point average;
3.satisfactory
completion of the research project. The subject of the research project will
depend upon that which is educationally most appropriate to the student and
mathematics education. The research project is equivalent in rigor to the
thesis, will be supervised by a committee of three faculty, and may include an
oral defense or presentation as part of the culminating experience;
4.satisfactory
completion of the Graduation Writing Assessment Requirement (GWAR); and
5.filing of an
application for the award of the Master's degree.
Upon completion of the CSU Dominguez Hills' graduation
requirements, award of the graduate degree must be approved by
the program, the school dean, and the faculty of the University.
Degree Requirements (30 -36 units)
The Master of Arts Degree in Mathematics requires
completion
of 30 units of course work and one of the following:
a.Passing score on a
comprehensive written examination. After completion of all course work or
during the last semester of course work, the MAT degree candidate may apply to
take the comprehensive examination. There is only one retake opportunity.
b.Completion of an
approved thesis or creative project (MAT 599 - 6 units). Students must have the
approval of a faculty thesis advisor prior to enrolling for thesis credit.
A.Core Courses (21
units)
MAT 500.Mathematics
Education Research
and Design Statistics (3)
MAT 515.Topics
in Advanced Finite Mathematics (3)
MAT 522.Foundations
of Algebraic Thinking (3)
MAT 543.Advanced
Problem Solving for Teachers (3)
MAT 545.History
of Mathematics Education (3)
MAT 557.Research
in Mathematics Education I (3)
MAT 559.Research
in Mathematics Education II (3)
B.Each student must
select one of the options below.
1.Middle School
Mathematics Option (9 units)
MAT 501.Foundations
of Geometric Thinking (3)
MAT 505.Foundations
of Mathematical Structures (3)
MAT 506.Foundations of Rational Numbers (3)
2.High School Mathematics
Option (9 units)
MAT 521.Geometry
for Teachers (3)
MAT 523.Theory
of Functions for Teachers (3)
MAT 525.Algebraic
Structures for Teachers (3)
C.Culminating Activity
(0-6 units).
MAT 599.Masters
Project (6) or
Comprehensive
Exam (0)
Course Offerings
The credit value for each course in semester units
is indicated for each term by a number in parentheses following the title. For
course availability, please see the list of tentative course offerings in the
current Class Schedule.
Students need to take the ELM test, or to have an
exception from the ELM test prior to enrolling in any mathematics course. The
ELM test score will be used to place the students into the proper mathematics
course.
Flexible course covering topics in intermediate
algebra and geometry beyond those that are covered in the basic remedial MAT
011-014 sequence. Aimed at preparing students for more technical university
level math and science courses (e.g. Pre-calculus). Does not count for the
Bachelor's degree. CR/NC grading.
MAT 016Algebra and
Geometry Review Part 6 (1).
Prerequisite: MAT 015.
Sequel to Mat 015. Flexible course covering topics
in intermediate algebra and geometry beyond those that are covered in the basic
remedial MAT 011-014 sequence. Aimed at prepareing students for more technical
university level math and science courses (e.g. Pre-calculus). Does not count
for the Bachelor's degree. CR/NC grading.
MAT 095Special
Topics
in Mathematics (3).
A course in a topic of special interest to both
faculty and students for which no current course exists. Topic will be
announced in schedule of classes. Repeatable for credit. CR/NC grading
Sets and set theoretic operations as related to
counting numbers and rational numbers and arithmetic operations. Real number
system and its origins, development, structure and use. Special emphasis on
problem solving, and the development and application of algorithms. Does not
satisfy General Education Quantitative Reasoning Requirement.
MAT 131Elementary
Statistics
and Probability (3).
Prerequisite: Fulfillment of ELM requirement.
A practical course in probability and statistics
including such topics as the binomial and normal distributions, confidence
intervals, t, F, and chi-square tests, linear regression and correlation, and
conditional probability. Satisfies the General Education Quantitative Reasoning
Requirement.
MAT 141 Computers
for Mathematics Teaching (3).
Prerequisite: Fulfillment of the ELM requirement.
Introduction to computers for teachers of mathematics.
Topics include flowcharting, programming in LOGO on microcomputers.
Applications of computers to problem solving, statistics, and other areas of
mathematics relevant to teachers of mathematics. Applications packages, CAI and
social issues are studied. A-C/NC grading. Does not satisfy General Education
Quantitative Reasoning Requirement.
MAT 143Problem
Solving in
Mathematics (3).
Prerequisite:
Fulfillment of the ELM requirement.
Objective is to increase students abilities to use
knowledge and experience when encountering new and unexpected situations.
Develop higher level thinking skills, learn to formulate, analyze, and model
problems. Choosing relevant information, making conjectures, devising plans and
testing solutions. A-C/NC grading. Does not satisfy General Education
Quantitative Reasoning Requirement.
Not available for credit to students who have credit
in MAT 191 or its equivalent or courses which have MAT 191 as a prerequisite.
Functions, linear equations, the derivative and its applications, the integral
and its applications, and partial derivatives. Satisfies the General Education
Quantitative Reasoning Requirement.
MAT 191Calculus I
(5).
Prerequisite: MAT 153 or equivalent with a grade of
"C" or better and fulfillment of ELM requirement.
Primarily for prospective elementary school
teachers. Geometry from an intuitive problem solving standpoint. Constructions,
symmetry, translations, rotations, patterns, area, volume, and the metric
system. Topics from graph theory and topology. Two hours of lecture and two
hours of activity per week. Does not satisfy General Education Quantitative
Reasoning Requirement.
MAT 241Programming
and Technology for Teaching Secondary School Mathematics (3).
Prerequisite: MAT 193 or equivalent with a grade of
"C" or better.
Introduction to application software appropriate for
the teaching of secondary school mathematics. The programs include spreadsheet,
geometric modeling, and statistics modeling. Writing simple programs for
graphing calculators to demonstrate and solve mathematical problems.
MAT 271Foundations
of Higher Mathematics (3).
Prerequisite: MAT 153 or equivalent with grade of
"C" or better. MAT 191 with grade of "C" or better is recommended.
Topics include logic, methods of mathematical proof,
set theory, relations and functions. Introduction to complex numbers and proof
strategies using ideas of vector algebra. Meant to prepare students for mathematics
program as well as oncepts
of computer science.
MAT 281Discrete
Mathematics (3).
Prerequisite: MAT 271 and CSC 121 or MAT 241 or CSC
111 or equivalent with grade of "C" or betterUpper Division
MAT 311Differential
Equations (3).
Prerequisite: MAT 211 and MAT 271 with a grades of
"C" or better.
Topics covered include first and second order linear
equations including existence and uniqueness theorems, series solutions;
nonlinear equations; systems of linear equations. Other topics may include the
Laplace transform, qualitative theory.
MAT 321Probability and Statistics (3).
Prerequisite: MAT 193 and MAT 271 or equivalent
with grade "C" or better.
A calculus based survey of topics in probability and
statistics emphasizing applicationsMAT 401Advanced
Analysis I (3).
Prerequisites: MAT 211 and MAT 271, or equivalent
with a grade of "C" or better.
Elements of set theory, numerical sequences and
series, continuity and differentiability of functions of one and several
variables.
MAT 403Advanced
Analysis II (3).
Prerequisite: MAT 401 or equivalent with a grade of
"C" or better.
Integration of functions of one and several
variables, sequences and series of functions, uniform convergence, power
series, differentiation of functions of several variables.
MAT 411Mathematical
Modeling (3).
Prerequisite: MAT 211, MAT 241, and MAT 271 or CSC
121 or CSC 111, or equivalent with a grade of "C" or better. MAT 311 or
equivalent and MAT 331 are recommended.
Prerequisites: MAT 311 with a grade of "C" or better
is required; MAT 213 is recommended.
Solutions to partial differential equations by
separation of variables and Fourier series. Applications to heat flow and
diffusion, wave motion, and potentials. Some discussion of existence and
uniqueness of solutions.
MAT 421Complex
Analysis (3).
Prerequisites: MAT 211 and MAT 271 with a grade of
"C" or better. MAT 331 and MAT 401 (may be taken concurrently) are recommended.
Complex numbers; point sets, sequences and mappings;
analytic functions; elementary functions; integration; power series; the
calculus of residues; and applications.
MAT 443History of
Mathematics (3).
Prerequisite: MAT 193 with a grade of "C"
or better.
Traces the growth and development of mathematics
from primitive origins to present, uses methods and concepts of mathematics to
present the topics.
MAT 447Number
Theory (3).
Prerequisite: MAT 271 with a grade of "C"
or better.
Divisibility, congruencies, prime number theory,
Diophantine Equations, and other topics from elementary number theory.
MAT 489Fundamental
Mathematics
and Teaching in Secondary Schools (3).
Prerequisite: 9 units of 300/400-level mathematics
with a grade of "C" or better.
Synthesis and analysis of secondary mathematics and
its teaching. Emphasis will be placed on algebraic thinking and its teaching in
high school. Forty hours of secondary classroom observations will be a required
activity in this course. A Certificate of Clearance is required.
MAT 490Seminar in
Mathematics
Education (3).
Prerequisite: 9 units of 300/400 mathematics
courses with a grade of "C" or better.
The synthesis and analysis of the secondary
mathematics curriculum from an advanced standpoint. Emphasis will be on the
integration of problem solving, investigations, reasoning, and communication as
recommended in state and national standards.
MAT 495Selected
Topics in
Mathematics (1-4).
Prerequisites: Consent of instructor and MAT 271Graduate
Graduate standing and consent of the graduate
program coordinator is prerequisite to enrollment in graduate (500 level)
courses.
MAT 500Mathematics Education Research Design and
Statistics (3).
Prerequisites: Students must have graduate standing
and must have completed one year of full time secondary mathematics teaching.
Includes topics such as normal distribution,
confidence intervals, t, F, chi-squared tests, linear regression, and
correlation. These topics are presented in the context of mathematics education
research in typical classrooms.
MAT 501Foundations
of Geometric Thinking (3).
Prerequisites: MAT 543 or concurrent enrollment.
Students must have graduate standing and must have completed one year of full
time secondary mathematics teaching.
Research on Various topics in geometry. Focus on
developing notions of rigorous proof and grade-appropriate explanations. Topics
are chosen from the Geometry areas and standards emphasized in K-12.
MAT 505Foundations
of Mathematical Structures (3).
Prerequisites: MAT 543 or concurrent enrollment.
Students must have graduate standing and must have completed one year of full
time secondary mathematics teaching.
Topics include the algebraic properties of sets and
operations applied to classical number systems, equivalence, modular
arithmetic, Diophantine equations, decomposition of natural numbers, special
families of natural numbers, current research on understanding and learning
these topics.
MAT 506Foundations
of
Rational Numbers (3).
Prerequisites: MAT 543 or concurrent enrollment.
Students must have graduate standing and must have completed one year of full
time secondary mathematics teaching.
Covers theory and applications of Rational numbers.
Focus on number systems, representation of numbers, equivalence classes,
rationality and irrationality, properties of the rational numbers system,
central ideas of proportional reasoning, and developing intuitive models of
standard rules and algorithms.
MAT 515Topics in
Advanced Finite Mathematics (3).
Prerequisites: Possession of a baccalaureate degree
and one year of full-time secondary mathematics teaching.
Topics from areas of Modern Mathematics which relate
to the high school mathematics curriculum such as: algorithms, graph theory,
coding theory, game theory, finite probability theory, difference equations,
voting, recursion.
MAT 521Geometry for
Teachers (3).
Prerequisites: MAT 543, graduate standing and one
year of full time secondary mathematics teaching.
Prerequisites: Students must have graduate standing
and must have completed one year of full time secondary mathematics teaching.
Patterns, functions, and multiple representations;
independent and dependent variables; discrete and continuous functions; linear
and nonlinear relationships in context; connections to arithmetic operations;
algebraic expressions and equations. Examines current research on the
understanding and learning of these topics.
MAT 523Theory of
Functions
for Teachers (3).
Prerequisites: MAT 543, graduate standing and one
year of full time secondary mathematics teaching.
Prerequisites: MAT 543, graduate standing and one
year of full time secondary mathematics teaching.
Topics relating to the high school Algebra
curriculum from an advanced standpoint including algorithms, fields,
polynomials, groups, fields, and rings.
MAT 543Advanced
Problem Solving
for Teachers (3).
Problem solving using non-routine strategies.
Problems to be representative
of several branches of mathematics and mathematically based disciplines.
MAT 545History of
Mathematics Education (3).
Prerequisites: Graduate standing and one year
of full time secondary teaching.
Traces the development of the mathematics curriculum
K-12 in the United States and internationally, concentrating both on content
taught at different stages and the teaching methods employed. Reviews the
various mathematics reform efforts over the past 170 years.
MAT 557Research in
Mathematics Education I (3).
Prerequisites: MAT 500 and 15 units of program.
Overview of the current research literature
pertaining to mathematics education in elementary and secondary schools. Topics
such as mathematical reasoning, communication, problem solving, algebra, and
geometry will be discussed and analyzed.
MAT 559Research in
Mathematics Education II (3).
Prerequisite: MAT 557.
Overview of the current research literature
pertaining to mathematics education in elementary and secondary schools. Topics
such as mathematical reasoning, communication, problem solving, algebra, and
geometry will be discussed and analyzed.
MAT 590Graduate
Seminar in
Mathematics Education (1-4).
Prerequisites: Possession of a baccalaureate degree
and one year of full-time secondary mathematics teaching.
