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Sponsored by the Pittsburgh Science of Learning Center
Rules
The Challenge
How generally or narrowly do students learn? How quickly or slowly? Will the rate of
improvement vary between students? What does it mean for one problem to be similar to another? It
might depend on whether the knowledge required for one problem is the same as the knowledge required
for another. But is it possible to infer the knowledge requirements of problems directly from
student performance data, without human analysis of the tasks?
This year's challenge asks you to predict student performance on mathematical problems from
logs of student interaction with Intelligent Tutoring Systems. This task presents interesting
technical challenges, has practical importance, and is scientifically interesting.
Technical Challenges
In terms of technical challenges, we mention just a few:
The data matrix is sparse: not all students are given every problem, and some problems
have only 1 or 2 students who completed each item. So, the contestants need to exploit
relationships among problems to bring to bear enough data to hope to learn.
There is a strong temporal dimension to the data: students improve over the course of
the school year, students must master some skills before moving on to others, and incorrect
responses to some items lead to incorrect assumptions in other items. So, contestants must pay
attention to temporal relationships as well as conceptual relationships among items.
Which problems a given student sees is determined in part by student choices or past
success history: e.g., students only see remedial problems if they are having trouble with the
non-remedial problems. So, contestants need to pay attention to causal relationships in order to
avoid selection bias.
Scientific and Practical Importance
From a practical perspective, improved models could be saving millions of hours of students'
time (and effort) in learning algebra. These models should both increase achievement levels and
reduce time needed. Focusing on just the latter, for the .5 million students that spend about 50
hours per year with Cognitive
Tutors for mathematics, let's say these optimizations can reduce time
to mastery by at least 10%. One experiment showed the time reduction was about 15% (Cen et al.
2007). That's 5 hours per student, or 2.5 million student hours per year saved. And this .5 million
is less than 5% of all algebra-studying students in the US. If we include all algebra students (20x)
and the grades 6-11 for which there are Carnegie
Learning and Assistment applications (5x), that
brings our rough estimate to 250 million student hours per year saved! In that time, students can be
moving on in math and science or doing other things they enjoy.
From a scientific viewpoint, the ability to achieve low prediction error on unseen data is
evidence that the learner has accurately discovered the underlying factors which make items easier
or harder for students. Knowing these factors is essential for the design of high-quality curricula
and lesson plans (both for human instructors and for automated tutoring software). So you, the
contestants, have the potential to influence lesson design, improving retention, increasing student
engagement, reducing wasted time, and increasing transfer to future lessons.
Currently K-12 education is extremely focused on assessment. The No
Child Left Behind act has put incredible pressure on schools to "teach to the test",
meaning that a significant amount of time is spent preparing and taking standardized
tests. Much of the time spent drilling for and taking these tests is wasted from the point
of view of deep learning (long-term retention, transfer, and desire for future learning); so
any advances which allow us to reduce the role of standardized tests hold the promise of
increasing deep learning.
To this end, a model which accurately predicts long-term future performance as a byproduct of
day-to-day tutoring could augment or replace some of the current standardized tests: this idea is
called "assistment", from the goal of assessing performance while simultaneously assisting learning.
Previous work has suggested that assistment is indeed possible: e.g., an appropriate analysis of
8th-grade tutoring logs can predict 10th-grade standardized test performance as well as 8th-grade
standardized test results can predict 10th-grade standardized test performance (Feng, Heffernan, &
Koedinger, 2009). But it is far from clear what the best prediction methods are; so, the
contestants' algorithms may provide insights that allow important improvements in assistment.
Fundamental Questions
If a student is correct at one problem (e.g., "Starting with a number, if I
multiply it by 6 and then add 66, I get 81.90. What's the number?") at one time, how likely are they
to be correct at another problem (e.g., "Solve for x: 6x+66=81.90") at a later time?
These questions are of both scientific interest and practical importance. Scientifically,
relevant deep questions include what is the nature of human knowledge representations and how
generally do humans transfer their learning from one situation to another. Human learners do not
always represent and solve mathematical tasks as we might expect. You might be surprised if you
thought that a student working on the second problem above, the equation 6x+66=81.90, is likely to be
correct given that he was correct on the first problem, the story problem. It turns out that most
students are able to solve simple story problems like this one more successfully than the matched
equation (Koedinger & Nathan, 2004; Koedinger, Alibali, & Nathan, 2008). In other words,
there are interesting surprises to be found in student performance data.
Cognitive
Tutors for mathematics are now in use in more than 2,500 schools across the US for some 500,000
students per year. While these systems have been quite successful, surprises like the one above
suggest that the models behind these systems can be much improved. More generally, a number of
studies have demonstrated how detailed cognitive task analysis can result in dramatically better
instruction (Clark, Feldon, van Merriënboer, Yates, & Early, 2007; Lee, 2003). However,
such analysis is painstaking and requires a high level of psychological expertise. We believe it
possible that machine learning on large data sets can reap many of the benefits of cognitive task
analysis, but without the great effort and expertise currently required.
Competition Rules
Conditions of participation: Anybody who complies with the rules of the
challenge (KDD Cup 2010) is welcome to participate. Only the organizers are excluded from
participating. The KDD Cup 2010 is part of the competition program of the Knowledge Discovery in
Databases conference (KDD 2010), July 25-28 in
Washington, DC. Participants are not required to attend the KDD Cup 2010 workshop, which will be held at
the conference, and the workshop is open to anyone who registers. The proceedings of the competition
will be published in a volume of the JMLR: Workshop
and Conference Proceedings series.
Anonymity: All entrants must identify themselves by registering on the KDD
Cup 2010 website. However, they may elect to remain anonymous by choosing a nickname and checking
the box "Make my profile anonymous". If this box is checked, only the nickname will appear in the
Leaderboard instead of the real name. Participant emails will not appear anywhere on the website and
will be used only by the organizers to communicate with the participants. To be eligible for prizes,
the participants will have to publicly reveal their identity and uncheck the box "Make my profile
anonymous".
Teams: To register a team, only register the team leader and choose a
nickname for your team. We'll let you know later how to disclose the members of your team. We limit
each team to one final entry. As an individual, you cannot enter under multiple
names—this would be considered cheating and would disqualify you—nor can you participate
under multiple teams. Multiple teams from the same organization, however, are allowed so long as each team
leader is a different person and the teams do not intersect. During the development period, each
team must have a different registered team leader. To be ranked in the challenge and qualify for
prizes, each registered participant (individual or team leader) will have to disclose the names of
eventual team members, before the final results of the challenge get released. Hence, at the end of
the challenge, you will have to choose to which team you want to belong (only one!), before the
results are publicly released. If a person participates in multiple teams, those teams
will be disqualified. After the results are released, no change in team composition will be
allowed. Before the end of the challenge the team leaders will have to declare the composition of
their team. This will have to correspond to the list of co-authors in the proceedings, if they
decide to publish their results. Hence a professor cannot have his/her name on all his/her students
papers (but can be thanked in acknowledgments).
A team can be either a student team (eligible for student-team prizes)
or not a student team (eligible for travel awards). In a student team, a professor
should be cited appropriately, but in the spirit of the competition, student teams should consist
primarily of student work. We will ask for participants to state whether they are a student
team prior to the end of the competition.
Data: Data are available for download from the Downloads
page to registered participants. Each data set is available as a separate archive to facilitate
downloading. For viewing accuracy on the Leaderboard, participants may
enter results on either or both development and challenge data sets, but results on the development
data sets will not count toward the final evaluation.
Challenge duration: The challenge is about 2 months in duration (April 1 - June 8, 2010).
To be eligible for prizes, final submissions must be received by June 8 11:59pm EDT (-4 GMT).
On-line feedback: On-line feedback is available through the upload results page and
Leaderboard.
Submission method: The method of submission is via the form on the Upload page. To be ranked, submissions must include results on test
portion only of the challenge or development data sets. Results on the development data sets will
not count as part of the competition. Multiple submissions are allowed.
Evaluation and ranking: For each team, only the last valid entry made by the
team leader will count towards determining the winner. Valid entries must include results on both
challenge data sets. The method of scoring is described on the Evaluation
page.
Reproducibility: Participation is not conditioned on delivering code nor publishing
methods. However, we will ask the top ranking participants to voluntarily fill out a fact sheet
about their methods, contribute papers to the proceedings, and help in reproducing their results.
Prizes: Thanks to our sponsors, Facebook, Elsevier, and IBM Research, we will be
offering the following prizes to student teams: | 677.169 | 1 |
Desmos Graphing Calculator Description
651
At Desmos, we imagine a world of universal math literacy and envision a world where math is accessible and enjoyable for all students. We believe the key is learning by doing.
To achieve this vision, we've started by building the next generation of the graphing calculator. Using our powerful and blazingly-fast math engine, the calculator can instantly plot any equation, from lines and parabolas up through derivatives and Fourier series. Sliders make it a breeze to demonstrate function transformations. It's intuitive, beautiful math. And best of all: it's completely free.
Features:
Graphing: Plot polar, cartesian, or parametric graphs. There's no limit to how many expressions you can graph at one time - and you don't even need to enter expressions in y= form!
Sliders: Adjust values interactively to build intuition, or animate any parameter to visualize its effect on the graph
Tables: Input and plot data, or create an input-output table for any function
Statistics: Find best-fit lines, parabolas, and more.
Zooming: Scale the axes independently or at the same time with the pinch of two fingers, or edit the window size manually to get the perfect window.
Points of Interest: Touch a curve to show maximums, minimums, and points of intersection. Tap the gray points of interest to see their coordinates. Hold and drag along a curve to see the coordinates change under your finger.
Scientific Calculator: Just type in any equation you want to solve and Desmos will show you the answer. It can handle square roots, logs, absolute value, and more.
Inequalities: Plot cartesian and polar inequalities.
Offline: No internet access required.
Visit to learn more and to see the free online version of our calculator.
Here you can find the links to the latest version of Desmos Graphing | 677.169 | 1 |
0205045 Modern Algebra
This text is intended for use in a first course in abstract algebra. In the present undergraduate curriculum, the first course often serves several purposes. The student is expected to learn a collection of facts, some methods and ideas, and to learn to read and write correct proofs. All of these requirements have been carefully considered in the preparation of this text. The material in Chapter 4, for example,presents the unique factorization theorem, with all the required preliminaries, first in the familiar setting of the integers, then in the less familiar but still concrete setting of the ring of polynomials over a field, and then finally in the very general situation of a Euclidean domain. There is considerable information contained in the exer- cises. Some important theorems are left to the exercises due to lack of time and space. The highly motivated student should be encouraged to read all the exercises even though it is not reasonable to assign all of them to be worked. There are some exercises scattered throughout the text deal- ing with two-by-two matrices. Even though no formal theory of matrices is presented in the text, the student should have no serious difficulty with these if the exercises on this topic are worked from the beginning. A number of topics that might be called "enrichment" material are marked with an asterisk (*) in the Contents. These would not ordinarily be covered in lectures but may be used for special projects, or as reading assignments for motivated | 677.169 | 1 |
Intended to provide a flexible approach to the college algebra and trigonometry curriculum that emphasizes real-world applications, this text integrates technology into the presentation without making it an end in itself, and is suitable for a variety of audiences. Mathematical concepts are presented in an informal manner that stresses meaningful motivation, careful explanations, and numerous examples, with an ongoing focus on real-world problem solving. Pedagogical elements including chapter opening applications, graphing explorations, technology tips, calculator investigations, and discovery projects are some of the tools students will use to master the material and begin applying the mathematics to solve real-world problems.
"synopsis" may belong to another edition of this title.
About the Author:
Thomas W. Hungerford received his M.S. and Ph.D. from the University of Chicago. He has taught at the University of Washington and at Cleveland State University, and is now at St. Louis University. His research fields are algebra and mathematics education. He is the author of many notable books for undergraduate and graduate level courses. In addition to ABSTRACT ALGEBRA: AN INTRODUCTION, these include: ALGEBRA (Springer, Graduate Texts in Mathematics, #73. 1974); MATHEMATICS WITH APPLICATIONS, Tenth Edition (Pearson, 2011; with M. Lial and J. Holcomb); and CONTEMPORARY PRECALCULUS, Fifth Edition (Cengage, 2009; with D. Shaw).
Review:
"It is obvious that the author has spent a great deal of time to incorporate technology in an appropriate way. I particularly like the way in which he asks the student to first check graphically the trig identity(s) he/she is trying to prove." "[The] Technology Investigations really help students to have a better and more meaningful understanding of the subject matter. They also help students to have a deeper conceptual understanding. Both the presentation of the materials and the problem sets are excellent. The text contains outstanding applied problems. Additionally, it contains well thought out "Discovery Projects."
"The use of the calculator investigations/explorations within the text does a very good job of illustrating the algebraic properties or solving techniques that are being discussed. The directions are easy to follow and it is clear as to what the student is actually trying to explore." "I found the text easy to read, there were plenty of examples for the students to use to help guide them with the homework, and the page layouts were neither cluttered nor confusing." | 677.169 | 1 |
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Calc2Learn is the ultimate educational calculator. Where a traditional calculator simply crunches numbers, Calc2Learn simplifies the process by requiring less button pushing and also provides a detailed explanation of how to do various math problems, lists formulas used in the problem, includes diagrams to help users visualize, and then includes an example problem and a detailed solution. Use your smartphone to do your homework! With Calc2Learn, students don't just mindlessly push buttons, they LEARN how to solve problems! A great study aid! Great for all ages! Developed in line with academic standards! Calc2Learn has over ***60*** functions as of this writing.
***Differences between Free and Donate versions: Both the free and donate versions provide access to all features. The free version is supported by advertisements while the DONATE VERSION HAS NO ADVERTISEMENTS. | 677.169 | 1 |
The Georgia College Department of Mathematics is now offering a
redesigned Math 1111 College Algebra course using the Emporium Model.
The goal of this course is to offer a fundamental understanding of algebraic
concepts which form an important component of an undergraduate education and to
enhance thealgebraic skills and knowledge necessary for
upper-level mathematics courses and for courses in many other disciplines. The
underlying principle of the Emporium Model is very simple:
"Students learn math by doing math not by listening to
someone talk about doing math."