Extensive reading in selected areas under the
guidance of faculty mentor. Repeatable course.
MAT 598Directed
Research (1-4).
Prerequisite: Classified graduate standing.
Students will design and conduct research projects
under the direct supervision of the instructor. Repeatable course.
MAT 599Masters
Project (6).
Prerequisite: Advancement to Candidacy.
Completion of classroom based project under the
guidance of faculty advisor. The culminating learning experience of the program
which emphasizes the application of the mathematics education curriculum in the
classroom.
MAT 600Graduate
Continuation Course (0).
Graduate students who have completed their course
work but not their thesis, project, or comprehensive examination,
or who have other requirements remaining for the completion of their degree,
may maintain continuous attendance by enrolling in this course. Signature of
graduate program coordinator required.
Infrequently Offered Courses
The following courses are scheduled on
a "demand" basis. Students should consult the department office for information
about the next schedule offering.
MAT 213Calculus IV
(4).
Prerequisite: MAT 211 or equivalent with a grade of
"C" or better.
Topics covered include vector calculus, line and
surface integrals, and the theorems of Green, Gauss, and Stokes.
Integrates previous work and experience by
emphasizing the application of theoretical models and research designs to the
field of mathematics education. Special emphasis will be given to analyzing,
organizing, and evaluating findings, and communicating the results. | 677.169 | 1 |
Your 911: Math Help on the Internet
Math Help is Available 24/7
In our technological age you have so many opportunities when you or your child can't solve a math problem. Math help online extends to more than just a problem on a given day. You can find help in pre-calculus, algebra, trigonometry, statistics and more on most sites; plus full courses on other sites. You have no reason to feel lost and alone with a math problem you can't solve or feel it's too late to learn a math subject at any age.
Websites that Offer Math Help
1. Mathway.com's menu contain the various math subjects. Once in a math subject you enter the problem, and then click the Help button to see examples. WebMath is a site that generates the solution for a math problem entered when the user clicks "Solve." What is very helpful is WebMath shows how a student goes from problem to solution.
2. Math.com takes any student from Kindergarten through high school, covering Algebra 1 and 2, Geometry, Statistics, Precalculus, and other advanced topics. The site provides practice problems and lessons. There are other resources such an information guide for hiring a tutor. And Math.com hasn't forgotten that math can be found--games are provided.
3. Khan Academy is a video-based free education source for anyone in the world. Of course, math is covered. Instruction takes a student through the entire subject, starting with the first section of a math course. A student moves forward only at their own pace, and doesn't move forward until they have mastered the earlier lesson.
4. Freemathhelp.com is a user-friendly home page. The math subjects offered are graphically and simply displayed. When you click the "More" button you find a page of the sections of a math course such as Shapes, Graphing lines, Formulas, etc. There is an interactive feature also on the home page where you can begin discussions on a particular challenge you are having. In the left menu are topics like homework help, test questions, problem solvers and more.
5. Mathplanet.com is free to use for study of the usual high school math subjects as well as offering SAT and ACT help. Like Khan Academy it's for anyone wanting to master a math course.
6. MyGeekyTutor.com is a paid tutoring sites that has been around since 2005, a very trusted site with tutors for all kinds of math subjects at all levels
Tutoring for Math Help
A larger commitment for math help online is going to sites to hire a tutor for from one to three hours a week. Service is often guaranteed if better grades don't result.
You only need to do a Google search for "math help online" to get many websites that offer math classes or specific help with a specific problem.
Statistics Homework Help: Provides You A Lot More Edge To Learning Social Science Courses
In comparison before, college today is much more interdisciplinary. Statistics is pretty necessary for social science courses. Sociology, demography, public health, as well as business administration are under social science programs but individuals taking up these courses are more humanities-oriented as opposed to being math and science-oriented. So, even if these social science courses students are great in analyzing information as well as in writing important figures, lack of interest in understanding statistics would probably be the reason for them to fail in the long run, making it hard for them to graduate and become a degree holder. Calculus along with other advanced math subjects are part in a few programs, while statistics is a required course in social sciences programs. Even though there is the proven fact that excellence in statistics is not needed in any career paths in these courses, having a specific level of knowledge in statistics has been required by completely different universities to all students taking up the course.
The statistics requirements in social science university programs are typically daunting to the humanities-inclined social studies student. Of course, students are not permitted to consult any individual during exams. But students now have the choice that will help them cope with this subject well. It is no other than the help with statistics. A great statistics homework help tutor greatly assists in developing the knowledge and comprehension of a student who find statistics very difficult. What makes social science students slow in comprehending statistics is that they don't have great study habits and this is where the tutor will intercede so that there'll be a significant advancement in the students subject performance. In addition, the majority of students need help from someone who is well-informed with regards to the totally different terms utilized in the subject because they are not really knowledgeable about it.
Obviously the instructor is a resource that students who're having difficulties can use for help. But, an instructor doesn't have all the time to explain further everything to his or her students. While they've got office hours, it will still be divided among many students who come and check out their offices. The difficulty of the subject may even leave some unanswered queries among students. Another thing is that the students might feel uncomfortable or unwilling to state exactly how baffled they were about a specific lesson as the instructor might think of them as extremely slow learners. One perfect example for this is when a student does well on an examination and the teacher don't believe the result simply because he or she is conscious that such student isn't even great during class discussions. In other words, a student won't have to bother about confusion or misunderstandings if they are under the comforts of statistics homework help. This will make everything great for the students since the tutor will provide good support and learning assistance to understand fully statistics courses.
Problems Faced By Parents When They Try To Get a Math Tutor for their Kids
There are a multitude of explanations why students of any degree may need statistics help, but we could say that it is particularly the case of college students where such need becomes more clear. What is the reason behind? Well, you could site different reasons why this is so, but the main factor is that the mathematics subject you have in college is truly more complicated than your math subjects in high school. In college, students encounter for the first time in their lives a not-too-gentle approach to subject topics they were utilized to go in a much milder, buffered way.
Some topics are taught in an informal and graphic oriented method with out detailed description, like for example the usage of the term bell-shaped curve when discussing normal distribution. There is more to that bell-shaped curve, and most students will only understand that there are a lot of things about this topic that they were not able to learn in high school as they take their first college stats class. They're first presented with a formal, mathematically consistent version of the normal distribution, and that is when several students begin to sink, and when the time comes for some help.
They didn't have a good foundation in mathematics that's why it is difficult for them to understand its idea as they find math in college level to be more abstract. The best statistics help they could get probably is the in form of a face-to-face trainer who could guide them through the more abstract concepts and help them with the solving of examples that can help them discuss the main concepts involved. They could always study on their own and grasp the concept by concentrating their time to the subject, proceed to the library, and have more examples from certain math books. But the problem is not that they can't understand the topic, the issue is that they're not sure when they are doing it appropriately. This is exactly where the aid of an expert is poorly needed because the expert can give them the guarantee that the solutions they have for the math problems are accurate.
There are other kinds of statistics help besides a one-on-one tutor. If you're diligent enough and is willing to put in some extra effort, you may opt for online tutorials, which you could combine with one-on-one tutorials. Most people tend to mistrust any online service, but like for every thing, there's good and bad, and commonly bad services are quite evident and are easy to spot, so this still remains a very valid option.
Failure to learn the subject can lead to a lot of problems, but college students can prevent them when they take action early. You should not always take complex subjects like statistics gently, so in the first sign of troubles in the subject, go on and find a tutor that will give you that required guidance that will let you tackle the subject with self-confidence.
Yow will discover more information on statistics help on this resource
Statistical Software: Pie Chart Builder
Statistics is the science that manages summarizing and analyzing information in a very significant way. There is a historical division in statistics which causes a distinction largely between two classes: descriptive and inferential statistics. The objective of the first one should be meaningfully identify sample data, in such a way the primary information concerning the main properties and distribution properties are well determined. The goal of the latter is to make summary about the population parameters.
In this article, we'll rather address descriptive statistics and certain tools that could make our life a lot easier when trying to describe samples. In this era of computerized gadgets, it is rather unlikely to consider any kind of descriptive analysis with out the use of some type of calculator or computer device. Probably the most typical graphical applications that we're going to find readily available are typically histograms and pie graphs. A histogram is actually a graphical means of describing the distribution of any continuous variable, unlike a pie chart allows to graphically showing you discrete variables.
There are different tools that enable you constructing pie charts, such as Excel, Minitab, etc, as well as other fine statistical software, however there is a number of online resources to make a pie chart over the internet. For example, when you go to google.com and enter "pie chart maker" you'll locate a ton of really beneficial resources which will support you with your task of constructing a very nice pie chart. See at the end of the write-up for some recommended website links.
The majority of those web resources will give some sort of chart wizard which will let you to construct your graph in a painless way. A great online graph maker will enable you to key in titles, axes titles, as well as other elements that will enable yourself to generate a great customized graph. A good online graph maker will likewise enable you to copy the rendered graph so that you can use it in your own laptop or computer.
There are plenty of web sources that can make an online graph that has nothing to envy graphs created by advanced statistical packages, so it is worth taking a look at them all and pick the best. Be aware though that if you wish to learn about how make a graph, you will most likely must look at your favorite stats book, because the online graphing website possibly won't show the details of how to do pie graphs, but rather, they will produce the graph. As a way to make a graph yourself, on paper, you still have to master the basics, but making use of a website to make graphs can certainly be a great starting point.
I have come across a lot of internet sites that feature a graph maker, on the other hand one of the best graph creator for pie charts is currently offered by mathcracker.com (see the website links towards the end of the write-up). The graph generator they offer is simple and sophisticated, so make sure to take a look at it. But be aware that most of web sites only provide 2D-graphs, so when you require a 3d pie chart you would probably must indicate it clearly in your google search. In case you want to make a graph online, make sure you check out this pie chart tool
Picking Relevant Math Homework Help On the web is certainly Becoming Increasingly Arduous
Math is certainly one of the subjects that will test your dedication. If you are a mother and father watching your kid, both your determination is going to be tested. It truly is evident that kids will likely not consistently get the right solution no matter if it is about things they have invested countless hours on. Whenever your girl or boy is having complications dealing with math problems, what is the simplest approach? You surely require help with math and you should not be reluctant to ask for it.
Academic institutions in these days would like every single youngster to be adept or perhaps no stranger to mathematical basics. The task in today's contemporary culture is that not necessarily all of children are good at mathematics. Math Help is certainly called for every so often. For example, in case your child is certainly good in sports activities and he is not skilled with math skills then this particular child will surely need a lot of help in the math department. In this instance your child could possibly have folks that happen to be really fascinated by arts rather than math. This is when it may be a clear matter of a really proficient girl or boy, although where natural talent happens to not to always be in math. This should not be a concern simply because you can nearly always find help with math. The most critical point in time when parents or guardians require help happens when is actually the moment for their little ones to try and do assignment, and that is the right moment when the aid of a tutor can be quite critical. All things considered still depends on the parents or guardians to gauge the actual advancement of the teenager using the support provided by the math coach In the beginning, a math tutor may easily judge what the most critical necessities are actually, in order to evaluate the fields and areas that need aid most urgently, whether it be Arithmetic, Trigonometry, anything. Perhaps maybe it's established that a new a bit more skilled math private tutor becomes necessary, and then the choice of an online math tutor is simply not out of the way.
In general terms, each time a young child doesn't like math, it is likely that a severe dislike is established which is certainly not easy to correct, and then for which factor a decent math private tutor will offer appropriate math help in terms that this teenager could certainly comprehend and in a method that the kid starts out to like, or at a minimum not to despise math concepts. A huge difference can be achieved by using a trained tutor when considering shifting high dislike towards mathematics which a kid could possibly be demonstrating.
It is incredibly prevalent for grown-ups to fail to be clearly trained in mathematics so therefore, they're just not capable of providing the guidance their kids will be needing. That happens when a good solid math coach, whether or not it's on its regular one-on-one mode as well as in the shape of a math homework help online business, can be helpful to change the situation towards a much more open area, at which math learning develops into basic and powerful.
It is extremely commonplace that numerous young children will only need to shed their own fear of doing below the standard in math, and a tutor can supply this sort of aid of producing a much more confident spirit. Math Help must be for all, not necessarily just for those who are doing poorly but for those who find themselves succeeding simply because they might also boost their own math skillsets a step forward, making it simpler for the future. | 677.169 | 1 |
Why use The Math You Need, When You Need It?
Have you ever felt that you spend too much time in class reviewing the quantitative skills you think your students should have gotten in high school? Do you wish your students could readily tackle quantitative problems in geoscience without so much hand-holding? Would you like to assign more quantitative problems in your introductory courses?
The Math You Need...is a web-based short course designed to instruct students in the quantitative skills they need, just before they need them to address geoscience problems in the classroom. Students complete a self-paced set of web pages and quizzes designed to bring them up to speed on a number of mathematical concepts that are introduced in most introductory geoscience courses. The examples and quizzes are designed so that instructors can choose questions that address the context in which they wish to introduce the mathematical concept.
Why is this effort important?
Quantitative topics pervade the geosciences; yet, many introductory textbooks gloss over the quantitative aspects and expect students to quickly grasp some relatively complex mathematical themes even when they are treated qualitatively (e.g., reading cumulative percent graphs, understanding exponential decay, etc). Furthermore, students who are uncomfortable or unfamiliar with mathematics often feel that there is little support. Faculty often feel time-constraints, administrative pressure or student feedback can keep them from including quantitative content in their courses (e.g., participants in 2006 QL workshop). The modules in The Math You Need... are math tutorials for students, completed just before they need to be able to use it in their geoscience course. The modules are designed to delve more deeply into the mathematics needed for introductory geosciences while supporting students who are math phobic or just need some math review.
There is good evidence that both retention and learning are increased when students feel they have support for difficult mathematical concepts (e.g., ACT, 2004; Baer et al., 2005). If they feel like they are given time to learn (or relearn) the mathematics they are more comfortable applying it later to "high-stakes" problems in their courses. At Highline Community College, a one-credit course called "MathPatch" has dramatically increased retention and student performance. Students felt that they had the support and did not feel lost because they knew that mathematical thinking was expected of them. They were supported and lived up to that expectation.
Why "self-paced" and "web-based"?
The Math You Need... can be used in conjunction with any introductory geoscience course. A pretest determines who needs the tutorials. Each appropriate tutorial can be assigned to those students who need (or want) the review of concepts they "should have learned in high school". These tutorials/reviews of quantitative skills are meant to reduce the time spent in class teaching remedial skills while increasing the quantitative support for those students who need it. Self-paced and web-based means that you don't have to spend time in (or out of) class that could be spent on geoscience topics. | 677.169 | 1 |
ExpressionsinBar
08-Oct-2015
Powerful computer algebra system in your menu bar.Ratings
DetailsConstants (π, e, etc.)
Integers, fractions, floating numbers
Sequences, lists, vectors, matrices, strings
Operators (+, -, *, /, ^)
Arithmetics on integers, rational, and floating numbers
Arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating point numbers (no practical limit to the precision except by the available memory) | 677.169 | 1 |
Maths Terms
Screenshots
Details
Description
Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.
Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics continued to develop, for example in China in 300 BC, in India in AD 100, and in the Muslim world in AD 800, until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.
Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered.
The application will be updated on the regular basis to include the new rules and the terms being introduced by new generations of mathematicians.
Going further, the application has a potential to include the links to the informative websites, to integrate with the social networking websites and thus to become a complete Mathematics bible | 677.169 | 1 |
A secondary mathematics curriculum of open-ended non-routine problems developed by a teacher of high school math over 10 years is described. An open-ended non-routine problem is one that requires problem recognition and orientation, effort, and persistence. It is open-ended in that it allows for various solutions, and requires the student to evaluate a variety of approaches and solutions. Every student can solve the problem, and each solution requires at least a few hours of work. In a sense, it corresponds to an essay in the language arts. A 4-year high school curriculum of non-routine problems has been developed and field tested. The core is a set of 60 non-routine problems, 16 for each year. Each item gives the student a chance to practice problem solving. In field tests over 10 years with the instructor's students, the problems have been refined. Students who have practiced these problems demonstrate "mathematical maturity" in their problem-solving approaches. Appendix A summarizes the non-routine problems for each grade level. Appendix B gives sample problem statements. Appendix C is a draft of teaching suggestions. (SLD) | 677.169 | 1 |
Department
Contents
Introduction
The Mathematics Department (Junior section), as the name implies, is responsible for delivering the S1-S3 Mathematics curriculum stated in the EDB CDC curriculum guide.
Mathematics not only concerns with computation and problem solving, it also concerns with the fundamental element that lies in all human knowledge - logic. Moreover, Mathematics is also a language - a language that is precise, concise and free from any ambiguity as in other natural languages. All these make Mathematics lies in the core curriculum of almost everywhere in the world.
Aims
The Department aims to:
help students to develop better problem solving skills;
IT skills in learning Mathematics;
to acquire greater power of analysis;
to develop independent and teamwork; and
to develop a web platform to provide better support for self learning and revision
Teaching methodology
Because the school offers two different curricula, the NSS and IB, in the senior level, the department uses the following methodologies in teaching so that students have enough exposure to decide which stream they will enter when graduated from the Junior level.
Traditional teaching will be used throughout the year serving as the basis for developing key concepts and skills. It is to maintain the efficiency in teaching and learning.
Exploratory approach involves students to work on some new areas of knowledge. Depending on the development of students, class teachers will design lessons asking students to explore, in group (cooperative learning) or individual, on some concepts of Mathematics.
Calculator policy
The NSS and IB have very different calculator policies. The NSS does not allow the use of graphics calculators while graphics calculators play importance role in IB curriculum. As students in junior forms have no public examination burden, the department thinks that offering both sides of the world should bring more good than bad to our students. Thus, we allow students to use any of the allowed calculators in these two curricula in their learning or examination. In fact, we think that the earlier they make use of calculator in their learning, the faster they will gain the benefits of it.
The department is having some TI-84Plus calculators, donated by Texas Instruments Inc. Students who would like to use graphics calculator to explore Mathematical concepts may borrow from the department. To maintain fairness in examinations and tests, explicit teaching materials on how to use the calculator will not be taught in normal lesson. In addition, the use of the allowed calculator will not have significant advantage in tests and examinations.
IT strategies
With the advances in information technology, students nowadays cannot have a solid foundation of their knowledge without it. So, the department is currently building a new website in order to support her students' in this area. That is why you are here.
All news about the department and learning materials will be centralized there. Please visit the website often to obtain the necessary support.
Ending words
The department is always practicing an "all time open policy". Students and parents are most welcome to give their comments and suggestions to make teaching and learning better. You may contact the department head through
Telephone: 27685641
Email: dbshyl@dbs.edu.hk
We promise that your comments and suggestions will be considered in depth. | 677.169 | 1 |
User Case Study: High School Students Use Maple to Explore and Learn Math beyond Textbooks
Appleby College gives their students an early start in advanced math by introducing them to tools used in university and industry.
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Educators in high schools around the world have discovered that Maple helps them give their students a head start in mathematics education. As a high school math teacher, Calvin Armstrong of Appleby College, a private high school in Oakville, Ontario, Canada, gives his students an early start in advanced mathematics by introducing them to tools used in university and industry. He wants his students to push boundaries and excel in their quest for knowledge. It is a philosophy that is embraced by Appleby College as a whole, making it known across Canada for academic excellence.
Being a math teacher, Calvin wants his students to expand their understanding of math and its application in the real world. While encouraging students to go beyond the obvious, he introduces them to tools and techniques that help them see beyond the theories in the textbooks, to implications in their future studies and work.
It is with this intention that Calvin introduced Maplesoft's technical computing software, Maple, to high school students. Maple is a powerful general purpose math tool designed to provide an environment for educators and students to explore and 'do' math. Used creatively, Maple helps students learn better and faster. It illuminates theory, clarifies the abstract and gives form and substance to general principles. Calvin first introduced Maple to his grade 12 classes. The students responded so positively, and it made such a big difference in their learning, that he decided to start early, and introduced the power of Maple as early as the 9th grade.
Here is what Calvin says about his students' use of Maple:
"Maple lets students push boundaries that they couldn't with other tools. It incorporates all the aspects of their mathematical understanding, from algebra to geometry and calculus. It takes all of their formal understanding from textbooks, and puts it into an algebraic context or a graphical context. Maple really is an environment for students to play mathematically. However, using Maple is not limited to mathematics; it can also be used in any stream of science or technical course. It is a tool that will start them in grade 9 and last them well into university.
We realized the potential in Maple to start students earlier - it is simple to learn, but powerful enough to let students grasp the concept.
— Calvin Armstrong, Appleby College
Initially, at Appleby, we were using Maple in the 12th grade calculus class, when students are almost heading out into the university, becoming familiar with advanced mathematics. We realized the potential in Maple to start students earlier - it is simple to learn, but powerful enough to let students grasp the concept. So we started them on Maple in Grade 9 mathematics. Linear systems are not only heavily algebraic, but it also has a graphical component. We started using Maple to teach the idea of substitution, leading the students through the algebraic process. We were very surprised to observe that not only did they grasp the idea of 2x2, but instinctively considered the possibility of having three variables, and figured out how to do a 3x3. Students advanced their own learning by asking themselves the question, 'what next?'
Very often we talk about math being a search for patterns. We as teachers want students to explore how a change in variable or value affects a given situation. Doing it by hand is extremely tedious, and the search for pattern overwhelms the pattern recognition itself. Graphing calculators can be clumsy and not very efficient. Doing animations with Maple gives students quick values, allows them to nicely move values on sliders, and provides animation. It can also be incorporated into one document that can be distributed to other students, or projected onto a whiteboard while the students explain the animation in progress. The document can be shared easily between students and the teacher. In fact, these documents can be shared with other students and faculty around the world, increasing chances of collaborative learning.
Maple is also a great companion for the math teacher. It provides the teacher great flexibility in the development of assignments and tests. It gives them flexibility in the creation of the graph, the ability to zoom in and out by changing parameters, and the means to develop a whole series of questions so that there is differentiation in the classroom. Maple really helps the teacher develop questions and lessons in a meaningful way without spending too much time.
Students quickly realize that Maple is a sophisticated tool with a breadth of options to explore. It helps students understand that mathematics is a growing idea, far beyond the text books. Maple helps in expanding the students' understanding of mathematics, and helps them realize it is not limited to what they are learning now. The fact that this software helps to explore and understand the depth and breadth of mathematics is a huge advantage for Maple."
Watch a video of Calvin Armstrong talking about his use of Maple in his math classroom: | 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 |
Summary: Math 7290 Fall 2007
Lie Algebras P. Achar
Course Information
Office: 266 Lockett Hall
Phone: 578-7990
E-mail: pramod@math.lsu.edu
Office hours: Tues. 2:00pm3:30pm or by appointment
Overview. Lie algebras are essential in many areas of mathematics and theoretical physics. In this course,
after covering the definition and basic properties of Lie algebras, we will study the structure theory of
semisimple Lie algebras and the classification of simple Lie algebras, and then take a brief look at their
representation theory. Throughout the course, we'll keep in mind the example of sl2, the smallest semisimple
Lie algebra. It's small enough (only 3-dimensional) to easily do explicit calculations in, and at the same
time interesting enough to give us a good idea of what goes on in higher-dimensional Lie algebras.
Textbook. For much of the semester, we will work from a set of notes by Anthony Henderson. These are
available in PDF format on the Blackboard page for the course. Important: The author has requested that
these notes not be made publicly available. In other words, don't post the PDF file on your own webpage.
At various points in the semester, I will distribute supplementary notes from other sources.
Course outline. A tentative list of topics for the semester is as follows:
Definition and basic properties (Chapters 13) 1 week
Modules and Representations; sl2 (Chapters 46) 2 weeks | 677.169 | 1 |
Mathematics
The Beauty of Mathematics
The math program is designed to help all students develop the capacity for mathematical thinking in a challenging, creative, and comprehensive way. Students progress mathematically at least as far as Calculus/Chaos Theory and often as far as AP Calculus.
Mathematics instruction is combined through the block system and year-long track classes. Main Lesson math blocks provide students with a unique and immersive mathematical experience. Students have time to explore mathematical ideas in a more creative way and within a historical context.
Students are also enrolled in year-long track courses in Algebra, Geometry, Advanced Algebra, Precalculus, and Calculus. Classes are divided by skill level; there is a traditional college prep track and an honor track. These courses are optional during senior year, though the large majority of students elect to enroll in a fourth year of study.
Blocks
Permutations and Combinations: 9th Grade
Students explore the many faces of chance: fate, destiny, randomness, risk. Introduction to the fundamentals of probability theory: definitions, the Law of Large Numbers, expected value, applications. Students work with frequency distributions and box-plots, and utilize different measures of central tendency: the mean, median, and mode.
Trigonometry: 10th Grade
Block begins with determining when two polygons are similar. Once introduced, the sine, cosine, and tangent functions are used in calculations involving right triangles and eventually in deriving the Law of Sines and the Law of Cosines for (not necessarily right) triangles.
Projective Geometry: 11th Grade
Block formalizes one of the central principles of perspective art: parallel lines meet at infinity. This block includes elements at infinity, the principle of duality, perspectivities and projectivities, projective generation of point and line conics, cross‐ratio and invariance, and, more specifically, study of the theorems of Desargues, Pascal, Brianchon, and Pappus.
Calculus/Chaos Theory: 12th Grade
Block introduces the historical and mathematical development of calculus and includes elementary aspects of both differential and integral calculus.
Algebra II
Honors Algebra II
Concepts and techniques of advanced algebra with emphasis on problem solving and mathematical modelings. Topics includes: matrices and determinants; complex numbers; the investigation of functions (linear, quadratic, and polynomial); transformations of functions; polynomials and rational functions and their graphs; real zeros of polynomials; complex zeros and the Fundamental Theorem of Algebra; exponential and logarithmic functions; and sequences and series.
Honors Pre-Calculus
Investigations encompass circular motions and the functions that describe it; vectors; dot products; matrices; and geometry on the surface of the Earth. Geometry and in two and three dimensions is integrated across topics and includes coordinate and transformational approaches. Counting, data analysis are included through the curriculum.
Practical and analytic trigonometry, later applied to the polar coordinate system, complex numbers, and vectors. studies of matrices, inverse functions, and sequences and series.
Prepares students for the SAT Subject Test in Mathematics - Level II.
AP Calculus
Basics topics of differential and integral calculus, including functions, limits, and the derivative and applications of differentiation, curve sketching, the integral, and applications such as rectilinear motion and volumes. Prepares students to sit for the AP exam.
In college, I realized how well the high school math program had prepared me. I was able to recall the beautiful, simple, and direct explanations offered both in my track classes and the Main Lesson blocks.