This model for redesigned courses has been implemented successfully
by many institutions including Virginia Tech, University of Alabama, University
of Idaho, UNC at Chapel Hill and Greensboro, Georgia State University, University of
Mississippi, Wayne State University, University of Arkansas, University of Nebraska,
Oklahoma State University, University of Central Florida, Auburn University, and
Southeastern Louisiana University.
The key elements of the success of this model are:
Interactive computer
software
Personalized on-demand
assistance
Mandatory student participation
Why is the Emporium Model so successful?
Students spend more time doing math problems rather
than simply listening
to someone talk about
doing them.
Students spend more time on
things they don't understand and less time on
things they have
already mastered.
Students receive immediate and
personalized assistance when they
encounter problems doing math.
Students are required to do math.
At Georgia College, students in Math 1111 College Algebra spend
one hour a week at a fixed time with their professor and then a minimum of three
flexible hours a week in the Math Emporium lab which is staffed with professors
and undergraduate learning assistants (ULA's).
During the meeting at the fixed time, professors
guide the students through theirresponsibilities, connect
concepts, work examples, and point out common student misconceptions. In the Math Emporium lab, professors
and ULA's offer
immediate and personalized
help with math concepts 44 hours per week. In addition, we offer
one-one/small group tutoring in one of the small rooms located
at the back of the lab.
All course materials are created using the web-based software
MyMathLab, which comes bundled with the e-textbook. Students navigate through the
chapters which include the textbook content, lectures and example videos,
animations and tutorial exercises, homework and quizzes. The Help Me Solve
This and View an Example buttons guide students through their homework
exercises offering instant feedback. The homework has an unlimited number of
attempts and the quizzes have up to three attempts before the due date, and they
can be accessed from home as well. The password-protected tests are only taken
in the lab under the professor's supervision.
This course redesign is not about putting the course
online.It is about creating a new
pedagogy in the light of the possibilities that technology offers with
strong considerations being given to the individual needs of students. | 677.169 | 1 |
Monday, September 28, 2009
Saxon Math : Saxon Math 65: An Incremental Development
This book is being used by my grandsons 6th grade, and I am helping him with his homework. I have three university degrees, including Bachelor, Master, and Doctorate in science, business, and economics. And I have taught at the university graduate and undergrate level for more than twenty years. I was astounded at the efficient and advanced technique used by the author, Stephen Hake, to gradually introduce most basic concepts of logic, arithmetic, alegebra, geometry,and other subjects to my 12 year old student in this book, in a practical manner with practical every day applications, so that he absorbed them as by osmosis, without actually knowing it. This will provide him with a solid foundation for the four years of mathematics he will receive in high school, and for his later studies at university level. Hake does this without muddying up the young students mind with such distracting technical terms as "algebra, geometry, solid geometry, trigonometry, logic,and other subjects," by introducing the basic concepts of each subject with practical problems that require the student to, unwittingly, apply them. | 677.169 | 1 |
Excel Essential Skills - Problem Solving Workbook Year 7
Excel Essential Skills - Problem Solving Workbook Year 7
Refine your problem-solving skills and get the results you want! Specifically written for the Year 7 Australian Curriculum Mathematics course, this book aims to provide students with the skills they require to excel in both the problem solving and reasoning proficiency strands of the Year 7 Maths curriculum.
Key features:
a focus on 50 different Key Skills
problem solving hints and examples with worked solutions.
.a step-by-step method for each question, with explanations and tips . | 677.169 | 1 |
Sigma Notation Guided Notes
Be sure that you have an application to open
this file type before downloading and/or purchasing.
194 KB|4 pages
Product Description
These guided notes designed for IB Math Topic 1 introduce students to Sigma Notation. Beginning with definitions and then including a table that compares Infinite & Finite Series, the notes continue with the Properties of Sigma Notation and teacher examples and problems for students to practice. Created by Math with Mrs. Holst! | 677.169 | 1 |
Teaching calculus and physics in an all-girl independent catholic high school
Tuesday, July 21, 2015
Derivatives First?
Last November I attended the DACTM/MDSTA conference. Most of the workshops I went to were either about Modeling Instruction or Standards Based Grading, but I did go to one workshop called "Start Calculus with Calculus". The idea was that, instead of starting with a lot of review and then an in depth study of limits, you start the class with interesting problems that lead students to develop the basic ideas of the derivative and the definite integral and what they physically mean. Shawn Cornally wrote about doing something similar with his calculus class. I was intrigued by the idea, but hadn't really given much thought to it until I was in my Modeling Instruction in Physics workshop this summer.
I have the joy of teaching two courses that are deeply intertwined. Rates of change and the accumulation of change are big ideas in both physics and calculus. So every time we examined the graphs of our data and interpreted the slope or the area under the graph, I thought about my calculus students as much as I thought about my physics students.
How can I change my teaching method so much for physics and not for calculus? Why can't I use the same experiences to teach students calculus as I use to teach them physics?
Now I'm spending a lot of time thinking about the best way to use what I learned this summer to teach derivatives and definite integrals.
Do I start with the constant velocity model? We'd start with a linear position graph, which my students have a very good understanding of. Drawing the velocity vs time graph would be easy, and it would be simple to look at the meaning of the area under the graph. Or, should I start with a uniformly accelerating model and explore the difference between average rate of change and instantaneous rate of change? Do I even look at integrals yet? Do I keep coming back to the same investigation time after time, looking at it through a new lens?
Will teaching this way ease students' troubles with creating mathematical models of situations? Will it lead them to see the big pictures of derivatives and integrals, or will they still loose sight of those ideas in the details of how to find them?
How do I move on into other contexts besides kinematics? How do I move into a formal study of limits? How/when do I come back to those early ideas?
My spring physics students become my fall calculus students. How will all of this change when they'll have already had those experiences in my physics class? Do I repeat the same investigations, or do I find new ones?
Do I really want to be completely reworking the flow of my calc classes when I'm also going to be reworking my physics courses? I have a lot of work to do!! | 677.169 | 1 |
This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.
"The book is devoted to the proofs of inequalities. As sources for considered inequalities the authors choose mathematical Olympiad of different level. … The book is really interesting and instructive for those students which suppose to develop their research skills and to increase their intuition." (Sergei V. Rogosin,Zentralblatt MATH, Vol. 1176, 2010)
"This book presents a calculus-free introduction to inequalities and optimization problems with many interesting examples and exercises. … the authors present solutions or hints to all exercises and problems appearing in the book. … Most books on Olympiad-level competitions have sections on inequalities, but the book under review focuses on this genre of problems in a particularly attractive and effective way, providing good practice material. I recommend this softcover volume to anyone interested in mathematical competition preparation." (Henry Ricardo, The Mathematical Association of America, October, 2010) | 677.169 | 1 |
Impact and interest
Abstract
George Polya's book, How to solve it (1945), is likely to have been one of the first books to focus on building students' skills as problem solvers. Polya, a Hungarian professor of mathematics, realised that it was not sufficient that his students knew their mathematical facts--they also needed to have a relational understanding of the subject in order to use mathematics as a tool. While Polya's book has provided much food for thought for mathematics educators at all levels throughout the decades, the legacy of his writing is in defining a heuristic or framework for students to solve problems | 677.169 | 1 |
About this product
Description
Description
This text provides an invaluable introduction to the mathematical tools that undergraduate economists need. The coverage is comprehensive, ranging from elementary algebra to more advanced material, whilst focusing on all the core topics that are usually taught in undergraduate courses on mathematics for economists. | 677.169 | 1 |
Yes maths coursework
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Science GCSE from 2016. Here are the main points: Totally exam-based. There is no practical exam, although you have to do certain practicals in school. Learning Support. Learner Services are here to support you throughout your time at South Staffordshire College from the point of your initial enquiry to help you. Letters: The EBacc and progress 8 curriculum have created a divisive hierarchy of subjects within schools, with maths and English at the top while the arts wallow at. | 677.169 | 1 |
Description - The Mathematics of Projectiles in Sport by Neville de Mestre
The mathematical theory underlying many sporting activities is of considerable interest to both applied mathematicians and sporting enthusiasts alike. Here Professor de Mestre presents a rigorous account of the techniques applied to the motion of projectiles. This equips the reader for the final section of the book in which an enlightening collection of sporting applications is considered, ranging from the high jump to frisbees and soccer to table tennis. The presentation should be accessible to most undergraduate science students and provides an ideal setting for the development of mathematical modeling techniques.
Buy The Mathematics of Projectiles in Sport by Neville de Mestre from Australia's Online Independent Bookstore, Boomerang Books. | 677.169 | 1 |
presents an elementary and concrete approach to linear algebra that is both useful and essential for the beginning student and teacher of mathematics. Here are the fundamental concepts of matrix algebra, first in an intuitive framework and then in a more formal manner. A Variety of interpretations and applications of the elements and operations considered are included. In particular, the use of matrices in the study of transformations of the plane is stressed. The purpose of this book is to familiarize the reader with the role of matrices in abstract algebraic systems, and to illustrate its effective use as a mathematical tool in geometry. The first two chapters cover the basic concepts of matrix algebra that are important in the study of physics, statistics, economics, engineering, and mathematics. Matrices are considered as elements of an algebra. The concept of a linear transformation of the plane and the use of matrices in discussing such transformations are illustrated in Chapter #. Some aspects of the algebra of transformations and its relation to the algebra of matrices are included here. The last chapter on eigenvalues and eigenvectors contains material usually not found in an introductory treatment of matrix algebra, including an application of the properties of eigenvalues and eigenvectors to the study of the conics. Considerable attention has been paid throughout to the formulation of precise definitions and statements of theorems. The proofs of most of the theorems are included in detail in this book. Matrices and Transformations assumes only that the reader has some understanding of the basic fundamentals of vector algebra. Pettofrezzo gives numerous illustrative examples, practical applications, and intuitive analogies. There are many instructive exercises with answers to the odd-numbered questions at the back. The exercises range from routine computations to proofs of theorems that extend the theory of the subject. Originally written for a series concerned with the mathematical training of teachers, and tested with hundreds of college students, this book can be used as a class or supplementary text for enrichments programs at the high school level, a one-semester college course, individual study, or for in-service programs fairly short Dover re-print edition is a good self-tutorial for students new to matrices. This book was originally published several years ago. but the mathematical notation is consistent with current texts. The first two chapters are moderately paced, covering such topics as real and complex matrices, Hermitian matrices, the inverse and rank of a matrix, and a brief introduction to systems of linear equations. The third chapter is a bit unique in focusing on application of matrices to transformations of the plane. I have encountered this topic in bits and pieces in various texts and I found this overview both interesting and helpful. The final chapter, titled Eigenvalues and Eigenvectors, was a bit too concise, touching too briefly on more complicated topics like diagonalization of matrices, Hamilton-Cayley Theorem, and quadratic forms. I recommend working through the fourth chapter (this is a short book) rather quickly to get a basic understanding, but then moving to more detailed treatments of eigenvalues and related topics elsewhwere. As a follow-up, I recommend another Dover edition - An Introduction to Matrices, Sets, ad Groups for Science Students. However, this text assumes substantial familiarity with manipulation of determinants. All in all, this book is a good buy and a good starting point for studying matrices.
There are 3+ typos on just the outside of the book itself. The organization of the book and how the information is presented is not helpful in trying to teach the reader about Matrices and Transformations. I would not recommend this book.
This is an excellent book concerning Matrices, both during the first time during education learning about Matrices, or by self studying, or just by interest, wanting to learn what Matrices is and how it's used.
I bought this book back in 1983 when I during engineering education started to having more to do with Matrices for example Eigenvalues (were Eigenvalue is from Germany, and meaning Own value). I bought it because I didn't like the book we used in the university. But after the education I still bought books concerning Matrices, and Determinants, among other caused by programming a Robots, where we have a 4*4 Matrix for each movable part of its arm and hand. And later during more Economic studying, where we often, like with Robots can end with very big total Matrices. It's an excellent book, one of those which are good to lend to a person quite new in Matrices.
As the number of Answers to Odd-number Exercises we are having a total of 130.
On the starting side, for starting on explaining Matrixes we get the following Matrix (here, by me, not a perfect drawing, as it's only for Determinants that we use such a straight line sides):
Electric Standard Portable model model model
Units of material | 20 17 12 | Units of labor | 6 8 5 |
In the book we gets 17 small figures, and to me, especially the geometrical drawings showing the changing in the figures, as on the front page, or rotation, or repositioning, in the co-ordinates, to me, are helpful.
And in the book the Matrix and Determinant figures probably are covering more area than the text.
This relatively slim volume provides an excellent summary of matrix algebra and its relationship to geometric transformations. Indeed, as a quick reference to matrix definitions and operations, it's quite good, I think, with a fairly transparent, straightforward and understandable approach. Beyond basic applications to transformations, however, it doesn't provide any real insight into the application of matrices elsewhere. With that limitation understood, however, it remains highly useful. A fine choice, especially at the price.
Fantastic! As a professional, I picked this book for review of and self-study. The ordering of topics is straightforward and logical. There are just enough exercises in each section to reinforce the material and prove relevant theorems. | 677.169 | 1 |
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This is a test on how to plot points on a coordinate plane when given an ordered pair. Also included is how to get ordered pairs from a table and how to fill in a table when given an equation or function notation. This prepares the student for functions. | 677.169 | 1 |
is an introduction to linear algebra. The main part of the book features row operations
and everything is done in terms of the row reduced echelon form and specific algorithms.
At the end, the more abstract notions of vector spaces and linear transformations on vector
spaces are presented. However, this is intended to be a first course in linear algebra for
students who are sophomores or juniors who have had a course in one variable calculus
and a reasonable background in college algebra. I have given complete proofs of all the
fundamental ideas but some topics such as Markov matrices are not complete in this book but
receive a plausible introduction. The book contains a complete treatment of determinants
and a simple proof of the Cayley Hamilton theorem although these are optional topics.