– Trevor Sargent, Class of 2011; computer science major
The Exeter Method
Faculty teach honors math courses using an integrated problem-centered curriculum developed by Phillips Exeter Academy. Students receive a carefully developed series of math problems in lieu of a textbook or set of lectures, then present their well-reasoned solutions for discussion amongst the class. The seminar-style approach requires students to ask effective questions, answer inquiries, and critically assess their own work.
The mathematics department includes Dr. Cynthia Renegar, Kevin Farey, and John Jackson. | 677.169 | 1 |
9780072409666College Algebra
COLLEGE ALGEBRA is written for a one-semester or two-quarter college algebra course at the freshman level. 'Me emphasis of the text is to help students think critically and to discover how algebra applies to the world around them. In order to make the material more relevant, an abundance of applications can be found in the examples as well as the exercises sets. A fall-colour design highlights key equations, rules and procedures for problem solving. The colour of a graph corresponds to the colour of its equation so students can clearly distinguish between the graphs of more than one equations, The authors' treatment of functions is unusually rich in applications. Inverse functions (Sec. 4.6) are introduced after conic sections so that students will have had more experience with graphing and can more easily visualise this concept. In response to the AMATYC and MAA guidelines and the NCTM standards, several features involving writing, critical thinking, discussion, exploration and technology appear in the text. Notes discussing the usefulness of technology can be found in the margins at appropriate points to invite further exploration. Graphing calculator exercises appear throughout the problem sets. 'These exercises, which are noted with an icon, encourage the student to interpret what they are seeing on the calculator. Every chapter opens with a brief discussion of the significance of the material in the chapter and how it can be applied. Each chapter closes with a feature entitled ENCORE which is an interesting example that illustrates the usefulness of the mathematics covered in that chapter. ENCORES help students appreciate the connection of mathematics, specifically algebra, to the real | 677.169 | 1 |
Product Description
The Chemistry Tutor: Learning by Example DVD Series provides an introduction to chemistry through step-by-step example problems. Emphasis is placed on giving students confidence in their skills by gradual repetition so that the skills learned are committed to long term memory. This episode covers significant figures in chemistry calculations, focusing on why the number of decimal places in the calculated answer to a problem should take into account how many decimals were provided in the provided statement. Grades 9-Adult. 48 minutes on DVD.
DVD Playable in Bermuda, Canada, United States and U.S. territories. Please check if your equipment can play DVDs coded for this region. Learn more about DVDs and Videos | 677.169 | 1 |
Access
Available online
More options
Contents/Summary
Bibliography
Includes bibliographical references (p. [200]) and index.
Publisher's Summary
This book covers the material of an introductory course in linear algebra: sets and maps, vector spaces, bases, linear maps, matrices, determinants, systems of linear equations, Euclidean spaces, eigenvalues and eigenvectors, diagonalization of self-adjoint operators, and classification of matrices. The book is written for beginners. Its didactic features (the "book within a book" and multiple choice tests with commented answers) make it especially suitable for self-study. (source: Nielsen Book Data) | 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 | 677.169 | 1 |
Tagged Questions
For questions related to the teaching and learning of mathematics. Note that Mathematics Educators StackExchange may be a better home for narrowly scoped questions on specific issues in mathematics education.
How to learn mathematical topics in-depth? For instance, if you want to learn about Symmetry, you would use Google, you'll get results. Unfortunately, what you'll find is tutorials for beginners. But ...
me and my algebra 2 teacher got into an argument about if it is possible to solve a system of equations with four missing variables by substitution. he said it is not possible because you could not ...
After tutoring someone about polynomial manipulation, my mind went back to this equivalence:
$(a+b)\times (c+d)=ac+ad+bc+bd$
I realized that, while it can be memorized as it is, it has a very simple ...
Most authors define functions this way:
Given the sets $A$ and $B$. A relation is a subset of $A\times B$. Then given a relation $R$, we define $Dom_R=\{x|(x,y)\in R\}$ and $Img_R=\{x|(y,x)\in R\}$.
...A large volume of mathematical demos were written in Java. Then came security warnings of all sorts. Currently it does not seem viable to direct students to such demos.
Do you think an organization ...
I am currently taking an honors introduction to analysis course, and it seems to me that to me defining all of the concepts in terms of sequences allows for much cleaner proofs, and the concepts are ...
I have two questions about the following problem, taken from Challenging Problems in Algebra by Posamentier and Salkind: (1) Why is the answer not 1 person? (2) The answer given, without solution, is ...
Regarding the subtraction and borrowing a digit from upper digits, I know how that works for more than one digit numbers. However, I can not figure out for one digit numbers! It is an obvious thing ...
I am giving tomorrow an introduction to Python to undergraduates and have to present how it can be used to solve some mathematical problems. I have been looking for some nice or challenging problems ...
I'm looking for a way to show my calc 1 students not to use the limit laws without knowing that the individual limits exists. I could use $$\lim_{x\to 0} x^{2} \sin(1/x),$$
but by doing it wrong, one ...
So, I was doing a Calculus problem a few minutes ago and just recalled something that my real analysis professor said during a lecture years ago...
To provide context, take the function $f$ defined ...
This is not a duplicate question because I am looking for an explanation directed to a general audience as to the mistakes (if any) in Numberphile's proof (reproduced below). (Numberphile is a YouTube ...
a local government is planning to build new roads that will divide a forest into several fragments the roads can follow several different designs each of which design will minimize the edge effect on ... | 677.169 | 1 |
The Real World Learning Objects (RWLO) Resource Library is "an online repository of Internet-based unique and compelling learning objects designed so that community college faculty can easily access and adapt for use in their classes." The RWLO Library provides core instructional internet-based activities focused on topics in higher education mathematics, science, educational technology, and
A collection of games and puzzles for math review, this page provides visitors with a number of ways to engage in math topics. There are ten java-based and eleven non-java flashcard collections on concepts including inequalities, algebra, and geometric shapes. In the Game Room, visitors will again find java and non-java applications to practice arithmetic, algebra, and geometry. The Homework... | 677.169 | 1 |
A new school year is here, and many students are diving into new levels of math. Fortunately, this year, you have Wolfram|Alpha to help you work through math problems and understand new concepts. Wolfram|Alpha contains information from the most basic math problems to advanced and even research-level mathematics. If you are not yet aware of Wolfram|Alpha's math capabilities, you are about to have a "wow" moment. For the Wolfram|Alpha veterans, we have added many math features since the end of the last school year. In this post, we're highlighting some existing Wolfram|Alpha math essentials, such as adding fractions, solving equations, statistics, and examples from new topics areas like cusps and corners, stationary points, asymptotes, and geometry.
You can access the computational power of Wolfram|Alpha through the free website, via Wolfram|Alpha Widgets, with the Wolfram|Alpha App for iPhone, iPod touch, and the iPad! Even better, the Wolfram|Alpha Apps for iPhone, and iPod touch, and the iPad are now on sale in the App Store for $0.99 though September 12.
If you need to brush up on adding fractions, solving equations, or finding a derivative, Wolfram|Alpha is the place to go. Wolfram|Alpha not only has the ability to find the solutions to these math problems, but also to show one way of reaching the solution with the "Show Steps" button. Check out the post "Step-by-Step Math" for more on this feature.
You can find this widget, and many others, in the Wolfram|Alpha Widget Gallery. Customize or build your own to help you work through common math problems. Then add these widgets to your website or blog, and share them with friends on Facebook and other social networks.
Wolfram|Alpha computes things. While the use of computations to predict the outcomes of scientific experiments, natural processes, and mathematical operations is by no means new (it has become a ubiquitous tool over the last few hundred years), the ease of use and accessibility of a large, powerful, and ever-expanding collection of such computations provided by Wolfram|Alpha is.
Virtually all known processes occur in such a way that certain functionals that describe them become extremal. Typically this happens with the action for time dependent processes and quantities such as the free energy for static configurations. The equations describing the extremality condition of a functional are frequently low-order ordinary and/or partial differential equations and their solutions. For example, for a pendulum: Frechet derivative of Integrate[x'[t]^2/2 – Cos[x[t]], {t, -inf, inf}] wrt x[tau]. Unfortunately, if one uses a sufficiently realistic physical model that incorporates all potentially relevant variables (including things like friction, temperature dependence, deformation, and so forth), the resulting equations typically become complicated—so much so that in most cases, no exact closed-form solution can be found, meaning the equations must be solved using numerical techniques. A simple example is provided by free fall from large heights:
On the other hand, some systems, such as the force of a simple spring, can be described by formulas involving simple low-order polynomial or rational relations between the relevant problem variables (in this case, Hooke's law, F = k x):
Over the last 200+ years, mathematicians and physicists have found a large, fascinating, and insightful world of phenomena that can be described exactly using these so-called special functions (also commonly known as "the special functions of mathematical physics"), the class of functions that describe phenomena between being difficult and complicated. It includes a few hundred members, and can be viewed as an extension of the so-called elementary functions such as exp(z), log(z), the trigonometric functions, their inverses, and related functions.
Special functions turn up in diverse areas ranging from the spherical pendulum in mechanics to inequivalent representations in quantum field theory, and most of them are solutions of first- or second-order ordinary differential equations. Textbooks often contain simple formulas that correspond to a simplified version of a general physical system—sometimes even without explicitly stating the implicit simplifying assumptions! However, it is often possible to give a more precise and correct result in terms of special functions. For instance, many physics textbooks offer a simple formula for the inductance of a circular coil with a small radius:
While Wolfram|Alpha knows (and allows you to compute with) this simple formula, it also knows the correct general result. In fact, if you just ask Wolfram|Alpha for inductance circular coil, you will be simultaneously presented with two calculators: the one you know from your electromagnetics textbook (small-radius approximation) and the fully correct one. And not only can you compute the results both ways (and see that the results do differ slightly for the chosen parameters, but that the difference can get arbitrarily large), you can also click on the second "Show formula" link (near the bottom of the page on the right side) to see the exact result—which, as can be seen, contains two sorts of special functions, denoted E(m) and K(m) and known as elliptic integrals: More »
Version 1.1 of the Wolfram|Alpha App for the iPhone & iPod is now available in the App Store. The new version includes a number of new features that continue to improve the app's unique mobile Wolfram|Alpha experience. Perhaps its most iconic feature, the specialized keyboards that greet you when you first open the Wolfram|Alpha App, have been painstakingly constructed to ease the burden of entering queries, whether you're converting from pounds to euros or computing a numerical value for the Weierstrass p-function . Our goal in creating these keyboards was to form families of characters that naturally occur together both in common use and in traditional mathematical applications. We also wanted mathematical expressions to look and feel natural to enhance usability and understanding. Version 1.1 has four specialized keyboards: the default keyboard, the "math" keyboard accessed by the right-shift key , the "Greek" keyboard accessed by one press of the left-shift key , and the "symbol" keyboard accessed by a second press of the left-shift key.
To determine the optimal keyboard layout, we scoured Wolfram|Alpha's server logs for the most commonly entered phrases that have characters with meaning in Wolfram|Alpha. Given that Wolfram|Alpha is built on Mathematica, one of its core strengths is advanced mathematics. True to form most of the commonly typed characters are related to math. For example, you would generally type the word "integrate" to compute an integral on the Wolfram|Alpha website. In the Wolfram|Alpha App you could simply type the key on the math keyboard. The same is true for other symbols common in math, such as and . Specifying geometric shapes, such as a triangle, is straightforward as well.
Have you ever given up working on a math problem because you couldn't figure out the next step? Wolfram|Alpha can guide you step by step through the process of solving many mathematical problems, from solving a simple quadratic equation to taking the integral of a complex function.
When trying to find the roots of 3x2+x–7=4x, Wolfram|Alpha can break down the steps for you if you click the "Show steps" button in the Result pod.
As you can see, Wolfram|Alpha can find the roots of quadratic equations. Wolfram|Alpha shows how to solve this equation by completing the square and then solving for x. Of course, there are other ways to solve this problem! More » | 677.169 | 1 |
Product Description
This teacher's guide contains the instructions for Educators Publishing Service's Computation Basics series. A short placement exam and overview of the program is provided; instructions for each unit for each of the six books in the series are provided. Unit instructions include the instructional objective, and some additional notes or teaching tips if necessary. 17 pages, booklet. | 677.169 | 1 |
Find a Frazer, PA Algebra 2For example, I have created a simulation tool for assessing geothermal ground source heat pump vertical loop performance. This software produces a closed form solution for the propagation of heat through rock which utilizes the separation of variables method for solving Bessel function solutions. I was a C level engineering manager for GE, and named engineer of the year. | 677.169 | 1 |
Math Magic Revised Edition
How to Master Everyday Math Problems
About the Book
Don't live in fear of math any longer.
Math Magic makes math what you may never have imagined it to be: easy and fun!
Scott Flansburg -- "the Human Calculator" who believes that there are no "mathematical illiterates," just people who have not learned how to make math work for them -- demonstrates how everyone can put their phobia to rest and deal with essential every-day mathematical calculations with confidence. This is the book for millions of otherwise successful adults who are afraid to balance their checkbooks and don't know how to figure interest on savings or credit, and for the millions of students who dread their math classes and live in fear of the SAT math section.
In Math Magic, Scott Flansburg shows the reader how to:
Master the basics, including the real way addition, subtraction, multiplication, and division work
Simplify calculations through estimation
Quick-check answers
Convert metric measures to more familiar ones
Figure tips, taxes, and percentages -- never get short-changed again!