The Jordan form is presented as an appendix. I see this theorem as the beginning of more
advanced topics in linear algebra and not really part of a beginning linear algebra course.
There are extensions of many of the topics of this book in my on line book [Linear algebra On web page].
I have also not emphasized that linear algebra can be carried out with any field although I have done
everything in terms of either the real numbers or the complex numbers. It seems to me this
is a reasonable specialization for a first course in linear algebra.
# Hardcover: 624 pages
# Publisher: Wiley; 9 edition (December 27, 2004)
# Language: English
# ISBN-10: 0471669601
# ISBN-13: 978-0471669609 | 677.169 | 1 |
Begin a series of lectures on different proof techniques by looking at direct proofs, which make straightforward use of a hypothesis to arrive at a conclusion. Try several examples, including proofs involving division and inequalities. Then learn tricks that mathematicians use to make proofs easier than they look. | 677.169 | 1 |
QUIZZES THAT STUDENTS LOVE
QUIZZES THAT STUDENTS LOVE
"It was so simple but challenging", quipped one student after the quiz. Definitely students love this type of quiz. They find the quiz on finding the determinants, inverse matrices, and eigenvalues/eigenvectors give them the opportunity to test how far their learning progresses on that particular course. That is, taking a simple but challenging quiz!
Engineering Mathematics 2 Batch 2012-2013 Second Semester
What makes it simple? It is simple because the given matrices during the quiz were almost similar to the examples discussed in details during classroom session except a change on one of the entries in every row. This type of quiz is challenging because it is open notes, books, and other related materials. Laptops are allowed where they can use the program MS Excel. But everybody has to observe the" strictly no borrowing materials from the classmates!" rule.
Another word of caution! Solutions must be legibly written and presented in detail or step by step. Laptops are used only for counterchecking or guide as their works in progress. That's it and nothing more!
WHY THIS TYPE OF QUIZ WORKS?
Open books, notes, and related references during quizzes are welcomed by engineering students. Mathematics especially dealing on matrices is difficult to work with. As matrix size increases, the difficulty in computation also increases. Rules are sometime complicated and requires complete understanding before our confidence of getting correct answer develops. Memorization of procedures does not work well if without understanding as you will soon forget the procedures as the solution progresses. Most often in matrices a change of a single element or entry will change the whole environment of computation. The solution is very sensitive to the slight changes in the initial condition of the matrices. Just like chaotic theory, any error in a single step can produce large error in the final answer. That's why open notes, books, etc during quizzes works well with matrices. The main objective is to make students familiar the algorithm on how to get to the final answer.
The reason is clear. Let the students learn the basics of matrices operation. With almost all computation nowadays done by a computer, we are preparing our students to this world ahead. It is then the classroom learning works in the open fields after completing their course. In a real world, computers and engineers work hand in hand in the industrial fields.
WHAT WAS THE RESULT?
As expected silence engulfed the whole classroom as quiz started. Everybody was busy and concentrated on their works. No ogling for solutions on another paper. All eyes were on their own paper. Time limitation for the quiz was enforced. A real world in a classroom!
What was the result on that quiz? Only sixty percent (60%) passed. Failed students came to me with various reasons. Some confided that they had not prepared well and not listening during classroom lectures. In summary, failed students had reasons with the same denominator. They same old stories! Still clinging to their old ways of bad habits! They vowed to change the old ways. They blamed themselves for failing the quiz! One thing is certain…not blaming to the lecturer!
So, what is next? Some wept and admittedly vowed to change for a better! Then I told these poor youngsters, "Go and change your ways for it is not too late, more quizzes are coming. Unless you change your ways, you will not pass this course"
Sounds biblical? Yes. Students must change their ways in order to pass the course. Jesus at the early part of his preaching often told the crowd to change the ways and believe the good news so that they will not be perished. Everybody must be prepared.
"He said, "The time has come; the kingdom of God is at hand. Change your ways and believe the Good News.""
– Mark 1,15
"I tell you: no. But unless you change your ways, you will all perish as they did."
– Luke 13,3
That's it. Failed students must change for a better for they will they will not only pass this course but one day they will also meet the One sitting on the throne for final judgment to all mankind. | 677.169 | 1 |
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Introduction to Dynamic Programming introduces the reader to dynamic programming and presents the underlying mathematical ideas and results, as well as the application of these ideas to various problem areas. A large number of solved practical problems and computational examples are included to clarify the way dynamic programming is used to solve problems. A consistent notation is applied throughout the text for the expression of quantities such as state variables and decision variables. This monograph consists of 10 chapters and opens with an overview of dynamic programming as a particular approach to optimization, along with the basic components of any mathematical optimization model. The following chapters discuss the application of dynamic programming to variational problems; functional equations and the principle of optimality; reduction of state dimensionality and approximations; and stochastic processes and the calculus of variations. The final chapter looks at several actual applications of dynamic programming to practical problems, such as animal feedlot optimization and optimal scheduling of excess cash investment. This book should be suitable for self-study or for use as a text in a one-semester course on dynamic programming at the senior or first-year, graduate level for students of mathematics, statistics, operations research, economics, business, industrial engineering, or other engineering | 677.169 | 1 |
Secondary sequences and series lessons come with a starter, learning objectives, key words, plenty of teaching slides/examples, questions or worksheets with answers and plenary. This is part of a bigger bundle on sequences / series, that can be purchased with additional A-Level lessons. The bundleNOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thanks.
This lesson builds on the previous lesson introducing arithmetic sequences and series. This lesson focuses on where and how to use the formula for finding the sum of a series. It does look at some more challenging questions and when to use one formula as opposed to another, i.e. looking at efficiency arithmetic sequences and series and is now included material for the new GCSE syllabus as well as for C1 at A-Level. This is an essential lesson to build understanding and become familiar with notation before moving onto more challenging A-Level content / revelation was one of the cornerstones of why I became passionate personally with mathematics. I have used various slides from this PowerPoint to do maths assemblies as well. Pupils love this lesson and some of the slides are mind blowing. Love it !!! This builds on pupils understanding of sequences and does lend well to looking at series (different ways of writing rules or describing sequences). What I am saying is this lesson is brilliant in terms of adding the WOW factor as well as leading nicely into part 6 of the bundle/ series on sequences the fourth lesson in the series. It looks at other sequences that are not linear or quadratic. These are becoming increasingly popular in GCSE exams as it stretches pupils understanding and not just their ability to pass exams. It also includes other sequences problems that don't neatly fit into the previous lessons. This is one of my favourite lessons to teach, because there are so many different types of sequences and it does make you think is on quadratic sequences and goes through two methods to solve quadratic sequences. One method builds on their understanding of linear sequences as well, which is helpful. The other builds on their understanding of substitution and simultaneous equations. I teach both methods even though the majority of pupils will adopt the first method. I have found that giving pupils more understanding and methods, does pay dividend in the long run builds on an excellent first lesson on linear sequences to build in linear sequences within patterns/diagrams and more real life contexts around linear sequences. The goal here is to get pupils to build on their understanding from lesson one and to become more familiar with exam style questions linear sequences. Starting off with looking at the term to term rule and then quickly building into looking at the position to term rule or the nth term rule. This is a tricky topic for pupils and so there are quite a few teaching slides/ examples explaining what it is and why it is important. It goes onto looking at using the rule to work out another term further along in the sequenceFoldables can be used as a revision or summary exercise at the end of a topic. As the answers are hidden pupils can use these to 'test' themselves or ask someone else such as a parent to test them. They also make a great addition to any class book, making it an interactive notebook.
This foldable requires pupils to recall the formulae needed for the Core 1 Arithmetic Sequences of A Level Mathematics. It comes complete with solutions and instructions.
Thank you for looking, we hope the NumberLoving resources are useful to colleagues.
Get in touch via @numberloving or numberloving@outlook.com | 677.169 | 1 |
The eighth-grade standards contain both content that reviews or extends concepts and skills learned in previous grades and new content that prepares students for more abstract concepts in algebra and geometry. Students will gain proficiency in computation with rational numbers (positive and negative fractions, positive and negative decimals, whole numbers, and integers) and use proportions to solve a variety of problems. New concepts include solving two-step equations and inequalities, graphing linear equations, visualizing three-dimensional shapes represented in two-dimensional drawings, applying transformations to geometric shapes in the coordinate plane, and using matrices to organize and interpret data. Students will verify and apply the Pythagorean Theorem and represent relations and functions using tables, graphs, and rules | 677.169 | 1 |
Higher
The Higher Course in Mathematics develops learners' mathematical rigour and the ability to use precise and concise mathematical language assumes a particular importance at this stage.Candidates who complete a Higher Mathematics course successfully are expected to have a competence and a confidence in applying mathematical techniques, manipulating symbolic expressions and communicating with mathematical correctness in the solution of problems.The course has obvious relevance for candidates with interests in fields such as commerce, engineering and science where the mathematics learned will be put to direct use.The Higher Mathematics Course is at SCQF level 6. | 677.169 | 1 |
Algebra 1 Review Workshop: July 9-13
This workshop will provide a review of topics students will need for success in Algebra 2. These topics include equations and inequalities, absolute value, linear relations, functions, polynomials and factoring, exponents, square roots, and rational expressions. | 677.169 | 1 |
Mathematics
Math isn't just a numbers game; it's an adventure, as you investigate, analyze, model, predict, discover. The technologies for mathematical discovery are in the DNA of the Lindsay Center at St. Paul's. But curiosity and creativity are the most important tools in exploring math – and finding out what math means and can do.
SPS students examine the use of real-world applications to illustrate and reinforce mathematical ideas. And it works in the other direction too: mathematical concepts help explain real-world phenomena. As they learn problem-solving strategies, students develop mathematical habits of mind – a way of thinking that they use almost everywhere else, in writing, in music, and of course in science experimentation.
The SPS math program is built around a core sequence of courses – Geometry, Algebra 2, and Precalculus – with most students choosing to study further, through Calculus, Linear Algebra, Vector Calculus, and more, including such offerings as Problem Solving and the History of Mathematics. As in other areas of the curriculum, Independent Study allows students to create their own math courses.
Department Head
List of 1 members.
Mrs. Laura Hrasky
Laura Hrasky teaches mathematics at St. Paul's School. She is the head of a girls house, coaches girls varsity tennis, and serves as a lifeguard in the SPS pool.
Mrs. Hrasky grew up in Newton, Mass., and attended a public high school. She spent many summers working at an overnight camp in New Hampshire and as a result fell in love with the sense of community that living with others offered, which led to her interest in living and working in a boarding school.
Mrs. Hrasky graduated summa cum laude and earned Phi Beta Kappa honors at Tufts University, and received her master's degree in education from Tufts the next year. She taught middle school for four years in Cheshire, Conn., and was a math teacher, dorm parent and coach for nine years at the Pomfret School in Pomfret, Conn., before joining the SPS faculty in 2002.
Mrs. Hrasky enjoys the outdoors with her husband and young son. "I have been swimming since I was little, and I love taking the time to swim in the wonderful pool here at school, as well as in Lake Winnipesauke, where my family spends the summer." | 677.169 | 1 |
Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems. This side of the subject can be approached through the equations of a variety, and the syzygies of these equations are a necessary part of the study. This book is the first textbook-level account of basic examples and techniques in this area. It illustrates the use of syzygies in many concrete geometric considerations, from interpolation to the study of canonical curves. The text has served as a basis for graduate courses by the author at Berkeley, Brandeis, and in Paris. It is also suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. As an aid to the reader, an appendix provides a summary of commutative algebra, tying together examples and major results from a wide range of topics.
David Eisenbud is the director of the Mathematical Sciences Research Institute, President of the American Mathematical Society (2003-2004), and Professor of Mathematics at University of California, Berkeley. His other books include Commutative Algebra with a View Toward Algebraic Geometry (1995), and The Geometry of Schemes, with J. Harris (1999).
The author taught at Brandeis University for twenty-seven years, with sabbatical time spent in Paris, Bonn, and Berkeley, and became Director of the Mathematical Sciences Research Institute in Berkeley in the Summer of 1997. At the same time he joined the faculty of UC Berkeley as Professor of Mathematics. In 2003 he became President of the American Mathematical Society. He currently serves on several editorial boards (Annals of Mathematics, Bulletin du Société Mathématique de France, Springer-Verlag's book series Algorithms and Computation in Mathematics).
"This book is devoted to offer … an approach to the study of this algebraic subject (syzygy = relation among generators of a module) … . a student would learn a lot of algebraic geometry from it. The double bet of the book is to be able to be a complete textbook … and at the same time to become a useful reference text for research work on the subject. I would say that both aspects of the bet have been gained … ." (Alessandro Gimigliano, Zentralblatt MATH, Vol. 1066, 2005)
"This book may be regarded as a complement to the author's Commutative Algebra … . It begins by explaining syzygies and their connection with the Hilbert function, and turns to describing various aspects of algebraic geometry … . Two appendices provide the background in commutative algebra and local cohomology. Together with exercises, it gives a good survey of topics often not covered." (Mathematika, Vol. 52, 2005)
"This monograph is devoted to the geometric properties of a projective variety corresponding to the properties of its syzygies … . Altogether, this is a most welcome addition to the literature and will help many a reader bridge the gap between the abstractions of algebra and the more tangible field of geometry." (Ch. Baxa, Monatshefte für Mathematik, Vol. 150 (1), 2006)
"This very interesting book is the first textbook-level account of syzygies as they are used in algebraic geometry. … The reader will find two very good and useful appendices. … The book can be read, without any problem, by a student who has received already a little introduction in commutative algebra and algebraic geometry. I highly recommend this nice and deep textbook for all students and researchers studying algebraic geometry or commutative algebra." (Dominique Lambert, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008) | 677.169 | 1 |
Algebra 1 Linear Exponential Foldable
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This graphic organizer is designed to help students compare and contrast the equations, graphs, and tables of linear and exponential functions. Students will begin by folding the template across the red line ("hamburger" style) and then cut along the black line to create two flaps. The students can then interact with the foldable to see how increasing and decreasing linear/exponential functions look as equations, tables, and graphs.