Master algebra using the nine easy steps to algebra
Math Magic is for all of us who need and want to improve our understanding of math. With the help of Flansburg, the Guinness World Record holder as the Fastest Human Calculator, you can do math just like | 677.169 | 1 |
Hi Alice,
Here's an opposing view for you from another Teacher2Teacher Associate.
You'll see that Chris' definition is not the same as Martha's. He's talking
about a course, Algebra I, not just algebraic reasoning.
Let us know if this information is useful to you.
-Kristina, for the T2T service
Chris wrote:
As a math teacher, I am convinced that it is often not appropriate for some
middle school students to take Algebra I. Since Algebra is the study of
patterns, one could argue that algebraic reasoning occurs in grades much lower
than fifth grade. Therefore, the argument that it should be taught to all in
middle school because it is taught in fifth grade, is not logical. Formal
algebraic operations is an abstract thinking process that can be daunting for
some middle school students. Unfortunately, it is in states like Florida that
mandate algebra to all that creates this problem. You push a kid too early
into Algebra, and you could limit the potential of that student because their
foundation will be weak. When states like Florida mandate Algebra for all,
what ends up happening is that the Algebra that is taught, because it must
reach all students, is watered down, lacking in rigor and depth, and
demonstrably inferior to what the program should be.
Algebra for all middle school students (11-14 year olds) is not something we
should pursue as a nation unless we are willing to sacrifice the math
potential of many of our students.
Chris Mahoney
Brookwood School | 677.169 | 1 |
Hi, my high school classes have just begun and I am shocked at the amount of renaming units of length middle school math with pizzazz book d homework we get. My basics are still not clear and a big assignment is due within few days. I am really upset and can't think of anything. Can someone guide me?
Hey friend ! Studying renaming units of length middle school math with pizzazz book d online can be a disaster if you are not a professional at it. I wasn't an expert either and really regretted my decision until I found Algebrator. This little software has been my buddy since then. I'm easily able to solve the questions now.
Even I've been through that phase when I was trying to figure out a solution to certain type of questions pertaining to perpendicular lines and percentages. But then I came across this piece of software and it was almost like I found a magic wand. In the blink of an eye it would solve even the most difficult questions for you. And the fact that it gives a detailed step-by-step explanation makes it even more useful . It's a must buy for every algebra student. | 677.169 | 1 |
Find a Lowry, CO Algebra 2...This is at least partly true. The problems you encounter in algebra 1 are more challenging than those you encounter in arithmetic. However, you often use the same techniques you used in arithmetic to solve algebra 1 problems! | 677.169 | 1 |
Synopses & Reviews
Publisher Comments
This textbook is ideal for an undergraduate introduction to probability, with a calculus prerequisite. It is based on a course that the author has taught many times at Berkeley. The text's overall style is informal, but all results are stated precisely, and most are proved. Understanding is developed through intuitive explanations and examples. Graphs, diagrams, and geometrical ideals motivate results that might otherwise look likely purely formal manipulations. | 677.169 | 1 |
I am interested in taking this online course on machine learning. As it stands my math is very elementary, and I am basically learning math from scratch on khan academy. Programming-wise I have a decent amount of experience, and a good overall understanding. My question is, what math skills are required for me to be able to effectively understand and utilize machine learning Jim G., durron597, gnat, GlenH7, Snowman
I started the course as well. Its been a while since I did any Maths. There is an optional bit in the course about the linear algebra. Its fairly well explained, but the notation can be a bit confusing. You can rewind the videos though, which helps.
– wobbily_colJun 27 '14 at 12:50
2 Answers
2
That course is specifically designed to be accessible to folks without 'much' math background. Of course 'much' is a relative term. In this case it means 'knowledge of calculus is helpful but not required'. The course does use some results from differential calculus, but you can answer the quizzes and complete the programs without knowing calculus yourself. You just won't understand where some of the formula you have to implement are coming from.
You absolutely will need to be comfortable with basic linear algebra (manipulating vectors and matrices) and working with logarithmic and exponential functions. | 677.169 | 1 |
Saxon Math Homeschool 7/6 teaches math with a spiral approach, which emphasizes incremental development of new material and continuous review of previously taught concepts.
Building upon the principles taught in Saxon Math 6/7, the
The Tests and Worksheetsbook provides supplemental "facts practice" tests for each lesson, as well as 23 cumulative tests that cover every 5-10 lessons. The included "activity sheets" are designed to be used with the activities given in the student worktext. Five optional, reproducible, recording forms are also included.
The Solutions Manual provides answers for all problems in the lesson (including warm-up, lesson practice, and mixed practice exercises), as well as solutions for the supplemental practice found in the back of the student text. It also includes answers for the facts practice tests, activity sheets, and tests in the separate tests & worksheets book.
Saxon Math 7/6 is designed for students in grade 6, or for 7th grade students who are struggling with math.
Saxon Math 7/6 will help middle-school students gain a solid foundation of algebraic reasoning and geometric skills as they prepare to move on to higher-level math and algebraic reasoning in Saxon 8/7 or Algebra =. It teaches math with a spiral approach, which emphasizes incremental development of new material and continuous review of previously taught concepts.
This The back of the book contains supplemental problems for selected lessons and concepts.
p>This Saxon Math Homeschool 7/6 Tests and Worksheets book is part of the Saxon Math 7/6 curriculum for 6th grade students, and provides supplemental "facts practice" tests for each lesson, as well as 23 cumulative tests that cover every 5-10 lessons. The included "activity sheets" are designed to be used with the activities given in the (sold-separately) student worktext.
A testing schedule and five optional, reproducible, recording forms are also provided; three forms allow students to record their work on the daily lessons, mixed practice exercises, and tests, while the remaining two forms help teachers track and analyze student performance.
Solutions to all problems are in the (sold-separately) Solutions Manual.
This Saxon Math Homeschool 7/6 Solutions Manual provides answers for all problems in the textbook lesson (including warm-up, lesson practice, and mixed practice exercises), as well as solutions for the investigations and supplemental practice found in the back of the student text. It also includes answers for the facts practice tests, activity sheets, and tests in the tests & worksheets book. Answers are line-listed, and are organized by type (lessons & investigations, facts practice tests, tests, etc.).Learning--and teaching!--math does not have to be difficult! Give your students and yourself the tools to succeed with this Saxon Teacher and Saxon 7/6 kit combination! Introduce your middle-schoolers to the concepts they'll need for upper-level algebra and geometry, including functions and coordinate graphing; integers; multiplying decimals and fractions; radius, circumference, and pi; compound interest; exponential expressions; prime factorization; statistics and probability; and complementary and supplementary angles. This kit includes Saxon's 4th Edition Math 7/6 textbook, solutions manual, and tests/worksheets book.Boost your students understanding of Saxon Math with DIVE's easy-to-understand lectures! Each lesson concept in Saxon's textbook is taught step-by-step on a digital whiteboard, averaging about 10-15 minutes in length; and because each lesson is stored separately, you can easily move about from lesson-to-lesson as well as maneuver within the lesson you're watching. Taught from a Christian worldview, Dr. David Shormann also provides a weekly syllabus to help students stay on track with the lessons. DIVE teaches the same concepts as Saxon, but does not use the problems given in the text; it cannot be used as a solutions guide.
Math 7/6 covers fractions, decimals, percent conversions and unit multipliers, as well as circumference, pi, angles, graphing, and prime factors. For use with 4th Edition.
Get everything you need for a successful and pain-free year of learning math! This kit includes Saxon's Math 7/6 textbook, solutions manual, and tests/worksheets book, as well as the DIVE Math 7/6 CD-ROM. A balanced, integrated mathematics program that has proven itself a leader in the math teaching field, Math 7/6 covers compound interest; functions and coordinate graphing; integers; exponential expressions; divisibility concepts; prime factorization; ratios and proportions; radius, circumference and pi; statistics and probability; and complementary and supplementary angles.
The DIVE software teaches each Saxon lesson concept on a digital whiteboard, averaging about 10-15 minutes in length; because each lesson is stored separately, you can easily move about from lesson-to-lesson as well as maneuver within the lesson you're watching. DIVE teaches the same concepts as Saxon, but does not use the problems given in the text; it cannot be used as a solutions guideThis kit includes:
Set of Teaching Tape Saxon Math 7/6 DVDs, 4th Edition
Saxon Math 7/6, 4th Edition Student Text; 744 pages, softcover.
Saxon Math 7/6, 4th Edition Tests & Worksheets book, softcover.
Saxon Math 7/6, 4th Edition Solutions Manual, softcover.
Sign Up To Receive Exclusive Email Offers You can unsubscribe at any time | 677.169 | 1 |
Concepts inProgramming for learning in mathematics and science | 677.169 | 1 |
Applied Mathematics for Physical Chemistry/i>…
See more details below
Paperback
Temporarily out of stock online.
Overview students succeed in their course.
This book features:
Introductory chapters that deal with coordinate systems, functions and graphs, and the use of logarithms.
Chapters on differential and integral calculus.
A chapter of mathematical methods in the laboratory, including error analysis, propagation of errors, linear regression calculations, and preparing graphs.
An introduction to differential equations.
A chapter illustrating the use of Fourier series and Fourier transforms.
Problems at the end of each chapter, with answers to all problems in an appendix.
New to this edition:
A completely revised chapter on Numerical Methods and the Use of the Computer that illustrates how to complete calculations using Microsoft Excel™.
General Properties of Logarithms. Common Logarithms. Natural Logarithms.
4. Differential Calculus.
Functions of Single Variables. Functions of Several Variables-Partial Derivatives. The Total Differential. Derivative as a Ratio of Infinitesimally Small Changes. Geometric Properties of Derivatives. Constrained Maxima and Minima.
5. Integral Calculus.
Integral as an Antiderivative. General Methods of Integration. Special Methods of Integration. The Integral as a Summation of Infinitesimally Small Elements. Line Integrals. Double and Triple Integrals.
6. Infinite Series.
Tests for Convergence and Divergence. Power Series Revisited. Maclaurin and Taylor Series. Fourier Series and Fourier Transforms. | 677.169 | 1 |
Math 42 for iPhone and iPad not only solves math problems but helps you better understand them
Math 42 is an amazing little app for iPhone and iPad that functions both as an all-in-one calculator and as a learning tool. Aimed at 5th to 12th grade level students, you can get the help you need solving problems in many different categories. When you get stuck, Math 42 can even take you step by step through how to solve a particular problem.
Whenever you get stuck on a math problem, it doesn't typically help to just stare at the solution and wait for it to click. This is where Math 42 really stands out and actually helps students understand different types of math including the following -
Simplifying expressions
Binomial decomposition
Fractions
Equations (linear and quadratic)
Polynomial long division
Derivation
Not only can students practice these topics in Math 42, they can also input their own problems and have them solved. Each solution can also be explained step by step which makes for a great learning aid when you get stuck.
Whether you're a student studying math or a parent who really just doesn't remember enough of this kind of stuff to be of much help, Math 42 is a great option to have on handMath 42 for iPhone and iPad not only solves math problems but helps you better understand them | 677.169 | 1 |
Find a KemahI help students develop the ability to see computational problems from a mathematical perspective. Discrete math is normally divided into six areas: sets, functions, and relations; basic logic; proof techniques; counting basics; graphs and trees; and discrete probability. I show students how these topics are interwoven with computer science applications | 677.169 | 1 |
...LA has a lot of practical applications including statistics, computer science and probability, so a deep knowledge of LA can go a long way. Understanding LA requires some basic mathematical thinking (solving systems is nothing more than doing simple arithmetic and algebra) - past this there is a... | 677.169 | 1 |
Math for Economists
Math for Economists
This is a free course offered by the Saylor Foundation.'...
More
This is a free course offered by the Saylor Foundation.
' evaluate the options and select from the best alternatives. Advanced courses in economics typically utilize mathematical techniques beyond basic calculus; so, gaining practice in fundamental skills can serve as a good basis for further study. Of note, this course applies precalculus and calculus; this is different from "applied math," which economists typically use to refer to probability and statistics.
This course begins with a survey of basic optimization tools and then applies them to solve problems over several periods in time. These optimization tools describe feasible choices and then direct you to the best possible solution. In essence, they will help you evaluate an economic environment and determine the best course of action. The role of risk in financial decisions is explored in relation to individual choices and macroeconomic processes. The equitable distribution of resources is then considered. In other words, this class will explore whether an optimal solution is indeed also fair to the participants and society. A specific application, game theory, is presented as one of the major recent advances in economic theory. The final topic returns to microeconomic problems such as taxes, elasticity, and specific types of supply and demand curves.
The materials included in the course offer a framework that you can use to apply quantitative skills. You should liberally use Saylor course materials (MA001, MA003, MA005, ECON103/MA101, and MA102) to refresh their general techniques. This course fits into the major as a bridge between quantitative theory and specific applications to problems in economics. Completing this course can greatly help students successfully build a toolkit for the intermediate courses, ECON201 and ECON202 for Economists to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Math for Economists
Select this link to open drop down to add material Math for Economists to your Bookmark Collection or Course ePortfolio | 677.169 | 1 |
Course description: An introductory course designed to acquaint
the student with applications of mathematics in the life of the consumer.
Special attention will be given to the algebraic derivation of formulas, the
reduction of real life situations to mathematical models, and the mathematics
employed in banking, credit, taxes, insurance, installment buying, and
annuities.
Text: Biehler, The Mathematics of Money 2/e. Lulu, 2010.
Calculator: You will
need a calculator.The TI-30 or
better is highly recommended for this class.It is your responsibility to know how to use your calculator.