It is advised that teachers walk through and instruct the students on how to use the foldable. There are places that are intentionally left blank so that students can fill them in as the teacher guides them along. Students are also encouraged to color in and fill in extra information to make the foldable more unique and personalized.
The foldable is designed to be made from one sheet of computer paper. Two different titles are included in this package so that teachers can choose what is more suitable for their students. | 677.169 | 1 |
Product Description
Book Description:
Senior Secondary School Mathematics For Class 11 is in accordance with the latest syllabus issued by the Central Board Of Secondary Education for students of intermediate classes. The Central Board Of Secondary Education is the premiere board for secondary education in private and public schools in the country. It is a board which is under the direct control of the Government of India. The Board aims at providing a robust, holistic and vibrant atmosphere for education in the country, so that the foundation for achieving excellence in all spheres can be laid. It also seeks to provide quality education and promote cultural, intellectual and social awareness.
The book has been written keeping in mind the need to include all requirements of the syllabus in a simple, comprehensive and easily understandable way. It also pays attention to grading of problems according to the level of difficulty. Every chapter has solved examples and a complete set of unsolved questions for practice. Difficult questions also carry hints for the students to be able to solve them easily. The book contains chapters titled Sets, Trigonometric Functions, Mathematical Reasoning, Relations, Mathematical Induction, Coordinate Geometry, Sequence and Series, Quadratic Equations, Limits, Derivatives, Conic Sections, Calculus, Straight Lines, Introduction to 3D Geometry, Statistics and Probability.
Senior Secondary School Mathematics For Class 11 was published by Bharatiya Vidya Bhavan.
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helpfulReview by adhvithi
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Very helpful for study.
Every solution and in easy language. (Posted on 12/17 | 677.169 | 1 |
Course info
Grade: 9-12 Credit: 1.0
Prerequisite: C- or better in Intermediate Algebra recommended.
The course will address solving equations, inequalities, and systems. The course will examine the following types of functions: linear, quadratic, polynomial, exponential, logarithmic, rational, and trigonometric. Additional topics include powers, radicals, sequences and series, and probability and statistics. Students study each mathematical idea in depth through application and practical problems, providing opportunities to understand the importance of math in everyday life. | 677.169 | 1 |
Ask and Learn from your Classmates
By Vic Odarve
It is the simplest thing to do for the students to learn more and pass the course.
Last semester, I had a quiz in Mathematics consisted of four problems. The last problem was the most difficult. Thus, it required an extra mile solution – deeper analysis- so to speak! As expected, the results after marking: only 2 out of 380 students got perfect scores. No wonder, it was difficult. But one of these students who got perfect scores caught my attention. It was intriguing! This student had never been in my list as top performers of the class! After rechecking, I found her script was perfect from the initial steps of the solutions until the very end. The solutions were well presented. Presentation was so detailed that no appreciable error can be seen. When the class resumed, I returned their individual papers or scripts and let her solved the problems on the board. To my surprise she explained very well; discussed solutions perfectly that the class applauded her. "Thank you, well done", I commended her after the discussion. Oh my God, I was awed and shocked in disbelief?
Engineering Mathematics
After a week, I happened to meet and talk her in the library how she was able to solve the last problem. "Yes, very difficult sir but I was able to ask help from my classmate few days before the quiz and we discussed together". That's it. It was her secret! Asking help from her classmates! She was referring to the other one who always got perfect score in all of my quizzes –a gifted student in Math!
No doubt! She learned by asking help from her classmates during study and propelled her way to get perfect scores! A simple act yet effective in Mathematics! Asking help from your classmates or teachers is one of the options to learn and pass this course.
Every student runs into problems in Mathematics courses from time to time. Even the bright ones! This is a part of learning process. But students who ask help from teachers or classmates appear to move and recover the lessons easily. Problems are likely getting past by asking help. Resourceful students are doing this way.
Classroom lecture!
By asking, students are benefited! The students may ask help from their classmates and get perfect scores during exams! But every student must know the art of asking either from her teacher or classmates in order to learn most out of it. The following tips help students maximize the benefits of asking from their classmates;
1. Do the explanations. Show the way how you come up the solutions until the steps you lose. The reason is clear: the one who does the explaining will learn the most.
2. When you are working in group or sharing some ideas, share your opinions with others. Don't let only one person do all the talking. Participate! | 677.169 | 1 |
Sixth Form: Mathematics
MINIMUM REQUIRMENTS: GRADE 6 IN GCSE MATHEMATICS (A GRADE 7 IS HIGHLY RECOMMENDED; EXCEPTIONAL STUDENTS CAN SUCCEED WITH A GRADE 6 AT GCSE BUT THIS IS UNUSUAL)
SUBJECT LEADER: Mr B Boxall
BOARD: (OCR) MEI
A2 SYLLABUS: H640
EXAMINATIONS: 100%
COURSEWORK: None
What is A-Level Mathematics?
The course covers topics from Pure Mathematics (61%-67%) and both Mechanics (15% - 17%) and Statistics (18% - 22%). Students are also required to become familiar with a specific large data set which will be made available in advance of the final examinations.
Throughout the course students are required to demonstrate the following overarching knowledge and skills: mathematical argument, language and proof and mathematical problem solving, using a problem solving cycle and modelling. Knowledge is developed of the methods of how todo Mathematics. Calculators and formula books will not provide easy answers but understanding how we can use technology, in particular graphing tools and spreadsheets, will permeate the subject.
The course is assessed via three 2 hour exams:
Paper 1: Pure + Mechanics 100 Marks
Paper 2: Pure + Statistics 100 Marks
Paper 3: Pure + Comprehension 75 Marks
Papers 1 & 2 have a section A of shorter questions with minimal reading and interpretation.
What makes a good Mathematician?
Successful A-Level mathematicians are prepared to persevere at problems, using other textbooks and web based resources outside of lessons when they need further guidance. Questions are multi-stage and it is essential to develop the ability to produce a logically progressive answer. The ability to manipulate fractions and algebraic expressions successfully is a key requirement at A-Level, so students selecting the course will need to be competent at this. Students studying the course having achieved a GCSE grade 6 would need to be extremely confident in their algebra skills. All students are expected to complete our "Transition Materials" towards the end of their summer holiday and hand them in at the end of the first week of A-Level study in preparation for an Algebra Test.
What can I expect to learn in Mathematics?
Pure Mathematics underpins the study of all other areas of mathematics and includes proof, algebra, trigonometry, calculus and vectors. Mechanics is the mathematics used to study the physical world, modelling the motion of objects and the forces acting on them, such asmoments, where the turning effect of a force is considered. Statistics involves statistical sampling, data presentation and probability leading to the study of statistical distributions with special properties, such as the Binomial Distribution.
Sixth Form mathematicians are encouraged to attend conferences; for example, the University of London's 'Maths in Action'. Here students learn about topics varying from the mathematical modelling behind juggling to the maths in quantum physics' string theory. A broader understanding of the subject is also encouraged by way of a reading list.
Where could Mathematics take me?
A-Level Mathematics is an excellent basis for a wide range of university courses and careers as the skills it developsare in high demand by employers and universities. In addition to developing the ability to solve problems and think logically, the study of Mathematics provides opportunities to develop team-working skills, resilience, effective communication of complex ideas and the ability to use your own initiative.
A-Level Mathematics supports the study of a wide range of other A-Level subjects. The Sciences all rely on good algebraic and graphical skills, statistical techniques and the use of a range of functions including logarithms and trigonometry. Economics, Psychology, Business, Computing and Geography all bene?t from students having ?uent and con?dent mathematical skills.
A good number of students have gone on to study Mathematics at university, including both Oxford and Cambridge. Other destinations include Mathematics and Engineering at Nottingham, as well as Economics, Biology, Law and French at various other universities. Please look also at Further Maths especially if you may want to study a Maths-based degree. | 677.169 | 1 |
Category Archives: Mathematics
A little over 20 years ago the Harvard Calculus Consortium sought to remake the calculus curriculum. "We believe that the calculus curriculum needs to be completely re-thought," began the text by Andrew Gleason and Deborah Hughes Hallett, both of Harvard University. They sought to get "our students to think." In doing so they proposed "The Rule of Three." "Our project is based on our belief that these three aspects of calculus—graphical, numerical, analytical—should all be emphasized throughout." The Rule of Three, today often known today as The Rule of Four with the now addition of verbal, rests at the heart of math education. While the Calculus Consortium's book may no longer own major market share, it has had a remarkable influence on all Calculus textbooks and indeed on all math textbooks in both K-12 and college. It is a widely shared belief that such multiple-linked representations must be central to 21st century pedagogy. It is clear that students learn in different ways. It is certain that they need to see mathematics from different perspectives.
Spreadsheets are Rule of Four platforms. They are function machines which naturally represent mathematics graphically, numerically, analytically, and verbally. They show a function as a graph, as a table, as a formula, and we can describe them with text and visuals. They did not start out that way. The first spreadsheet, VisiCalc invented by Bob Frankston and Dan Bricklin was designed to be a visual calculator to automate the accountants' worksheets. Three years after VisiCalc's debut in 1979, Mitch Kapor added graphs and tables to create Lotus123 which brought the IBM PC into every business. And Excel from Microsoft came out for the new Macintosh 2 years later not only simplifying the interface but adding beautiful texts and visuals to spreadsheets. Today, the mature spreadsheet technology is the standard quantitative tool for business worldwide. It is not only available on every major platform, but its format and design are the basis for displaying and interacting with quantity on the Web.
In a spreadsheet we can write a formula, use that formula to create a table of values, and use that table of values to make a wide variety of different graphs and charts. Change the formula and the table and graph changes automatically. Change the table and the graph changes automatically. Spreadsheets are dynamic and highly interactive. They even let you embed variable quantities in text to add units to quantities our dynamic values to verbal descriptions. Once a student builds a model in a spreadsheet, it is naturally a multiple-linked representation that can played with and explored. Spreadsheet models designed with functional thinking as multiple-linked representations are therefore simulations of which students can ask "What if…"
If you use Link Sheets in your classroom, if you believe that every student has a learning style, if you like to have students explore different representations, if you want to get your "students to think" then try using ourWhat if Math spreadsheets or develop your own built on the Rule of Four.
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Small changes, seemingly inconsequential acts, can have momentous repercussions. Dead birds set off the environmental movement. An assassin's bullet protesting an exhausted empire started a world war that brought down the ruling monarchies of Europe. A tax on tea turned into a revolution. Such a small change occurred in America's classrooms a little over a half century ago. School desks were unscrewed from the floor. That seemingly small change, which on its surface seemed to be just about furniture, precipitated a major reduction in class size and a revolution in expectations of good teaching. Desks bolted to the floor, locking students in straight rows facing a teacher in the front of the classroom, optimized the use of space. My 5th grade Chicago classroom with fixed desks held 51 students in 6 rows with 8 desks per row and three portables. It also defined Miss O'Hearn's teaching style. My 6th grade suburban classroom with moving desks had 25 students. Desks could be rearranged, students could interact with each other, learning in groups was enabled, and teachers could give students individual attention toward student-centered learning. Small changes can have great effects even in education.
We have the opportunity to make such a small, seemingly inconsequential change that could profoundly transform our schools by allowing students to use the internet on their Common Core Math tests.
We need only change the wording in the test's directions to allow and not prevent student use of a computer/tablet/smart phone. The tests are designed to be given online already. They give the students digital tools to use to solve some of the problems. What if we simply extended that existing open technology requirement to every question and enable students to use most any available program or website? What if they could use Google search to solve an arithmetic problem, or open Excel, Sheets, Numbers, Wolfram Alpha, Khan Academy, Wikipedia or any website they wanted to find an answer? What if, as the PARCC initials stand for, we are serious about the tests assessing "college and career readiness?" A realistic 21st century college or career problem would quite naturally expect the solver to have internet access. College tests are generally open book and every online course must, by its very nature, allow internet access. So why not really prepare our students for college and career?
The consequences of such a minor change in the assessment directions would be far reaching and revolutionary. Teachers would stop teaching the algorithms and stop giving students arithmetic and algebra algorithm worksheets. Why teach long division if the tests don't require it? Why spend all of that classroom and homework time on operations on fractions if students won't be tested on it? Why teach students to factor equations using paper and pencil algorithms if they can get the answer online? This mechanical symbol manipulation that today makes up the bulk of student practice time would simply vanish. Creative experiences using technology to solve math problems would naturally replace it, for those will be the "basic skills" required by the tests. Spreadsheets and other quantitative technologies would replace pencil and paper. Mathematics would become more interesting to students for they would no longer need to ask, "Why am I learning this stuff for when I can solve this problem on my old phone or calculator?" Math classrooms could be filled with creative "What if…" experiences.
Not only would there be more time for authentic problem solving in math, but there would be more time for the other STEM subjects, and more time for the arts, for physical education, for history, for the manual arts, for project and performance oriented activities. So many of us dream of an educational system that is rich and creative, but we are overwhelmed by a system seemingly sluggish to innovate, overwhelming in complexity, and demanding in tradition that it seems to make substantial change all but impossible. Yet there are times and circumstances when small, seemingly inconsequential acts can have monumental impacts. Allowing students to use the Web when they take their Common Core math assessments could well be as revolutionary for students today as unscrewing the desks were in the 1950's.
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For those of you who have been following my blogs, I apologize for taking so long to get out a new one. I have been working a wonderful new project that i am not yet ready to show you, but I promise to do so very soon.
Meanwhile I had a fascinating afternoon yesterday attending a seminar on SketchUp, what they call the 3D program for everyone. Google just sold it to a company called Trimble, a construction company.This program is for designers what WordPress is for bloggers.
As I watched amazing demo after amazing demo, all I could think about was America's K-12 math program, indeed our entire educational focus. To put it bluntly, it has nothing to do with the real world jobs of the 21st century. For here were architects, designers, engineers, interior decorators, landscape architects, and more using this program in their daily work to both design and to demonstrate. Here was an amazingly large community of people contributing their ideas and their actual work to other users of the program, developing "plug-ins" to do a variety of tasks SketchUp was not designed for.