Bring it to class each day.I will
assume you have it for group work, quizzes and tests.
Course objectives: The student will
be able to do calculations
involving decimals and percents quickly and accurately;
be able to set up and solve
word problems involving therate * base = percentageequation and its applications;
be able to use formulas and
technology to calculate simple and compound interest, present value,
annuities, and periodic payments;
understand
of the meaning of annual percentage rate and annual percentage yield.
Grades: Your course grade will be determined as follows.
3 tests, 1 composite quiz grade
...drop lowest of these 4 ......... 48% of the final grade
Class participation (group work) ............................................ 15% of the
final grade
Writing assignment(s)
............................................................. 15% of the final
grade
Final exam
.............................................................................
22% of the final grade
Homework: Homework is assigned regularly, and everyone is
expected to do it. Homework will not be collected without warning, and it
is your responsibility to do the assigned problems. Feel free to work
with others on homework, and ask me about problems you cannot solve.
Quizzes: Given frequently (but not every day), quizzes are
given at the start of the period. They are intended to see if you have
read the material and done the simple exercises. Quizzes are always
short, and they are open book and notes. Often they will be taken
directly from the homework. Quizzes that are missed for any reason cannot
be made up. You may miss one quiz without penalty, but you will be
assigned a grade of 0 for any additional
quizzes that you miss.
Class participation: Often you will be asked to work in groups
in class. Working in small groups of three or four, you will be asked to
solve a problem and present your results to the class. Missed class
participation sessions cannot be made up, but you will be allowed one absence
from a class participation session without penalty. You will receive a
grade of 0 for each additional missed
session.
Writing assignments: As a general education course, Math 114
will require more writing than in some non-general education mathematics courses.
There will be at least one writing assignment in this course. Writing
assignments will be graded both for mathematical correctness and for writing
style. More details and a grading rubric will be provided with the
assignments.
Attendance: Your attendance is expected at all classes.
Makeup tests will be given reluctantly, and then only upon presentation of a
doctor's excuse. Makeup test are always more difficult than regular
tests, regardless of the reason for absence. You may not make up missed class
participation sessions nor quizzes.
Do not leave in the middle of a class, even to get a drink of water or to
answer your cell phone. Students who leave in the middle of class for any
reason disrupt the class and break the teacher's concentration.
Honor code: I subscribe to the LongwoodUniversity
honor system, which, among other things, assumes you do not cheat and that you
take responsibility for seeing that others do not. Infractions will be
dealt with harshly. A student who is convicted of an Honor Code offense
involving this class will receive a course grade of F, in addition to any
penalties imposed by the Honor Board. | 677.169 | 1 |
Shipping prices may be approximate. Please verify cost before checkout.
About the book:
This book is concerned with the calculus of several variables and provides an introduction to elementary differential and difference equations. The emphasis is on practical problem-solving rather than the proof of formal theorems. Many worked examples are supplied as well as problems for the student to solve, together with their solutions. The techniques are illustrated with applications drawn chiefly from economics, statistics and operational research. Some elementary knowledge of the calculus of one variable is assumed but revision material is supplied throughout the text. A confident approach to problem-solving is not possible without some understanding of the background theory. In this book the theory is presented systematically but informally. Wherever possible, geometric arguments are used and the text is illustrated with numerous diagrams. Particular care has been taken to make the main body of the text suitable for students who are studying independently of a taught course. The book will interest students at universities and other higher education institutions. At the London School of Economics, the course on which this book is based is attended by students reading for a variety of different degrees and with a wide disparity in their previous levels of mathematical training. Some are graduates and some are first-year undergraduates. It is hoped that this book will attract a similar audience: not only of economists, statisticians and other social scientists but also physical scientists, engineers and mathematiciansTarquin Group via United Kingdom
Softcover, ISBN 0521289521 Publisher: Cambridge University Press, 1983 Usually dispatched within 1-2 business days
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Better World Books via United States
Softcover, ISBN 0521289512895 | 677.169 | 1 |
Christian Bär
Universität Potsdam, Germany
Hardback
£77.00
The link between the physical world and its visualization is geometry. This easy-to-read, generously illustrated textbook presents an elementary introduction to differential geometry with emphasis on geometric results. Avoiding formalism as much as possible, the author harnesses basic mathematical skills in analysis and linear algebra to solve interesting geometric problems, which prepare students for more advanced study in mathematics and other scientific fields such as physics and computer science. The wide range of topics includes curve theory, a detailed study of surfaces, curvature, variation of area and minimal surfaces, geodesics, spherical and hyperbolic geometry, the divergence theorem, triangulations, and the Gauss–Bonnet theorem. The section on cartography demonstrates the concrete importance of elementary differential geometry in applications. Clearly developed arguments and proofs, colour illustrations, and over 100 exercises and solutions make this book ideal for courses and self-study. The only prerequisites are one year of undergraduate calculus and linear algebra.
• Assumes only one year of undergraduate calculus and linear algebra
• Equips the reader for further study in mathematics as well as other fields such as physics and computer science
• Over 100 exercises and solutions
Review
'The book under review presents a detailed and pedagogically excellent study about differential geometry of curves and surfaces by introducing modern concepts and techniques so that it can serve as a transition book between classical differential geometry and contemporary theory of manifolds. the concepts are discussed through historical problems as well as motivating examples and applications. Moreover, constructive examples are given in such a way that the reader can easily develop some understanding for extensions, generalizations and adaptations of classical differential geometry to global differential geometry.'
Zentralblatt MATH | 677.169 | 1 |
Anchor Chart for Algebra II on Parent Functions and Transformations- Should make this and add to it as we touch on each.
Not a bad idea to have my students work on this type of presentation. Anchor Chart for Algebra II EOC Review on Parent Functions and Transformation ... made by Aubrey Wright and Evan Payne (April 2013).
Fibonacci sequence in our hand. That is cool... Also, The ratio between the hand, forearm, and upper arm is also Fibonacci... You know what that makes our arms? Fractals... Man math is the best ever...
Fibonacci sequence in our hand. Also, The ratio between the hand, forearm, and upper arm is also Fibonacci (the Golden Ratio or the Golden Mean). The human body is quite possibly the best example ever of fractals (sacred geometry).
.Fibonacci sequence in our hand bones. I do admit, even though I don't like math, Fibonnacci is quite fascinating.
Fibonacci sequence in our hand… I literally just curled my hand over and over in awe
Slope Infographic - great study guide for main ideas about the slope of a line, and easy ways to learn them! bibliography: author: Teacher spay
Slope Infographic - great study guide for main ideas about the slope of a lineTrigonometry Laws and Identities Math Reference Sheet (1 page PDF) ;; I could probably use this.. as it's been 7 years since I studied this last
Trigonometry Laws & Identities #school. my teacher: you have a strong back ground in math who'd you have for math? LOL. I took calculus in high school -___- . sigh, I took math 151 because it was the only math really required for nursing school. so just to cover by bases, even though I tested out of it... I took it. I thought hey, free A. Big mistake -___- switching the overall focus means taking all the other math classes. I hate math, even if I have a "strong background" in it. #medschoolprobs | 677.169 | 1 |
books.google.com - An Introduction to the Mathematics of Financial Derivatives is a popular, intuitive text that eases the transition between basic summaries of financial engineering to more advanced treatments using stochastic calculus. Requiring only a basic knowledge of calculus and probability, it takes readers on... Introduction to the Mathematics of Financial Derivatives | 677.169 | 1 |
Algebra 1
9780078738227
ISBN:
0078738229
Pub Date: 2007 Publisher: McGraw-Hill Higher Education
Summary: THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! "Glencoe Algebra 1" is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments.
McGraw-Hill Staff is the author of Algebra 1, published 2007 under ISBN 9780078738227 and 0078738229. Five hundred ...seventy four Algebra 1 textbooks are available for sale on ValoreBooks.com, four hundred six used from the cheapest price of $6.06, or buy new starting at $29 corner wear, highlighting, underlining and/or writing, but still a good rea... [more]ULTIPLE COPIES AVAILABLE! Glencoe: Algebra 1, Student Edition [Hardcover]. Copyright-2008, ISBN:0078738229 | 677.169 | 1 |
Maths
IIST ISAT 2011 MATHEMATICS SYLLABUS
SETS, RELATIONS AND FUNCTIONS: Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions;. one-one, into and onto functions, composition of functions.
COMPLEX NUMBERS AND QUADRATIC EQUATIONS: Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.
PERMUTATIONS AND COMBINATIONS: Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.
Matrices as a rectangular array of real numbers, equality of matrices,
addition, multiplication by a scalar and product of matrices, transpose of a
matrix, determinant of a square matrix of order up to three, inverse of a square
matrix of order up to three, properties of these matrix operations, diagonal,
symmetric and skew-symmetric matrices and their properties, solutions of
simultaneous linear equations in two or three variables.
Addition and multiplication rules of probability, conditional probability,
Bayes Theorem, independence of events, computation of probability of events
using permutations and combinations.
GUJCET : Gujarat Common Entrance
Test
Gujarat Common Entrance Test (CET) Engineering
Examination Gujarat Common entrance Test (CET) is conducted by The Education
Department, Govt of Gujarat and it has assigned The Gujarat Secondary and Higher
Secondary Education to hold CET for admission into various medical, engineering
and pharmacy courses in the state of Gujarat. The information booklet and the
application form prepared by the Board is available on the payment of Rs.
250/-via Demand Draft from any nationalized bank payable at Gandhinagar/Ahmedabad
in favour of "Secretary, Gujarat Common Entrance Test (CET) Cell, Gandhinagar"
Exam Pattern
Admission to courses will be based on 40% weightage of GUJCET score and 60%
weightage of 12th Marks. For admission to MBBS, 70% marks in 12th are also
required. Please note that marks of either PCM (without practicals) or PCB
(without practicals) are considered so effective weightage is somewhere between
21-28% for GUJCET Exam.
III. VECTOR ALGEBRA: (a) Algebra of vectors – angle between
two non-zero vectors – linear combination of vectors – vector equation of line
and plane (b) Scalar and vector product of two vectors and their applications
(c) Scalar and vector triple products – Scalar and vector products of four
vectors
Karnataka Common Entrance Test (KCET) | Result and Answer Keys of Exam 2010
Karnataka Examination Authority
Common Entrance Test
Karnataka
Karnataka Common Entrance Test Result 2010 has been announced by Karnataka Examination authority. Answer keys are also published by Karnataka examination authority. There are four subject in Karnataka CET entrance exam - Physics, Chemistry, Biology and Mathematics
MATHEMATICS SYLLABUS
MATRICES AND DETERMINANTS:
Types of matrices, addition and multiplication
of matrices-Properties, computation of inverses,
solution of system of linear equations by matrix
inversion method. Rank of a Matrix – Elementary
transformation on a matrix, consistency of a
system of linear equations, Cramer's rule,
Non-homogeneous equations, homogeneous linear
system, rank method.
THEORY OF EQUATIONS,
SEQUENCE AND SERIES
Quadratic equations – Relation between roots and
coefficients – Nature of roots – Symmetric
functions of roots – Diminishing and Increasing
of roots – Reciprocal equations. Arithmetic,
Geometric and Harmonic Progressions-Relation
between A.M., G. M ., and H.M. Special series:
Binomial, Exponential and Logarithmic series –
Summation of Series. VECTOR ALGEBRA
Scalar Product – Angle between two vectors,
properties of scalar product, applications of
dot products. Vector Product – Right handed and
left handed systems, properties of vector
product, applications of cross product. Product
of three vectors – Scalar triple product,
properties of scalar triple product, vector
triple product, vector product of four vectors,
scalar product of four vectors. Lines – Equation
of a straight line passing through a given point
and parallel to a given vector, passing through
two given points, angle between two lines. Skew
lines – Shortest distance between two lines,
condition for
two lines to intersect, point of intersection,
collinearity of three points. Planes – Equation
of a plane, passing through a given point and
perpendicular to a vector, given the distance
from the origin and unit normal, passing through
a given point and parallel to two given vectors,
passing through two given points and parallel to
a given vector, passing through three given
non-collinear points, passing through the line
of intersection of two given planes, the
distance between a point and a plane, the plane
which contains two given lines, angle between
two given planes, angle between a line and a
plane. Sphere – Equation of the sphere whose
centre and radius are given, equation of a
sphere when the extremities of the diameter are
given.
ISAT Mathematics Sample Questions 2010
Question 2:
Last year there were 80 students enrolled in the eighth-grade class. This year
the
number of students enrolled in the eighth-grade class increased by 10%.
How many students are enrolled in the eighth-grade class this year?
A. 88
B. 8
C. 90
D. 81
Question 3 :
A company packs its coffee into cylindrical containers. The height of each
container is 6
inches, and the radius of the container is 3 inches.
Which is closest to the volume of one of these cylindrical containers?
A. 36 cubic inches
B. 113 cubic inches
C. 54 cubic inches
D. 170 cubic inches
Question 4 :
The student council is making snack bags for a class trip. Each snack bag will
contain:
• 1 type of drink
• 1 type of cookie
• 1 type of fruit
To make each snack bag, they will choose from 2 types of drinks, 4 types of
cookies,
and 2 types of fruit.
How many combinations of 1 type of drink, 1 type of cookie, and 1 type of fruit
are
possible?
A. 48
B. 8
C. 3
D. 16
Question 8 :
Between which two consecutive integers is ?
A. 6 and 7
B. 100 and 101
C. 75 and 76
D. 17 and 18
Question 10 :
Amy has of a yard of string to make bracelets. Each bracelet requires of a yard
of string.
What is the greatest number of bracelets Amy can make with this length of
string?
A. 3
B. 6
C. 4
D. 8
Question 12 :
Which point on the number line below represents the value ?
A. Point Q
B. Point S
C. Point P
D. Point R
Question 14 :
Paula multiplied a number by 16. Her result is a positive number less than 16.
Which of
these did Paula multiply by 16?
A. A number greater than one
B. A number less than zero
C. A number between zero and one
D. Zero
With just a few more days to go for the joint entrance exams for India's
premier Institutes of Technology, popularly known as IIT JEE, students are in
for the final push. Here rediff.com in collaboration with TCYonline present mock
papers for mathematics, physics and chemistry for JEE students to improve their
speed and sharpen their skills.
Q1. A boat takes time t to go downstream from point A to point B and time
2t to go upstream from point B to point A . If the speed of the stream is v and
the speed of the boat with respect to the stream is u , then which of the
following gives the correct relationship between u & v ? a) u = v
b) u = 3v
c) v = 2u
d) v=3u
Q2. Which of the following is correct about the acceleration of a particle
describing a uniform circular motion ? a) The acceleration is constant both in magnitude and direction
b) The acceleration is constant in direction but not in magnitude
c) The acceleration is constant in magnitude but not in direction
d) The acceleration is neither constant in magnitude nor in direction
Q3. Five identical resistors of resistance 1 each, are connected along the
four edges and one of the diagonals of a square. A potential difference of 1 V
is applied across the other diagonal. What will be the current in the resistor
along the diagonal ? a) 0.5A
b) 1 A
c) 5A
d) zero ... [..] | 677.169 | 1 |
3. Apply the knowledge, skills and abilities to enter and succeed in a defined profession or advanced academic program. (Professional Competence)
4. Appreciate cultural diversity and constructively address issues that arise out of cultural differences in the workplace and community. (Cultural Awareness)
Minimally
5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility)
Outcome Assessment Strategies
At least one project plus some combination of the following:
Class participation
Group projects
Presentations
Portfolios
Research papers
Homework assignments
Written paper
Quizzes
Exams
Other assessments of the instructors choosing
Course Activities and Design
This course will be delivered through a combination of lecture and student activities including group and individual problem solving during class. Emphasis is to be given to applications from outside the mathematics classroom. Applications will come from the broadest possible range of disciplines.
Course Content (Themes, Concepts, Issues and Skills)
Limits
Introduction – instantaneous rate of change and the need for limits
One and two-sided limits; Squeeze Theorem
Continuity and The Intermediate Value Theorem
Limit Theorems and Evaluating Limits
Limits at infinity and infinity as a limit
Limit definition of derivative
Derivatives as functions; Higher order derivatives
Derivatives and the shape of graphs
Derivatives
Derivatives of polynomials and the binomial expansion theorem
Derivative of the exponential function
Derivative Theorems; Product Rule – Quotient Rule
Derivatives of Trig functions
Chain Rule
Implicit Differentiation
Derivatives of inverse functions; Derivative of Cosh and Sinh
Tangent line approximations and differentials
Applications
Related Rates
Extreme Value Theorem and closed interval problems.
First and Second Derivative Tests
Calculus and Graphing
Mean Value Theorem for Derivatives
L'Hospital's Rule
Newton's Method
Optimization
Department Notes
Answers to all application problems will be given in complete sentences with correct units. The grade will include at least one project | 677.169 | 1 |
It's the familiar TI-84 Plus functionality in a sleek new design that features a crisp color screen. Visualize concepts clearly and make faster, stronger connections between equations, data and graphs in full color | 677.169 | 1 |
Details
A diagnostic test with explained answers to help students identify their strengths and weaknesses
Advice on using a graphing calculator
A detailed review of all test topics, including polynomial, trigonometric, exponential, logarithmic, and rational functions; coordinate and three-dimensional geometry; numbers and operations; and much more
Six full-length model tests with answers, explanations, and self-evaluation charts
An enclosed CD-ROM presents two additional model tests with answers and | 677.169 | 1 |
and Introduction to Algebra; Integers; Introduction to Equations and Algebraic Expressions; Fractions, Ratio, and Proportion; Operations on Fractional Expressions; Polynomials; Solving Equations; Decimals and Percents; Graphing and Statistics; Measurement and Geometric Figures. For all readers interested in basic college mathematics.
"synopsis" may belong to another edition of this title.
From the Back Cover:
This book is designed to help a variety of readers bridge the gap between arithmetic and algebra. Slightly more rigorous than most arithmetic books -- but not as difficult or comprehensive as elementary algebra books -- it uses an innovative, integrated arithmetic/algebra approach that develops algebraic skills using "small steps," spirals topics throughout, emphasizes that algebra rules are just an extension of arithmetic, and teaches readers the specific study skills necessary to accommodate their individual learning styles -- including skills for "translating" the language of mathematics into plain English. Covers: Addition and Subtraction of Whole Number Expressions. Multiplication and division of Whole Number Expressions. Signed Numbers. Fractions and Ratio and Proportion. Equations and Polynomials. Fractional Expressions. Decimals and Percents and Radical Expressions. Graphing and Statistics. Measurement and Geometric Figures. For those with math anxiety or frustration who need to make the transition from arithmetic to algebra.
About the Author:
John Tobey received his BA in mathematics from Wheaton College in Wheaton, Illinois in 1965, his MA in mathematics education from Harvard University in 1966, and his PhD in mathematics education from Boston University in 1980. He has taught in the mathematics department at the United States Military Academy at West Point and has served as the mathematics Department Chairman at North Shore Community College in Danvers, Massachusetts for five years. John has served as the president of the New England Mathematics Association of Two Year Colleges. He has received the NISOD award for outstanding teaching from the University of Texas at Austin. John is the author of seven mathematics books published by Pearson Education. John has spoken to many mathematics departments and at many professional meetings throughout the country on the topic of developmental mathematics education and distance learning in mathematics. He lives in Massachusetts.
Jeffrey Slater has been a professor at North Shore Community College for thirty-eight years and received the Teacher of the Year in 2002. Jeff travels around the country speaking on student retention and is also a consultant to the Federal Government. He lives in Marblehead, Mass. with his wife Shelley and his yellow lab Gracie.
Jamie Blair has directed the Mathematics Learning Center at Orange Coast College for the past seventeen years. She designed, developed, and implemented the Center, and as a result of this effort has provided technical expertise related to the particulars of the Math Center to numerous other two-year colleges and at many conferences. In 2007 Jamie was appointed to the Team of Basic Skills Specialist by the California State Academic Senate. She is also currently participating on Title 3 committees on her campus. She specializes in teaching students who have never been successful in mathematics. She is an expert in the area of basic skills in relation to the learning needs of students. She lives in California. | 677.169 | 1 |
Advanced Linear Algebra features a student-friendly approach to the theory of linear algebra. The author's emphasis on vector spaces over general fields, with corresponding current applications, sets the book apart. He focuses on finite fields and complex numbers, and discusses matrix algebra over…
Non-commutative Algebras and Rings
The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis,…
Introduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves,…
Recursion Theory and Descriptive Complexity
This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories…
Introduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It avoids the usual groups first/rings first dilemma by introducing semigroups and monoids, the multiplicative structures of rings, along with…
The Search for Linearity in Mathematics
Renewed interest in vector spaces and linear algebras has spurred the search for large algebraic structures composed of mathematical objects with special properties. Bringing together research that was otherwise scattered throughout the literature, Lineability: The Search for Linearity in…
Cremona Groups and the Icosahedron focuses on the Cremona groups of ranks 2 and 3 and describes the beautiful appearances of the icosahedral group A5 in them. The book surveys known facts about surfaces with an action of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5,…
Structures and Applications
A Discovery-Based Approach to Learning about Algebraic Structures
Abstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be… | 677.169 | 1 |
An easy introduction to the mathematics: in which the theory and practice are laid down and familiarly explained ... A complete and easy system of elementary instruction in the leading branches of the mathematics; ... Adapted to the use of schools, junior students at the universities, and private learners, especially those who study without a tutor. In two volumes, Volume 1
Popular passages
Page xxvi - Just so it is in the mind ; would you have a man reason well, you must use him to it betimes, exercise his mind in observing the connection of ideas and following them in train. Nothing does this better than mathematics, which therefore I think should be taught all those who have the time and opportunity, not so much to' make them mathematicians as to make them reasonable creatures...
Page 124 - State and reduce the terms as in the Rule of Three Direct. 2. Multiply the first and second terms together, and divide the product by the third ; the quotient will be the answer in the same denomination as the middle term was reduced into.
Page 256 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 454 - A hare is 50 leaps before a greyhound, and takes 4 leaps to- the greyhound's 3, but 2 of the greyhound's leaps are as much as 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Ans. 300.
Page 311 - Multiply the whole number by the numerator of the fraction, and divide the product by the denominator ; or divide the whole number by the denominator of the fraction, and multiply the quotient by the numerator. | 677.169 | 1 |
Algebra 2, Student Edition
9780078738302
ISBN:
007873830X
Edition: 1 Pub Date: 2006 Publisher: Glencoe/McGraw-Hill
Summary: THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! "Glencoe Algebra 2" is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments.
McGraw-Hill Education is the author of Algebra 2, Student Edition, published 2006 under ISBN 9780078738302 and 0078...73830X. Three hundred fourteen Algebra 2, Student Edition textbooks are available for sale on ValoreBooks.com, one hundred forty one used from the cheapest price of $15.81, or buy new starting at $36 | 677.169 | 1 |
Essential Linear Algebra
$129.95
hardcover, 264 p., Revised Ed., published 2012.
This text introduces linear algebra with an emphasis on concept and theory. The first third of the text discusses the two main views of linear equations: linear systems of equations and linear transformations. The middle third delves into the more abstract with the introduction of subspaces, image and kernel, coimage and cokernel, coordinates, and orthogonal projections. Determinants are introduced in two and three dimensions first, where the effect of row operations may be easily visualized. In n-dimensions, determinants are then introduced as anti-symmetric, multilinear mappings appropriately normalized. Finally, eigenvalues and eigenvectors are introduced, and spectral theory is developed.
Product Description
This text introduces linear algebra—boiled to its essence—presented in a clear and concise fashion. Designed around a single-semester undergraduate course, Essential Linear Algebra introduces key concepts, various real-world applications, and provides detailed yet understandable proofs of key results that are aimed towards students with no advanced preparation in proof writing. The level of sophistication gradually increases from beginning to end in order to prepare students for subsequent studies.
We begin with a detailed introduction to systems of linear equations and elementary row operations. We then advance to a discussion of linear transformations, which provide a second, more geometric, interpretation of the operation of matrix-vector product. We go on to introduce vector spaces and their subspaces, the image and kernel of a transformation, and change of coordinates. Following, we discuss matrices of orthogonal projections and orthogonal matrices. Our penultimate chapter is devoted to the theory of determinants, which are presented, first, in terms of area and volume expansion factors of 2×2 and 3×3 matrices, respectively. We use a geometric understanding of volume in n-dimensions to introduce general determinants axiomatically as multilinear, antisymmetric mappings, and prove existence and uniqueness. Our final chapter is devoted to the theory of eigenvalues and eigenvectors. We conclude with a number of discussions on various types of diagonalization: real, complex, and orthogonal. | 677.169 | 1 |
Discrete Mathematics For Teachers: Preliminary Edition
9780618433926
ISBN:
0618433929
Edition: 1 Pub Date: 2004 Publisher: Houghton Mifflin Company
Summary: Part of a new generation of textbooks for in-service and pre-service teachers at the junior-senior level, this text teaches in three main ways: it extends students' breadth of knowledge beyond, but related to, the topics covered in elementary and middle-grade curriculums; it increases prospective teachers' depth of mathematical understanding by providing problems rich in exploration and mathematical communication; an...d it models the most current ways of teaching mathematics. Many Section Openers begin with a motivating lesson that introduces a new topic in an understandable, real-world context. Exercise Sets at the end of every section provide more traditional practice and are labeled either Proof Exercises or Writing Exercises. Exploratory Exercises at the end of every section lead students to investigate topics outside the framework presented in the section. The final exercise in each section is a writing exercise.
Ed Wheeler is the author of Discrete Mathematics For Teachers: Preliminary Edition, published 2004 under ISBN 9780618433926 and 0618433929. Four Discrete Mathematics For Teachers: Preliminary Edition textbooks are available for sale on ValoreBooks.com, one used from the cheapest price of $8.68, or buy new starting at $39.14.[read more] | 677.169 | 1 |
The Math Goodies Newsletter
- The Math Goodies Newsletter is e-mailed to more than 14,000 opt-in subscribers around the world on the 1st and 15th of each month.
Mathematical and Physical Journal for Secondary Schools (KöMaL)
- KöMaL regularly reports on national and international competitions, prints articles on interesting results in mathematics and physics, and includes book reviews. For more than 30 years all the new problems have appeared in English as well as Hungarian.
Plus Magazine
- An online mathematics journal for schools. Part of the Millennium Maths project.
Proof
- International newsletter on the teaching and learning of Mathematical proof.
Quanta Magazine
- Published by the Simon s Foundation for public understanding of research developments in mathematics and the physical and life sciences. Text free online.
Teaching Mathematics and its Applications
- Provides forum for mathematics teaching for students from upper secondary/high school level through university. Emphasis on applications of mathematics and modelling. Readership consists of teachers, students, and researchers. Provides online access to articles. | 677.169 | 1 |
Goodyear SATGretchen OJonathan H.