Are we teaching our students to use technology, to work with sophisticated programs, to be part of a community of users and developers? Are they learning to create, to explore, to learn from each other? Are we preparing our children with the skills they will need for the 21st century? Are we imagining them working with tools like SketchUp? Or are we preparing them for the jobs and work of the 20th century? | 677.169 | 1 |
This sixth edition of INTERMEDIATE ALGEBRA retains the same basic format and style as the fifth edition. Each section of the book can be discussed in a forty-five to fifty minute class session. Intended for schools that teach the course in a lecture environment, students are able to prepare for class by answering the "Getting Ready for Class" questions.
"synopsis" may belong to another edition of this title.
About the Author:
Charles P. "Pat" McKeague earned his B.A. in Mathematics from California State University, Northridge, and his M.S. in Mathematics from Brigham Young University. A well-known author and respected educator, he is a full-time writer and a part-time instructor at Cuesta College. He has published twelve textbooks in mathematics covering a range of topics from basic mathematics to trigonometry. An active member of the mathematics community, Professor McKeague is a popular speaker at regional conferences, including the California Mathematics Council for Community Colleges, the American Mathematical Association of Two-Year Colleges, the National Council of Teachers of Mathematics, the Texas Mathematics Association of Two-Year Colleges, the New Mexico Mathematics Association of Two-Year Colleges, and the National Association for Developmental Education. He is a member of the American Mathematics Association for Two-Year Colleges, the Mathematics Association of America, the National Council of Teachers of Mathematics, and the California Mathematics Council for Community Colleges. | 677.169 | 1 |
Worksheet Chapter 6.1 College Prep Algebra
In this algebra worksheet, students solve a variety of problems. They find the greatest common factor of polynomials, factor polynomials and trinomials, and solve algebraic equations and real life story problems. Nine of the hundred problems require the interpretation of a story. | 677.169 | 1 |
Wednesday, October 5, 2016
Quiz #2 (Day 34)
There are several things that I wish to discuss in this post. First of all, the first Saturday in October marks the biannual book sale at my local library. Recall that last year, I purchased Mandelbrot's book on Fractal Geometry from the October book sale.
So what did I purchase at the book sale this year? Well, I always like to purchase at least one textbook on a subject or grade level that I want to teach. Since I'm now working at a middle school, of course I wanted a middle school text. And the book I got was Saxon's Algebra 1/2, third edition.
This marks the second time I've bought a Saxon text -- the first was Math 65, second edition. The Saxon texts lie right at the heart of the battle between traditionalists and progressives. Now that I am a full-time teacher, I don't wish to spend as much time discussing the traditionalist debates. But in today's post, I will bring up a little bit of the debate since I just purchased another Saxon text.
The Saxon texts are popular with traditionalists. Integrated math texts, on the other hand, are unpopular with traditionalists. The irony here is that the Saxon texts for high school math are -- you guessed it -- integrated, long before Common Core! So far, I've yet to see a traditionalist satisfactorily explain why he or she likes Saxon integrated math but not Common Core integrated math. Notice that the fourth editions of Saxon are not integrated, but the third editions are -- and it was a third edition that I purchased at the book sale.
One major concern of traditionalists is that students make it to AP Calculus by senior year, which usually means eighth grade Algebra I. But notice that the Saxon Algebra 1/2 text -- which is basically a Pre-Algebra text -- can nonetheless be given in eighth grade. Then freshmen can take Saxon Algebra 1, sophomores Saxon Algebra 2, and juniors Saxon Advanced Mathematics, as these are integrated texts that include Geometry. This does prepare students for senior-year Calculus.
I won't type out the entire contents of Saxon Algebra 1/2, but let's at least look at the lessons that are multiples of five:
Notice that Saxon Algebra 1/2 is approximately equivalent to Common Core 8. Indeed, there are many topics in Common Core 8 missing in Saxon Algebra 1/2. We see that Lesson 115 mentions transformations, but of course Saxon, like most pre-Core texts, doesn't cover transformations as extensively as Common Core. But more surprisingly, slope doesn't appear in Saxon Algebra 1/2 -- actually, there is an appendix covering both transformational geometry and slope as well as several other additional topics. But the main text omits slope. Systems of equations is yet another topic that Common Core 8 expects students to learn, but not Saxon Algebra 1/2.
We see that eighth graders can study from Saxon 1/2 -- a text less rigorous than Common Core 8 -- and yet make it to senior-year Calculus. This is part of why I think that students can proceed directly from Common Core 8 to Integrated Math II as freshmen, en route to AP Calculus.
I actually purchased one more math text, but I must admit that my reason for purchasing this book is pure nostalgia. I bought Mathematics Around the Clock, published in 1970. This text is considered part of the "California State Series," even though this was well before California State Standards.
The subject of this text is "clock arithmetic," more formally called "modular arithmetic." Here is a link discussing modular arithmetic:
There is no grade level associated with this text. The above link labels this as a "Stage 4" topic, which corresponds roughly to junior and senior years in high school, but I suspect that this text can be used with much younger students (though probably not younger than fourth grade, as these kids are still learning ordinary arithmetic). In fact, I was given a copy of this text when I was younger -- I no longer own that copy, which is why I said that I bought the book for nostalgic reasons.
Even though the above link describes what clock/modular arithmetic is, there's actually a song from Square One TV that discusses clock arithmetic:
The text begins with the modulo twelve system, just like the clock. It then moves on to modulo 7, 5, 4, 6, and others. Modular systems are examples of rings (as I mentioned in spring 2015 when reading another book), and prime modular systems are examples of fields. The words "ring" and "field" don't appear in the text, although the properties these satisfy (closure, commutative, etc.) do appear.
On page 39 of the text, I see the following section header:
"SOLVING NUMBER SENTENCES"
What the -- I heard from traditionalists that "number sentences" is a phrase invented by the Common Core, so how can it appear in a text written 40 years before the Core? Actually, this text usually uses the phrases "addition sentences" or "multiplication sentences" -- "number sentences" is an umbrella term covering both. The Common Core "number sentences" cover both equations and inequalities. I point out that inequalities don't make sense in modular arithmetic. Despite this, the clock arithmetic text doesn't use the word "equation" -- perhaps since it's awkward to call "9 + 8 = 5" an equation, even in mod 12 (or even more to the point, 9 + 8 = N).
Even though modular arithmetic is associated with the clock, on page 71, the modulo seven system is connected to the calendar. Notice that many of the algorithms I mentioned last week for calculating Rosh Hashanah and other holidays are examples of modular arithmetic -- for example, Conway Doomsday is done in mod 7, while Golden Numbers are an example of a modulo 19 system.
On page 86, there is a discussion of exponents in modular systems. There is a series of exercises that leads to the following theorem:
If N is any number in a prime modular system and N is not equal to zero, then N^(P - 1) = 1, where P is the prime number that is the modulus of the system.
This is actually a famous theorem -- even though the text doesn't call it this, it is actually known as Fermat's Little Theorem, named for the 17th century mathematician Pierre de Fermat. (I mentioned Fermat's Last Theorem in another post last year.)
When I first read about Fermat's Little Theorem in this book so many years ago, I knew how hard it is to determine whether or not a number is prime. I wondered to myself whether this theorem could be used to determine primality -- until I told myself, "Don't be silly -- of course we can't use this theorem, since raising numbers to powers is more difficult than trial division."
As it turns out, the first instinct of my young self was correct. The dominant method of determining whether a large number is prime is the Fermat method! As it turns out, exponentiation in a modular system is quite simple, especially if one uses repeated squaring -- for example, squaring a number four times is equivalent to raising it to the 16th power. With trial division, we can't prove a number is composite unless we stumble upon a factor and divide by it, but with the Fermat method, we could just plug in N = 2 into the formula, get a value other than 1, and instantly know that the number we're testing is composite.
The real problem with the Fermat method is the existence of Carmichael numbers -- numbers which are composite, yet the formula produces 1 for almost every value of N anyway. Modern primality tests usually begin with trial division for a few small factors, then the Fermat method, and then finally a more powerful method such as Miller-Rabin to test against Carmichael numbers.
Yesterday there was a Google Doodle to celebrate the anniversary of the Gregorian Calendar -- the calendar with which we are the most familiar. Actually, I'd argue that October 4th, 1582, was the last day of the old style Julian Calendar, as the first day of the new style calendar was October 15th. I would have posted about the Google Doodle yesterday, except that yesterday was my scheduled day off from blogging (as it was Day 33, and 33 is in the 0-class mod 3).
Oh, and by the way, not only was it Jewish New Year, but it was Islamic New Year as well. Notice that the Islamic Calendar is a pure lunar calendar -- each year is twelve lunar months, or about 354 days, with no attempt to harmonize with the solar calendar. For three consecutive years, the Jewish and Islamic New Years will be at the same time, until 2019 when the Jewish Calendar adds a leap month, but not the Islamic Calendar.
By the way, New York school system not only takes off the Jewish holidays also but also two major Islamic holidays. The Islamic New Year isn't one of them, and so it's not a day off in New York unless it coincides with the Jewish, or even (in over a decade, since there's no leap months) the Chinese New Year.
With all of this talk about calendars, yesterday I told my students about the Google Doodle and mentioned calendars as part of the review for today's quiz. It was a science quiz about the movements of the earth, moon, and sun.
Today I give today's quiz to all three grades. As I mentioned last week, the Wednesday schedule has been modified slightly. Now I see each of the three grades for one hour until nutrition, and then the seventh graders return after break for music.
Actually, the results of today's quiz are mixed. There are perfect scores in sixth and seventh, but not eighth grade. But eighth grade had relatively more students actually pass the quiz. The student with the lowest math grade ended up passing the quiz, while one of my harder working math students got only one question correct. Oh well -- at least I see my students' relative strengths in math and science.
Here is the song I sang yesterday while reviewing for the quiz. No, it wasn't Square One TV's "Time Keeper," since that has to do with a book I bought, not anything I taught in class:
EARTH, MOON, AND SUN
I know of how the earth goes,
It revolves around the sun every year.
I know of how the earth goes,
It revolves around the sun every year.
The earth's tilt is the reason,
That we have four seasons.
Winter, spring, summer, and fall,
That is all.
In the north, remember,
Winter's in December.
Tilts toward the sun in June,
It'll be summer soon.
I know of how the earth goes,
I know of how the earth goes,
I know of how the earth goes,
It revolves around the sun every year.
I know of how the moon goes,
It revolves around the earth every month.
I know of how the earth goes,
It revolves around the sun every year.
That's why every 30 days,
We can see every phase.
New moon, waxing crescent,
Half moon, waxing gibbous.
That's why every 30 days,
We can see every phase,
Full moon, waning gibbous,
Half moon, waning crescent.
I know of how the moon goes,
I know of how the moon goes,
I know of how the moon goes,
It revolves around the earth every month.
Note: In honor of Rosh Hashanah, this song is sung to the tune of the Hebrew song Hava Nagila.
Meanwhile, let's get back to the "Day in the Life" project. Today is the 5th, and so the monthly poster for the fifth is James Cleveland:
James Cleveland is a New York high school -- teacher? Unfortunately, I can't tell from his post whether or not he's teaching this year. He hasn't made his October 5th post yet, and his September 5th post was on Labor Day. He did write a post for the next day, which he labeled as the "First Day" (of school), but it's apparently more like a PD day, since he spent the entire day programming students for the new school year. Notice that New York is one of the few regions in the country where the first day of school is still after Labor Day.
So Cleveland might be a teacher who had to do office work before students arrived, but I can't be sure until he posts again. I was hoping that he might have caught up blogging on Monday, since after all, New York had a three-day weekend for Rosh Hashanah as well. All I can do is wait and see.
Despite the lack of "Day in the Life" teaching posts on Cleveland's blog, I do enjoy one of his recent blog posts. At the following link, he writes about the AP Calculus curriculum:
Readers of my blog know that I devote many posts describing the order in which math -- especially Geometry -- should be taught. Well, here Cleveland writes about why AP Calculus students should be taught integration before differentiation:
In general, I feel like area is a much more approachable subject than slope. My years of teaching Algebra I to 9th graders certainly seems to support that claim. But I also think it's easier to understand the linearity of integration than the linearity of slope. "If you add together two functions, the area under the new function is the sum of the areas under the old functions" seems much more evidently true than "If you add together two functions, the slope of the tangent line for each point of the new function is equal to the sum of the slopes of the tangent lines at the same points on the old functions."
I am not a Calculus teacher, of course. Still, I've discussed some of these same ideas in thinking about the Geometry curriculum. Which should we teach first: area or similarity (which leads to slope as per the Common Core)? The Geometry text we've been following for the first two years of this blog gives area first, but I rearranged it to similarity first so that we can get to slope faster. Nonetheless, I mentioned how a few proofs that use similarity (leading to slope) can be rewritten using area instead, which might be easier for students. After all, as Cleveland writes, "area is a much more approachable subject than slope." (Again, notice that Saxon Algebra 1/2 contains lessons on area, but not slope!)
Of course, I'm not really a Geometry teacher either. But, as we know, the middle school curriculum (especially Common Core 8) has a strong geometry component. So this is something I should be thinking about before my eighth grade class reaches the geometry unit.
Oh, and speaking of Geometry, let me conclude this post with a link to Sarah Carter's blog:
I didn't actually teach a science lesson from Carter's website today -- in fact, if this new Wednesday schedule holds, I won't have an extra period for eighth grade science (as a trade-off, I get to see my seventh graders now).
Then again, this post isn't actually Carter's. It's a "guest post" from an anonymous middle school teacher in Washington state -- and I'm always looking for middle school bloggers! But this is actually an advanced eighth grade class taking high school Geometry. In this post, the teacher explains how she teaches transformations to her class, using Foldable notes. | 677.169 | 1 |
PCI Educational Publishing Algebra City Student Edition is designed for students who struggling with algebra 1, students with learning differences and english language learners. Single pack student edition includes 4 student editions covering all 28 misconceptions and 1 student logins for Algebra City interactive activities valid for 12 consecutive months. It supports data-driven decision making using formative, summative and benchmark assessments. All assessments are handy via the ExamView Assessment Suite CD or as printable PDFs. ExamView scores the tests and renders a detailed report. Pretests at the program, book and unit levels indicates which misconceptions to focus on while posttests indicates whether mastery has been achieved or re-teaching is needed.- SKU: SSPC64395
This kit of student materials is designed to be used alongside the sold-separately Stewardship Instruction Pack and CANNOT be used independently. The Student Text provides four worksheets for each of the lessons in the instruction manual. Questions are not multiple-choice and must be supplied by the student. They include practical, math-based problems; questions that ensure mastery of basic financial terms, forms, and practices; and questions that encourage students to think about biblical principles and applications. The Test Booklet provides 30 end-of-chapter tests, one for each lesson. Comprehensive tests quiz students on the practical, mathematical, and biblical portions of the lesson. Answers are not included in this pack, but can be found in the manual sold with the Instruction KitThe Student Writing Intensive course from the Institute of Excellence in Writing is based on the IEW teacher's seminar Teaching Writing: Structure and Style, and provides a solid foundation of writing skills through direct writing instruction. This Level A course is designed for early elementary students in Grades 3-5Perfect for multiple children completing the Horizons for Threes course together, or younger students who need a new set of the consumables, this student workbook companion is designed to be used along with the sold-separately Horizons Preschool for Threes Student Workbook Companion and the teacher's guide that's included in the full Horizons Preschool for Threes Kit. The curriculum is designed so that students complete four worksheets in this Student Workbook, and one lesson in the aforementioned (sold- separately) Student Workbook Companion. The perfect pathway to creating a fun learning experience, the activities in this workbook develop age-appropriate skills to get kids ready for preschool. Each lesson corresponds to the daily Bible Story Reader selection. Through a developmental student activity book features scripts from the audio, writing and grammar exercises to supplement the text, and a section for journal entries. 192 pages, softcover. This resource is also known as Bob Jones French 2 Student Activity Manual.This curriculum for high school students is designed to provide students with a thorough understanding of all important physical, mental and social health issues. Written directly to teens from a caring and friendly perspective, Total Health presents a moral basis for a healthy lifestyle based upon scriptural principles. Anatomy, Body systems, food choices, exercise, diseases, stress, emergencies, responsibility, and more. Illustrations and photographs add visual interest to the text; at the end of each chapter, a review contains terms to define, questionsbased on the text, biblical application questions and suggested activities. 464 pages, indexed. Softcover.
The Student Writing Intensive course from the Institute of Excellence in Writing is based on the IEW teacher's seminar Teaching Writing: Structure and Style, and provides a solid foundation of writing skills through direct writing instruction. This Level B course is designed for middle school students in Grades 6-8Get everything you need to teach writing to students in grades 3-5 with this IEW value pack that includes both the teacher's Teaching Writing: Structure and Style course and the Student Writing Intensive Level A course...
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The Student Writing Intensive course from the Institute of Excellence in Writing is based on the IEW teacher's seminar Teaching Writing: Structure and Style, and provides a solid foundation of writing skills through direct writing instruction. This Level C course is designed for high school students and presumes no previous experience in the IEW writing method; it differs from the lowerat 1-2 weeks per lesson), and was recorded live with Andrew Pudewa. It teaches students how to use a wide range of structural models and stylisticFlexible and creative, WriteShop is an ideal homeschool writing program! WriteShop lessons give students a chance to practice various kinds of writing, including creative writing, expository writing, and narrative writing. Assignments teach descriptive and informative paragraphs as well as first-and third-person narratives, important techniques of style, and self-editing. Students learn to choose vivid, descriptive words and vary their sentences in order to build strong paragraphs. With each lesson, they learn and practice new skills, apply them to their current writing project, and edit and revise the composition several times. By the end of the lesson--after brainstorming, writing, editing, and revising-- they'll have a polished paper to be proud of! Students write one composition over...
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BUNDLE INCLUDED: 1. IdentaMaster® Biometric Software (1 license) 2. The Curve by Integrated Biometrics USB fingerprint scanner. SOLUTION: The IdentaMaster solution works effortlessly with the Curve by Integrated Biometrics fingerprint scanner. All you need is to install IdentaMaster application, plug-in your device and enroll. DEVICE: the scanner is featuring the patented Light Emitting Sensor (LES) offers the performance to fulfill the long-awaited promise of biometrics. This live finger sensing, high-resolution image generation technology surpasses both the security and usability of silicon and optical scanners in real-world performance. The low maintenance and durability of LES also add significant value from reduced operational costs and extended hardware life. IdentaMaster comes...
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Prepare your student for responsible citizenship with a discussion of the principles and mechanics of a constitutional republic. Material discussed includes the Constitution, the three branches of government, political parties, elections, foreign policy, and more, all from a biblical perspective. The material can be taught in one or two semesters. 434 pages, softcover. Non-consumable; answers should be written outside of the book. This 3rd edition features a new chapter on state and local governments as well as Christian worldview boxes that are designed to help students think scripturally and critically about governmental issues.This resource is also known as Bob Jones American Government Student Text, Grade 12, 3rd Edition.
The ESV Student Study Bible is adapted from the ESV Study Bible and is ideally suited for students who are serious about God's Word-who want to learn more about what the Bible teaches and how the Bible applies to all of life.With 12,000 clear, concise study notes, the ESV Student Study Bible provides numerous other features- including nearly 900 Did You Know? facts, 120 Bible character profiles, and 15 topical articles. It also features a glossary of key terms, more than 80 maps and illustrations, an extensive concordance, and 80,000 cross- references. These and many other features make it the most comprehensive and content-rich student Bible available today. Features:12,000 clear, concise study notesIntroduction s and timelines for each Bible book80+ maps and illustrations throughout15Give your high school students a fun and helpful way to build study skills and reinforce lessons from Apologia's Exploring Creation with Chemistry, 3rd Edition (sold- separately). The simple layout integrates study notes, questions from the text, and room to record experiment data within a clean, fresh workspace. This student notebook journal is divided into sections that correspond to the text. First, an introduction provides rubrics, notes and schedules. This is followed by each module's notebooking pages, which include blank note-taking pages along with room to answer the on your own questions, study guide questions, and extra practice problems. This is followed by the Experiments section, which features lab reports for every experiment in the text; forms include the objective,...
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The American Government Student Activity Manual is part of the BJU Press American Government, 3rd Edition curriculum. This guide gives students an opportunity to analyze primary documents and study the context in which they were written. A variety of reinforcement, enrichment, and review activities will help students develop analysis, evaluation, comprehension, and application skills. Selected chapter reviews provide opportunities to prepare for tests. 162 non-reproducible pages; consumable workbook.
This student notebook is designed to be used with the Apologia American Literature Text (not-included and sold-separately.Ev ery study question from the textbook is included, with plenty of space for students to record their answers. This notebook also contains chapter tests, semester exams, and detailed, step-by-step instructions for writing insightful and persuasive literary analysis papers on Nathaniel Hawthorne's short story The Birthmark and Robert Frost's poem Mending Wall. This notebook provides college-prep assignments needed to fully engage in this course. Spiralbound. Grades 9-12.
This student activity book accompanies BJU Press' sold-separately World History Student Text, 4th Edition. Helping to reinforce concepts, people, and places from the text while developing reading skills, exercises are based upon maps and included primary document excerpts. Chapter review sections include short answer and multiple-choice questions. 268 perforated pages, softcover. This resource is also known as Bob Jones World History Student Activity Book, Grade 10, 4th Edition.
Designed for high school students who already have an understanding of how to write a general or persuasive essay, this course will instruct students in conducting research, citing research, evaluating sources, outlining, drafting, arrangement, writing with an objective style, addressing counterarguments, and more. Student Book lessons are primarily divided between beginning research papers and intermediate research papers, with one major paper prompt assigned for each. The chapter-based exercises include rubrics, checklists, fill-in-the-blank note outlines, and short writing exercises which are designed to teach skills students will need to apply in their papers. A final advanced essay allows students to tie together their newly learned skills, which completes the course. The teacher's...
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Structured to build student skills by progressively introducing more detail and more difficult concepts, this workbook provides a detailed introduction to the basics of how to write a research paper. Divided into Beginning, Intermediate, and Advanced sections, individual chapters focus on the prompt, note- taking/research, sources, construction, drafting, and style. This guided approach helps to break down the many steps involved in writing research papers into a manageable, understandable progression of steps to take. Detailed lessons integrate multiple examples and writing samples, which are followed by workbook exercises that help students to apply newly-learned skills. At the end of the three levels, students write a paper, eventually integrating all concepts. Designed for students...
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This BJU Science 4th grade student text presents science through bright photographs, updated text and interesting sidebars. Children will learn of creation through a biblical lens as chapters highlight interesting facts about insects & spiders, plants, electricity, light, force, the moon, erosion, digestion, bones, and muscles. Quick check sections review and reinforce concepts learned, while the last page of each chapter provides key terms and concepts. Experiments, activities and projects are also included for a hands-on, interactive year of science! The updated edition now includes a worldview- shaping lesson from Answers in Genesis. 295 pages, softcover with glossary and index. This resource is also known as Bob Jones Science Grade 4 Student Textbook, 4th EditionGet everything you need to teach writing to middle school students with this value pack that includes the teacher's Teaching Writing: Structure and Style course, the Student Writing Intensive Level B course, and Fix It! Grammar Teacher's Guides for Books 1 & 2Adapted from the best-selling adult study, students learn to hear God. The video, The Xperience is a 9 week drama designed for students in grades 7-12 in a study of Experiencing God, Youth Edition. As teens watch the story unfold in this drama, they will discover parallels between the video and the priciples in Experiencing God. The Leader Kit includes:The Xperience Video Drama on DVD 1 Youth Leader Guide (which contains teaching plans for weekly meetings and discussion questions related to the drama) 1 Youth Member Book
This student text is part of the BJU Press Economics curriculum for grade 12. Students will be introduced to the key principles of economics, from household purchases to the stock market. Five units (15 chapters) ensure students gain a foundational understanding of economics as a science as well as the economics of countries, businesses, the financial markets, and the government. Biographical sketches on famous economists are included throughout; in addition, each chapter includes personal finance sections that provide practical information about budgeting, banking, debt, credit, and interest. Sections are concluded with a set of section review questions, and chapters end with content questions, application questions, and a list of terms. Written from a biblical perspective, students will...
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This course picks up where the Student Writing Intensive Level B left off and advances writing even further; the SWI Level B course (or equivalent instruction) is a prerequisite for this course. IEW's Student Writing Intensive (SWI) Continuation Course Level B picks up where the SWI Level B primary program left off and teaches more of the stylistic techniques and writing formats, including stories, writing from pictures, 5-paragraph essays, and reports from longer sources. This program is perfect for students who enjoyed the first class and want more, or for those who would benefit from additional exposure, or for students who wish to supplement other writing programs. Students continue to use the same binder and charts, while learning new models and techniques not previously presented in...
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This course picks up where the Student Writing Intensive Level A left off and advances writing even further; the SWI Level A course (or equivalent instruction) is a prerequisite for this course. IEW's Student Writing Intensive (SWI) Continuation Course Level A (following the SWI Level A primary program) teaches more of the stylistic techniques and writing formats, including writing from pictures, editing, basic essays, and more. This program is perfect for students who enjoyed the first class and want more, for those who would benefit from additional exposure, or for students who wish to supplement other writing programs. Students continue to use the same binder and charts, while learning new models and techniques not previously presented in the SWI. This course can be taught over one to...
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Your students will embark on a grand tour without ever leaving home with BJU Press' 9th grade Cultural Geography textbook. Each unit opens with a biblical link and short introductory essay. Chapters include various fact boxes; bolded important terms; Let's Go Exploring map skill exercises; Earth Matters boxes on the challenges of fulfilling the Dominion Mandate; notes on cultural information; section quizzes; chapter reviews; and more. Full color pages are filled with photographs and illustrations, providing a unique visualization of the vast span of cultures and countries across our globe. This new edition features a new opening chapter and is filled with photographs, charts, maps, and first-person accounts that make this virtual world tour an exciting and stimulating exploration of...
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The BJU Press Biology Student Text shows students the amazing display of God's power and glory in the living world. Students will learn about the chemical processes of life, ecology, cells, microorganisms and plants, animals, and the human body through full-color chapters that include clear images, galleries of photos, case studies, margin boxes, inquiry-based investigations, vocabulary definitions, and section review questions. Chapters end with review questions and case study questions. When studying topics such as Creation and evolution, abortion, STDs, euthanasia, and other controversial topics, students are pointed to Scripture as the ultimate authority and are encouraged to develop a biblical perspective about these topics. 561 pages with index and glossary, softcover. 5th Edition...
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Get everything you need to teach writing to middle school students with this value pack that includes the teacher's Teaching Writing: Structure and Style course, the Student Writing Intensive Level B course, and Fix It! Grammar Teacher's Guides for Books 3 & 4BJU Press' French 2 curriculum builds on the foundation laid in French 1. Students will develop linguistic survival skills with an expansion of vocabulary and reading skills. Oral and reading comprehension sections will expose students to French literature, and help students to understand the language in the context of French-speaking lands. Culture is taught as well. 352 pages, hardcover. This resource is also known as Bob Jones French 2 Student Text | 677.169 | 1 |
Run a Quick Search on "Topology for Computing" Afra J. Zomorodian to Browse Related Products:
Short Desription
Written by a computer scientist for computer scientists, this book teaches topology from a computational point of view, and shows how to solve real problems that have topological aspects involving computers. Such problems arise in many areas, such as computer graphics, robotics, structural biology, and chemistry. The author starts from the basics of topology, assuming no prior exposure to the subject, and moves rapidly up to recent advances in the area, including topological persistence and hierarchical Morse complexes. Algorithms and data structures are presented when appropriate.
If You Enjoy "Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics) (Paperback)", May We Also Recommend: | 677.169 | 1 |
Fun Self-Discovery Tools
Introduction to Variables and Solving Equations
Rating:
Description:
To explain what variables are, why and how they are used, and how to isolate them in equations (i.e. how to solve a one-variable algebraic equation.) This slideshow also introduces coefficients as well as the algebraic "shorthand" ways to signify multiplication and division.