...This is where you really start getting into core math topics needed in later math classes. You learn all about exponents, lines, parabolas, and a lot of the cartesian plane (graphing). Biology is so unique because we can observe this topic in our every day lives. It is nature in its most basic form. | 677.169 | 1 |
An interactive applet and associated web page that demonstrate how to find the perpendicular
distance between a point and a line that is either vertical or horizontal,
given the coordinates of... More: lessons, discussions, ratings, reviews,...
A discovery worksheet that allows students to find the formal definition for Riemann sums. It ends with practice questions that students can do on their own. Included in the teacher sheets is an art... More: lessons, discussions, ratings, reviews,...
Tutorial fee-based software for PCs that must be downloaded to the user's computer. It covers topics from pre-algebra through pre-calculus, including trigonometry and some statistics. The software pos | 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 |
introduction presents the mathematical theory of probability for readers in the fields of engineering and the sciences who possess knowledge of elementary calculus. Presents new examples and exercises throughout. Offers a new section that presents an elegant way of computing the moments of random variables defined as the number of events that occur. Gives applications to binomial, hypergeometric, and negative hypergeometric random variables, as well as random variables resulting from coupon collecting and match models. Provides additional results on inclusion-exclusion identity, Poisson paradigm, multinomial distribution, and bivariate normal distribution A useful reference for engineering and science professionals title of this book is a bit of a misnomer. A more apt title would have been "First Graduate Course in Probability" or "A Second Course in Probability". The book description describes this as an introduction for students with an understanding of only elementary calculus. However, I believe that very few people with a background in only elemetary Calculus are going to be able to follow this text which presupposes facility with proof techniques like mathematical induction and a moderate level of mathematical maturity. Ross does not do any hand holding. Proofs are short and to the point, explanations are terse and compact, "obvious" steps are skipped and left to the reader to fill in. So if you are not prepared to follow terse mathematical explanations that are short on cursory explanation, then this may not be the book for you.
For math majors and other students with a strong mathematics background, however, this may serve as a useful reference. It is concise, elegant and chock full of example problems with solutions. But it all depends on what you are ready for. Some may find the excessive number of example problems distasteful and prefer a less cluttered treatment. Others may find that, despite the examples, the book is not "applied" enough. In my opinion, this book is not suitable as a first course in probability for anyone but mathematics majors. You will get the most out of this book if you are already familiar with the subject, or if you have a talented teacher to fill in the numerous gaps. For actuarial students and engineers, you may want to look for a more expository volume like "Introduction to Probability" by Bertsekas.
Contrary to its title, this book has helped me through several probability courses. I used this book not only to study for the first actuary exam, but also as a supplement for my intermediate and doctoral-level probability/inference courses. Ross fills in gaps left by texts such as Rice, Cassella and Berger, etc., by spelling out properties of various distributions, and showing how they relate to eachother, and by doing many many examples.
Incidentally, save yourself the money and get an earlier edition. I have the fifth edition, which was not even the current edition at the time that I bought it, and it's perfect as is.
This was a textbook for a probability course that I took, and I did not find it very useful at all. The book is incredibly thick and large, but there is relatively little information in it. The extra bulk is not due to explanatory prose, discussion, or optional topics, but rather, an abundance of examples, some of which are good, but some of which are inappropriate and/or poorly carried out. In particular, I find that the order in which the examples are presented is not optimal, and the amount of examples on a given topic is not optimal either. There also needs to be much more discussion, instead of just going over specific problems.
Overall, the book is unreadable, even though it's at an elementary level.
The only redeeming quality of this book is that its exercises are fairly challenging, interesting, and there is a "self-test" section at the end of each chapter which provides fairly good explanations of how to carry out the problems.
My last criticism of this book is that it's clear that the publisher is trying to milk this for as much money as its worth--by the 7th edition, the book should be very refined, and honestly, looking at previous editions I see absolutely no improvement. I honestly question any book that goes beyond 3 or 4 editions...I think it's a money-making scam and you shouldn't waste your time with it when there are so many good texts on probability out there.
I've only read the first four chapters of this book so far, but overall, I am enjoying the book. In order to give a sense of how difficult the book is (or perhaps how slow I am in picking up the material) - it sometimes takes me a full hour just to read 3 pages. Furthermore, sometimes, I have had to put the book down and reread the pages another day to be able to comprehend the material. This is with a goal of really trying to understand each page. My math background includes classes in Calculus, Linear Algebra, and Introductory Differential Equations. Each chapter has three sets of problems: chapter problems, theoretical problems, and self-test problems. The self-test problems have concise solutions that also can take a some time to understand. There are also a few typos here and there - not that many though. I would recommend this book only to those who are highly disciplined and persistent with studying math. I would also recommend finding a person knowledged in Probability for questions you'll definitely have. For me, I've had to also do a lot of the problems to really understand the material. Lastly, this book has been my first introduction to probability.
Every student like examples, but Ross over-uses them, to the point of insanity. He introduces most of the material in the course of working specific problems (c.f. in the abstract). I, for one, think this is an extremely poor way to present mathematical material; after reading an example, you will have to distill the salient techniques and concepts from it. This can be quite difficult, since his examples are often quite involved, yet not worked with clarity and thoroughness. Thus, it's sometimes hard to see where the example ends and the theory starts; put another way, you'll understand what the author is doing without understanding *why* he's doing it. | 677.169 | 1 |
Find a Hellertown PrealgebraAlgebra 2 is the continuum of Algebra 1. That is, Algebra 2 uses the same operations on advanced algebraic operations, introduce square roots and simplifying and perform the same operations as equations. Polynomials seem to be most difficult because some contain fractions and fractions are a bit more difficult to perform operations with variables! | 677.169 | 1 |
Mathematical algorithms are a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. This book provides a bridge between algebraic geometry and geometric modelling algorithms, formulated within a computer science framework. Apart from the algebraic geometry topics covered, the entire book is based on the unifying concept... more...
Inequalities based on Sobolev Representations deals exclusively with tight integral inequalities of Chebyshev-Grüss and Ostrowski types, and of integral means. Applications illustrate inequalities that engage in ordinary and weak partial derivatives of the involved functions. more...
Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation. The first part of this book reviews the main results that have been proposed so far in the literature. As usual with polynomial computations, the polynomial GCD problem can be expressed in matrix form:... more...
Numerous examples and indexed definitions make this detailed guide to polynomial theory in error-correcting codes a highly accessible resource. New codes and a unitary approach to block and convolutional codes will enhance readers? understanding of the topic. more...
Positive and sum-of-squares polynomials have received a special interest in the latest decade, due to their connections with semidefinite programming. Thus, efficient optimization methods can be employed to solve diverse problems involving polynomials. This book gathers the main recent results on positive trigonometric polynomials within a unitary... more...
The book presents foundations of the micropolar continuum mechanics including a short but comprehensive introduction of stress and strain measures, derivation of motion equations and discussion of the difference between Cosserat and classical (Cauchy) continua, and the discussion of more specific problems related to the constitutive modeling, i.e.... more...
Field Arithmetic explores Diophantine fields through their absolute Galois groups. The treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. more...
A collection of the various old and new results, centered around the following simple observation of J L Walsh. This book is particularly useful for researchers in approximation and interpolation theory. more... | 677.169 | 1 |
Measure Theory Book for My Background / Need Because you mentioned probability theory, you could look at "First Look at Rigorous Probability Theory" by Rosenthal. This will teach you the measure theoretic probability theory that you'll need for grad school. | 677.169 | 1 |
Contains a set of black line masters for interesting math number games that can be reproduced on A3 card for practical use in the classroom, strengthening students? knowledge of times tables and number skills. Activities to suit Grades 1-7 students.
more...
Blackline master book designed
to complement a remedial Math program for small groups of students.
Explains
the basic concepts of number, exploring in detail the processes of addition,
subtraction, multiplication and division.
Decimals are investigated in detail as
well as their relationship with percentages. The activities are sequenced in
line... more...
The present book ? through the topics and the problems approach ? aims at filling a gap, a real need in our literature concerning CFD (Computational Fluid Dynamics). Our presentation results from a large documentation and focuses on reviewing the present day most important numerical and computational methods in CFD. Many theoreticians and experts in... more...
This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. It fills a gap in the current published literature by delivering a case-study collection together with a self-contained course on major numerical methods developed and used by the finance industry. more...
This book covers basic computational issues arising in financial mathematics. This edition offers major revisions around such topics as calibration, Monte Carlo Methods, American options, and exotic options. It includes new figures and more exercises. more...
Emphasizing the connection between mathematical objects and their practical C++ implementation, this book provides a comprehensive introduction to both the theory behind the objects and the C and C++ programming. Object-oriented implementation of three-dimensional meshes facilitates understanding of their mathematical nature. Requiring no prerequisites,... more...
The development and growth of the many branches of Mathematics permeates all aspects of applied science and technology. This book examines these aspects and features contributions from several world-famous scientists from mathematics and related sciences. more...
Accessible Mathematics is Steven Leinwand?s latest important book for math teachers. He focuses on the crucial issue of classroom instruction. He scours the research and visits highly effective classrooms for practical examples of small adjustments to teaching that lead to deeper student learning in math. Some of his 10 classroom-tested teaching shifts... more...
This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements. more... | 677.169 | 1 |
This learning object from Wisc-Online covers simplifying algebraic expressions using division. The unit's activities include defining the terminology associated with algebraic operations, using the fundamental laws of algebra in simplifying algebraic expressions, removing the symbols of grouping and changing the signs of the appropriate terms to simplify algebraic expressions. Practice questions...
This learning object from Wisc-Online covers the fundamental laws of algebra. The interactive activity includes slides which cover the following topics: the commutative, associative and distributive laws as applied to addition and multiplication.
This learning object from Wisc-Online covers simplifying algebraic expressions using multiplication. The unit's activities include defining the terminology associated with algebraic operations, using the fundamental laws of algebra to simplify those expressions, removing the symbols of grouping and changing the signs of the appropriate terms to simplify expressions. Practice questions are also...
This lesson from Illuminations asks students to use matrix multiplication to transform digital images. Students will use matrix multiplication skills, look at the connections between geometric transformations and matrix multiplication, and discover the 2x2 identity matrix. The lesson is intended for grades 9-12 and will require one class period to complete. | 677.169 | 1 |
Mathknockout.com is an online business that delivers Math Video Tutorials to customers that are available for download directly from the website.
Job description:
I will be recording the Algebra 2 video tutorials myself. What I need is the content for these videos. I've listed the different topics below, a total of 15. So again, I need someone to create the content for the video. The content should be written in a way that I can use as a "script" while recording the videos. The content should include an explanation of all the topics and include multiples examples. . | 677.169 | 1 |
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Mathematics
Welcome to Mathematics at Delaware Tech where you will have the opportunity to work in a partnership with instructors and fellow students to achieve excellence in the math skills necessary for your program. We provide a supportive learning environment for all of our courses - both developmental and credit level. You will have access to different math resources to make you feel confident in your math classes. The Mathematics Department is here to help you succeed.
These courses are offered at the Dover, Georgetown, Stanton, and Wilmington campuses.
How We Can Help You Succeed
We have dedicated instructors.
Our class sizes are small.
We offer extensive free tutoring.
We provide courses for all levels.
Our classes are available in four locations throughout Delaware for your convenience.
What You Will Learn
Core Curriculum Competencies
The Core Curriculum Competencies listed below identify what you, as an associate degree graduate, will be able to do upon completion of your degree, regardless of your major. You will acquire these core competencies through your general education courses (i.e. English, math, etc.) and your program of study courses.
Use scientific and mathematical reasoning appropriate to the technology.
Related Associate Degree Programs
We are here for your success! Math is an integral part of any profession and we want to help you develop the tools you need to succeed in your career.
Delaware Tech has Associate of Arts of Teaching degrees in Mathematics Secondary Education (MSE) and Middle Level Mathematics Education (MLME). These associate degrees are the first step towards a career in teaching mathematics at a high school or middle school.
Every associate degree major requires at least one mathematics course. | 677.169 | 1 |
VCU Precalculus (Math 151)
The goal of VCU's Precalculus course is to prepare each student for success in Calculus. A student well-prepared for calculus will be able to model real-world problems and analyze their quantitative aspects, using strong algebraic and trigonometric skills.
The course is fast-paced, but designed to give a motivated student every opportunity to succeed. The prerequisite for Math 151 is Math 141 (a grade C or better is strongly advised), or satisfactory score on the VCU Mathematics Placement test. | 677.169 | 1 |
Innovations in Teaching Abstract Algebra…
See more details below
Paperback
Temporarily out of stock online.
Overview with Technology held on the DePauw University campus in June 1996. Unlike other books and materials that demonstrate one particular software package or pedagogical technique, this volume gives the reader an introduction to a wide range of ideas that have been used to teach abstract algebra over the past decade. The articles that appear here were chosen for several different purposes: to disseminate various technological innovations, to detail methods of teaching abstract algebra that engage students, and to share more general reflections on teaching an abstract algebra course. There is something of interest to stimulate anyone who teaches abstract algebra, whether a seasoned veteran or a relative newcomer. Choose a few ideas and try them out! A classroom that is active and shows students how creative and dynamic mathematics can be is an excellent learning environment.
Since many of the articles rely on colored diagrams, have downloadable materials, or are best read while using some particular software, the editors have created a website that accompanies the volume. | 677.169 | 1 |
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