I would consider this a good packet for someone who is preparing to begin study of algebra or has not done any algebra in a long time. Assumes a solid understanding of arithmetic but NO prior knowledge of algebra | 677.169 | 1 |
Linear Algebra with Applications (3rd Edition)
KEY BENEFIT: This trusted reference offers an intellectually honest, thought-provoking, sound introduction to linear algebra. Enables readers to grasp the subject with a challenging, yet visually accessible approach that does not sacrifice mathematical integrity. Adds over 400 new exercises to the problem sets, ranging in difficulty from elementary to more challenging. Adds new historical problems taken from ancient Chinese, Indian, Arabic, and early European sources. Strengthens geometric and conceptual emphasis. A comprehensive, thorough reference for anyone who needs to brush up on their knowledge of linear algebra.
"synopsis" may belong to another edition of this title.
From the Publisher:
This introduction to linear algebra focuses on dynamical systems -- continuous and discrete -- as a unifying theme, as motivation for eigenvectors, and in examples of major applications of linear algebra -- particularly systems of differential equations. Pedagogically strong ,it introduces abstract concepts gradually and gently -- without "spoon feeding" students. It uses visualization and geometrical interpretations extensively and features an abundance of both routine and thought-provoking problems and exercises involving abstract concepts and applications.
From the Back Cover:
With the most geometric presentation now available, this reference emphasizes linear transformations as a unifying theme, and enables users to "do" both computational and abstract math in each chapter. A second theme is introduced half way through the text—when eigenvectors are reached—on dynamical systems. It also includes a wider range of problem sets than found in any other book in this market. Chapter topics include systems of linear equations; linear transformations; subspaces of Rn and their dimension; linear spaces; orthogonality and least squares; determinants; eigenvalues and eigenvectors; symmetric matrices and quadratic forms; and linear differential equations. For anyone seeking an introduction to linear algebra.1453340
Book Description 2004496 | 677.169 | 1 |
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Naveen Ankganit has been one of the most popular and acceptable books for students appearing for different competitive examinations. However, since there have been some changes in the syllabi of these examinations, like incorporation of advance mathematics, there was a need to come out with a revised edition of this book. Based on the latest pattern of examinations, the book now includes ......
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This revised edition of A Modern Approach to Verbal & Non-Verbal Reasoning, while retaining the key strengths and structure of the previous edition, brings to the readers additional questions from various competitive examinations as per the latest pattern and trends. A section on recent questions (based on memory) and their answers/solutions from different competitive examinations like ......
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Over the years, Objective General Knowledge has been an indispensable book for the aspirants of different competitive examinations. Its popularity among its readers has never ebbed despite the presence of so many competing books from other publishers. To ensure this book retains the place of "first choice" among the readers, it has been revised in accordance with the current ......
Over the last 20 years this book has earned the reputation of being one of the market leaders in the subject and has helped you score high in the General English paper of most competitive examinations. With changing times and in keeping up with the modern trends in examination papers we have provided a Question Bank comprising questions from different competitive examinations held between ......
The revision comes 10 years after the first edition and completely overhauls the text not only in terms of look and feel but also content which is now contemporary while also being timeless. A large number of words are explained with the help of examples and their lineage which helps the reader understand their individual usage and the ways to use them on the correct occasion. ... | 677.169 | 1 |
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means,electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc. 222 Rosewood Drive, Danvers, MA 01923, (978)750-8400, fax (978)646-8600.Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201)748-6011, fax (201)748-6008. To order books or for customer service please, call 1-800-CALL WILEY (225-5945).
Preface
MATLAB® is a very popularlanguage for technical computing used by students, engineers, and scientists in universities, research institutes, and industries all over the world. The software is popular because it is powerful and easy to use. For university freshmen in it can be thought of as the next tool to use after the graphic calculator in high school. This book was written following several years of teaching the software tofreshmen in an introductory engineering course. The objective was to write a book that teaches the software in a friendly, non-intimidating fashion. Therefore, the book is written in simple and direct language. In many places bullets, rather than lengthy text, are used to list facts and details that are related to a specific topic. The book includes numerous sample problems in mathematics, science,and engineering that are similar to problems encountered by new users of MATLAB. This third edition of the book is updated for MATLAB 7.5 (Release 2007b). Other modifications/changes to this edition are: script files are introduced in Chapter 1 (this allows students to use script files for solving problems in Chapters 2 and 3), new coverage of the Workspace Window, the save and load commands,plotting figures with error bars, and instructions for using several Figure Windows at the same time. Chapter 6 was revised to include coverage on anonymous functions, function functions, function handles, subfunctions and nested functions. In addition, the end of chapter problems have been revised. There are many new problems (more than half), and the problems cover a wider range of topics. I wouldlike to thank several of my colleagues at The Ohio State University. Professors Richard Freuler, Mark Walter, and Walter Lampert, and Dr. Mike Parke read sections of the book and suggested modifications. I also appreciate the involvement and support of Professors Robert Gustafson and John Demel and Dr. John Merrill from the First-Year Engineering Program at The Ohio State University. Special thanksgo to Professor Mike Lichtensteiger (OSU), and my daughter Tal Gilat (Marquette University), who carefully reviewed the first edition of the book and provided valuable comments and criticisms. Professor Brian Harper (OSU) has made a significant contribution to the new end of chapter problems in the present edition. I would like to express my appreciation to all those who have reviewed the first... | 677.169 | 1 |
Abdominal cavity starts as high as the 4th intercostal space
Upper and lower parts of the abdomen are enclosed by two bony rings (the lower
margin of the rib cage superiorly, and the pelvis inferiorly)
The flexible lumbar vertebrae are located in the mid
Some Thoughts on How to Understand Proofs and to Write Them
Most people find it difficult to learn what constitutes a valid proof. Often ability in this
area comes about by some form of osmosis in which eventually it either sinks in or
it doesnt! I believ
General Structure of a Theorem
The purpose of a theorem is to present a mathematical truth. Of course, just stating that something is
true does not make it so. Mathematics history is littered with theorems that later were discovered to be
false. What that
MAS 3106 Linear Algebra
Problem Set 6 Due 2/24/11
Although they are not assigned, please look at problems 4 and 10 on Page 107 and problems 17
and 20 on page 108. They may be needed later in the course.
1.
Page 106, Problem 1
2.
Page 106, Problem 2df
3.
P
Problem Set 1 Due 1/20/11
1.
Page 6, Problem 7
2.
Page 553, Example 3. Show this is a field.
3.
Show Z 6 is not a field. What is required to show this?
4.
In a field F, define subtraction as on Page 554. If a, b, c F , prove a(b c ) ab ac
5.
Page 12, Prob
Proving Theorems Using the Principle of Mathematical Induction
The Principle of Mathematical Induction deals with the problem of proving an infinite number of statements.
Obviously it is impossible to prove each one separately, so we need a method of prov
Structure and Proof of If and Only If Theorems
Form of the theorem statement
General hypotheses that hold throughout all parts of the theorem
Conclusion: A if and only if B (where A and B are statements)
This is really a concise way of stating two theorem
Theorem Proofs for Several Equivalent Conditions
In this type of situation the theorem statement is of the following form:
Hypotheses
Conclusion: Then the following are equivalent:
(a)
(b)
(c)
where the number of statements (a), (b), (c), is usually at le
Theorem Proofs Using the Method of Contradiction
As always, in one form or another, a theorem being proved boils down to the
following structure:
Hypotheses
Conclusion: Then Statement A
where A is the statement to be proven using the hypotheses and previo | 677.169 | 1 |
About the Book
CliffsQuickReview Trigonometry provides you with all you need to know to understand the basic concepts of trigonometry — whether you need a supplement to your textbook and classes or an at-a-glance reference. Trigonometry isn't just measuring angles; it has many applications in the real world, such as in navigation, surveying, construction, and many other branches of science, including mathematics and physics. As you work your way through this review, you'll be ready to tackle such concepts as
Trigonometric functions, such as sines and cosines
Graphs and trigonometric identities
Vectors, polar coordinates, and complex numbers
Inverse functions and equations
You can use CliffsQuickReview Trigonometry in any way that fits your personal style for study and review — you decide what works best with your needs. You can read the book from cover to cover or just look for the information you want and put it back on the shelf for later. Here are just a few ways you can search for topics:
Use the free Pocket Guide full of essential information
Get a glimpse of what you'll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapter
Use the Chapter Checkout at the end of each chapter to gauge your grasp of the important information you need to know
Test your knowledge more completely in the CQR Review and look for additional sources of information in the CQR Resource Center
Use the glossary to find key terms fast
With titles available for all the most popular high school and college courses, CliffsQuickReview guides are a comprehensive resource that can help you get the best possible grades | 677.169 | 1 |
Covering all three approaches to Jacques Tits's beautiful theory of buildings, this accessible volume is suitable as a textbook introduction to the subject as well as a self-study text for researchers. It contains numerous exercises. more...
This book will help teachers introduce pre-college students to the ideas that develop the foundation of the engineering profession. It presents modeling activities in both technology-enabled and technology-immune approaches. more...
This book discusses mathematics learners in transition and their practices in different contexts; the institutional and socio-cultural framing of the transition processes involved; and the communication and negotiation of mathematical meanings during transition. Providing both empirical studies and significant theoretical reflections, it will appeal... more...
About the Book: The book `Fundamental Approach to Discrete Mathematics` is a required part of pursuing a computer science degree at most universities. It provides in-depth knowledge to the subject for beginners and stimulates further interest in the topic. The salient features of this book include: Strong coverage of key topics involving recurrence... more...
In a rapidly evolving local and global economy, skills related to mathematical problem solving, scientific inquiry, and technological innovation are becoming more critical for success in and out of school. Thus, Demystify Math, Science, and Technology addresses the need to cultivate these skills in young students so that ingenuity, teamwork,... more... | 677.169 | 1 |
Math Leap
Program Details Cost $45
The Math Leap program is designed to give students the opportunity to review their
math knowledge in a friendly, student-centered environment using ALEKS. The goal is
to help each student eliminate a semester or more of math!
The program begins with a pre-test that will determine the knowledge of each participant.
A customized study path will then be created for each student, focusing on the areas
that need the most work.
Participants will have access to online resources to help them master the necessary
concepts. Participants are expected to come to class every day for the three weeks
of the program. During class time, they will receive individualized instruction from
both the online software and a faculty member. They are also expected to work from
home.
Students will then be given a post-test to place into a higher math class. The post-test
placements will vary based upon the effort an individual puts forth during the program.
Students will need to obtain a free Summer Parking permit from parking services in
order to park on campus during the workshop. This can be done on their website You will need your UV ID number. If you do not have a UV ID number, call Tena at
(801) 863-8103.
During Fall and Spring semesters students can take MATH 100R.
This is a 1-credit block course. Students will access ALEKS, have faculty guidance,
and will establish official math placement before registration begins for the next
semester.
Students may also choose to do independent self-study. ALEKS can be accessed by following
these steps:
Log into myUVU
Under the student tab select My Academics
Scroll down to My Class Tools
Select ALEKS – Math Learning System
Follow instructions to sign up. There is a $15 fee.
Students will take the official placement test in the testing center for a fee of
$5. | 677.169 | 1 |
Subjects covered in college algebra how to write a report of a visit
Math Program Evaluation with COMPASS Research Reports 10 . For example, Calculus I or courses with college algebra and . courses. For more information on the COMPASS mathematics test, please visit our web site at.
the preliminary report of an MAA Task Force, indicate that only one in ten College Algebra (CA) students That is a long list of topics ; yet, it is only half the topics listed. For example, we ask our Algebra I students to figure costs of printing.
MATH 0701 to Required Courses Grade of C-|May not be taken Learn probability, for example, by discussing the gambler's fallacy and .. Topics covered will include some or all of the following: limits and continuity, illuminate the connections between secondary and college mathematics and between.
Salman Khan talk at TED 2011 (from murrayutah.info)
Subjects covered in college algebra how to write a report of a visit - Cat, mountain
Analysis and numerical solution of ordinary and partial differential equations. Download PDF of entire Graduate Bulletin. Students completing two years of college should comprehend positive and negative feedback loops. How can I tell if an e-mail message is really from my bank? USM Library Check Out Policies. Research standardized testing policies and learn about the SAT and ACT. This course develops Lie theory from the ground up. Topics covered include Banach and Hilbert spaces, Banach-Steinhaus theorem, Hahn-Banach theorem, Stone-Weierstrass theorem, Operator theory, self-adjointness, compactness. The content varies from time to time depending on the interests of the students. The core of the course focuses on setup and management of computer hardware specialized for scientific computing, and on its impact on commonly used strategies and methods for scientific computation.
Subjects covered in college algebra how to write a report of a visit - between
Math in the News. The goals of College Algebra should be to get students to internalize mathematics and come to understand certain ideas conceptually. Clearly, this lesson should be repeated in physical and social science courses, but it is crucial in applied mathematics. Nevanlinna theory, several complex variables. Go to Visit and Engage Plan Your Visit Social and Virtual Maps and Directions Northwestern Comes to You Apply Find instructions and tips for your Northwestern application. Does playing the lottery make sense? | 677.169 | 1 |
Be sure that you have an application to open
this file type before downloading and/or purchasing.
571 KB|2 pages
Product Description
Function Notation Maze Worksheet
My students love mazes and this is a great alternative to a traditional worksheet.
This is a 3-page PDF document that assesses a student's understanding of Function Notation.
The activity includes 2 different versions of the same maze, along with the answer key.
One version is written in the format Find f(x) = # and the other format is Find f(#). I wanted to make sure that I used both formats that could be seen in various textbooks.
As the student works the problems, they have to follow their correct answers to work their way towards the end of the maze.
The answer key is included.
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I welcome all feedback and ratings. I work hard to ensure that the items that I share are neat, useful and accurate. Although I do my best to catch errors in content or format, I am human and as such I am subject to make mistakes. If you discover an error or experience some form of technical difficulties with my items, I would appreciate the opportunity to correct the problem before a low rating and/or negative feedback is left. Simply submit the issue under the "Ask a Question" tab and I will do my best to resolve it in a timely manner. | 677.169 | 1 |
Support for the relevance of issues addressed in the Second Edition of How to Succeed in College Mathematics, includes:
•Remarks in the book from successful college mathematics students on what worked for them, and from unsuccessful college mathematics students on what did not work for them.
•Remarks in the book from college mathematics students on their response to these questions on course evaluation forms: What did you like about the course and instructor? What did you dislike about the course and instructor?
•Suggestions to the author from experienced college mathematics instructors on issues that should be included in the book.
•No one can argue against the relevancy of students understanding mathematics, and instructors teaching mathematics for understanding. What this means, and how it can be accomplished, along with important short- and long-term benefits of understanding mathematics, is presented and discussed in the book. There is hardly a section in the book that does not relate, in some way, to supporting "understanding" for students and instructors.
Mathematics students who struggled in the author's classes, mentioned that mathematics was always difficult for them. These students appeared to have one thing in common: They did not study mathematics for understanding. They learned content rotely and viewed most aspects of mathematics as isolated pieces of information. Their main efforts in their mathematics study were to memorize pieces of information and to mindlessly manipulate symbols. To succeed, they needed to make three changes: (1) have a strong desire to understand, (2) know what needs to be changed in their study to understand, and (3) persevere in their efforts to understand. A key responsibility of instructors is to support them in doing this.
A concise overview of topics in the book that relate to understanding mathematics is presented below.
Understanding specific mathematics means being able to connect or relate that mathematics to other things you know. The more things you can relate to what you are trying to understand, the better your understanding will be. The questions that a learner needs to answer when learning a specific topic in mathematics include these: (1) where did it come from, (2) what is its purpose, and (3) how is it applied? Thus, this necessitates students approaching their mathematics study from one of understanding, which includes working with other students. In addition, instructors need to support them in their efforts to get at understanding through exposition, conducting in-class discussions, making appropriate assignments, and evaluating students' understanding of mathematics.
Perhaps the most important thing an instructor can do to improve students' understanding of mathematics is to have them write about mathematics. These writing exercises should be included in assignments, study guides and examinations. In most exercises of this type, students are asked to write about how things are related or connected.
Understanding can be fleeting, and that is why it needs maintenance. Meaningful review of mathematics not only enhances maintenance; but it also advances understanding, since topics understood earlier are re-related to knowledge that has been better understood after the topics were initially developed.
Problem solvinghas to be the focus of mathematics study, and it, along with understanding, does not take place in a vacuum. What this means is that all that is studied in a mathematics course, including concepts, principles, and computational techniques, is done with the thought that this will help in solving problems. And this thought is acted on by solving problems, including those in a real world context. Mathematics work must point to solving problems, which needs to be the basic mathematical activity in a course. The more knowledge and understanding you have of specific concepts and principles, along with computational proficiency and a repertoire of problem solving skills, the better problem solver you will be. However, it is also the case that having problem-solving skills helps in understanding mathematics content. They can be applied in developing concepts, constructing theories, generalizing, and improving one's ability to abstract. So there you have it, a two-way street—being proficient in problem solving helps you understand mathematics content, and understanding mathematics content helps you become a better problem solver. That's a win-win situation.
This is not a book on quick fixes or on sound bites—such gimmicks for learning do not help students be successful. Is the content of the book relevant? Bet the farm on it!
Support for Credibility of Issues Addressed
Sources used in writing the Second Edition of How to Succeed in College Mathematics that lend credibility to the topics that are included and the advice given, include:
•Findings of educational psychology.
•Reports and journals of professional mathematics or mathematics education organizations, including the Mathematical Association of America (MAA), and the National Council of Teachers of Mathematics (NCTM).
•Research papers written by experts in the fields of mathematics, mathematics education, and education.
•The credibility of the author as evidenced by his formal training, teaching experience, and scholarship on the teaching and learning of mathematics (CLICK ABOUT RICHARD M. DAHLKE).
•Astute quotations. Carefully selected quotations serve many purposes, including (1) providing evidence for the relevance, credibility, and authority of the ideas they comprise, (2) giving cogent summaries of these ideas, (3) stimulating thought and discussion, (4) illuminating meaning and understanding, (5) giving perspective, (6) creating interest, and (7) preserving wisdom gained throughout the years. Look forward to being motivated and inspired by quotations carefully selected for the book. | 677.169 | 1 |
Other Titles by Rhonda Huettenmueller
If you are absolutely confused by absolute value equations, or you think parabolas are short moral stories, College Algebra DeMYSTiFied, Second Edition is your solution to mastering the topic's concepts and theories at your own pace. This thoroughly revised and updated guide eases you into the subject, beginning with the math fundamentals then introducing you to this advanced form of algebra. As you progress, you will learn how to simplify rational expressions, divide complex numbers, and solve quadratic equations. You will understand the difference between odd and even functions and no longer be confused by the multiplicity of zeros. Detailed examples make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key ideas.
It's a no-brainer! You'll learn about:
The x-y coordinate plane
Lines and intercepts
The FOIL method
Functions
Nonlinear equations
Graphs of functions
Exponents and logarithms
Simple enough for a beginner, but challenging enough for an advanced student, College Algebra DeMYSTiFieD, Second Edition is your shortcut to a working knowledge of this engaging | 677.169 | 1 |
TUTORING: .. Flex time tutoring : Flex time tutoring will take place from 12:08-12:38. This time frame is called academic time. 12:38-1:08 is open for lunch. Each day for academic time is devoted to each class period. The schedule is listed below: Monday- 1st period Tuesday- 2nd period Wednesday- 3rd period Thursday-4th period Friday-open to anyone who would like to stay with me.
AFTER SCHOOL TUTORING: I will stay after school from 2:40-3:40 at least once a week to help students further. These days will change depending on quiz/test dates and will be posted in our classroom for each week.
Supplies needed for my class:
one 3-ring notebook
loose leaf paper
graph paper
index dividers(5 pack)
Requested but certainly not required: Kleenex for our classroom.
Calculator***
***Calculator Advice: As you enter high school, a calculator is a wise investment. Everyone in my class will have access to the school's TI-84 Plus graphing calculators. However, you will need to have a calculator at home to do your homework. You need a scientific calculator with the ABC fraction button or a graphing calculator. The question is which kind of calculator is best? Some of my favorites are the TI-30x IIS and the TI-30x IIB (around $10-15). If you are considering taking higher level mathematics courses in the future you might consider investing in a graphing calculator (around $100). I would recommend any version of the TI-84 series. Please note that the TI-89, TI-92, and the TI-Nspire CAS will not be allowed in this class, they simply do too much. | 677.169 | 1 |
Algebra 2
Esplora argomenti correlati
Free Math Assessments or Quizzes for Algebra 2. These Algebra 2 Quizzes are aligned with the common core math standards. These Algebra 2 assessments can also be used as quick checks, spiral math review, and progress monitoringBook Review - Fire Pool by David E Owen
Algebra 2 Exponent Rule ReviewGraphing absolute value functions CHEAT SHEET
We started graphing absolute value functions in Algebra 2 this week. At the same time, I got a request for a reference sheet like one I had posted for graphing quadratics. It was great timing. I had one but it wasn't good, so the request was the kick in the pants I needed to make changes.
Algebra 2 - Combining functions dice game... using f(x) dice and g(x) dice gives a large set of practice problems. | 677.169 | 1 |
(480-517-8710 or 1-800-584-8775 or or from another seller.
Course Description and Competencies
Official Course Description
A problem solving approach to mathematics as it applies to life and the world of work. Development, demonstration, and communication of mathematical concepts and formulas that relate to measurement, percentage, statistics, and geometry.
Official Course Prerequisites
Grade of "C" or better in MAT082, or equivalent, or satisfactory score on District placement exam.
Select and use appropriate formulas in solving practical applications.
Solve linear equations and related applied problems.
Apply unit analysis skills to solve related applied problems.
Convert and solve applied problems within and between the U.S. system and metric system.
Define and use terminology associated with geometry.
Summarize, interpret, and use graphs to display statistical data.
Select and use appropriate technology to solve mathematical problems.
Course Requirements
You must complete all assignments in the course to be eligible to get a passing grade. The assignments which will be turned in and graded are the four Mail-In Quizzes found in the Course Packet. The other assignments given in the Course Packet, those involving exercises from the textbook, are not to be turned in; they are for your practice only.
Examinations: There are two required in-person exams (a midterm and final) for this course. It is strongly recommended that you study the Practice Exams prior to taking the Midterm and Final. See the Exams section below for more information on taking your Midterm and Final exams.
Note: You must earn a combined average of 60% on the midterm and final exams in order to pass the course.
Note: Keep a copy of all your assignments! Make sure that your submission can be read by your instructor. If you write lightly in pencil it may be difficult to read
Grading Procedure and Scale
Grading Procedure
There are 520 possible points for this course.
4 Mail-In Assignments/quizzes at 25 points each =
100 points
One Midterm Exam =
210 points
One Final Exam =
210 points
Total Points =
520 points
Note to student: You must earn a combined average of 60% on the midterm and final exams in order to pass the course. Students with an average on these exams of less than 60%, regardless of their performance on assignments, will not receive a passing grade.
Grading Scale
The final course grades will be determined by the following scale:
Grade Determination
Grade
Points
Percentage
A
468 - 520 points
90%-100%
B
416 - 467 points
80%-89%
C
364 - 415 points
70%-79%
D
312 - 363 points
60%-69%
F
0 - 311 points
0%-59%
Please Note point adjustments made for such things as "class participation" or other subjective factors.
Extra credit is not available for this course.
Exams
This course contains in-person exams which must be completed at an approved testing site.
Students who live within Maricopa county please see the testing information in your Print Based Student Handbook, or you may view it on the Internet at:
Students who live outside of Maricopa County or are registered with Disability Resources and Services may request to have exams proctored by submitting the Proctored Test Request Form during the first two weeks of class. Please contact the Testing Center at (480) 517-8560 or 1 (866) 517-8560 (Toll-free).
If you are testing at one of the Rio Salado Testing Centers, there is no appointment necessary to take your exam. Exams can be taken during normal hours of operation at any Rio Salado College testing site.
Your midterm and final exams have a 3 hour time limit. Please make sure you get to the testing site no later than 3 hours before closing.
You must complete the final exam by your course end date.
You may take your exam(s) before your course end date if and only if you have received all of your graded assignments.
Final Grade Options
Letter grade (A, B, C, D, F) - Awarded if the student completes all work, including the final exams.
Extension - Students may submit a withdrawal request on or prior to the "Deadline for Student to Withdraw with Guaranteed Grade of W" indicated in the college catalog.
Students should not contact their instructor to request a withdrawal. A student wishing to withdraw from a class within the stated timeline must do so by visiting my.maricopa.edu or by calling Student Enrollment Services at 480.517.8540 (1.800.729.1197 toll-free). In extreme circumstances, students do have the option of requesting a complete withdrawal from the college by providing Student Enrollment Services with appropriate documentation.
Credit/No Credit Option (P/Z) - This course may NOT be taken on a credit/no credit basis.
Scientific Calculator
Since our textbook makes numerous references to using a calculator in its "Calculator Tip" sections throughout the textbook, it is mandatory that students enrolled in MAT102 have their own scientific calculators.
A number of rather inexpensive scientific calculators are available for use in this course. All your calculator needs to be able to do is add, subtract, multiply, divide and compute square roots. Inexpensive scientific calculators that are manufactured by Texas Instruments (e.g., the TI-25X or 30 xa), Sharp (e.g., the EL-531 LB), and Casio (e.g., the fx-250HC) provide all of the functions that are noted above and several others. You will find these and similar scientific calculators at office supply stores and major discount houses ranging from $8 to $16, depending on their extra functions and whether or not batteries are required or they are powered by solar energy. A calculator that is capable of supporting you in this course can probably even be obtained at your local Dollar Store!
If your calculator has additional functions, then so much the better. These may be useful to you in this course, in follow-up mathematics courses that you may take, or even possibly in your work.
FYI: A more capable calculator's functions could include the following. Note, however, that all that yours needs to be able to perform are the functions that are shown in Bold type in the table below:
addition
[+]
subtraction
[-]
multiplication
[x]
division
[÷]
percent
[%]
square root
[ √ ]
square
[x2]
reciprocal
[1/x] or [x-1]
raising to a power
[yx]
sign change
[x/y]
value of Pi
π
store a value
[STO]
recall a value
[RCL]
trig functions
[SIN], [COS], [TAN]
the fraction key
[a b/c ]
powers of ten
[10 x ]
cube
[x3 ]
cube root
[?]
logarithmic functions
[log]
natural log function
[ln]
factorial
[n!]
Late or Missing Assignments
Assignments that have due dates are due on time according to the due dates. If you need to request an extension for an assignment, a request must be made to your instructor by voicemail at least one week prior to the due date.
Late points may be applied at the instructor's discretion.
Photocopy or Back-up Assignments Make sure that your submissions can be read by your instructor. If you write lightly in pencil it may be difficult to read.
The due date listed in your course calendar is the last date on which an assignment can be delivered to the Course Support Office.
Extra Credit
Extra credit is not available.
Notation for Homework Assignments
In each of this course's lessons, a number of recommended exercises and problems from the textbook are assigned for you to work. Shorthand nomenclature is used to designate which problems within a section of the textbook are assigned. For example, 'EOEOO' is used to designate "Every Other Every Other Odd" numbered problem in an assigned section of the textbook, e.g., 1, 9, 17, 25 ..., etc.
Assigned problems
Assigned problems are grouped into the following categories:
Recommended Exercises/Problems:
These are noted under the 'Assessment' section that is located near the end of each lesson description and consist of selected problems from the textbook. These exercises and problems are your recommended homework and are intended to prepare you for successfully completing the quizzes and the in-person exams. None of these are to be turned in!
Turn-In Assignments (Quizzes):
There are four such quizzes. These are provided in Appendix A of the Lesson Packet. They are to be completed and submitted after the completion of Lessons 3, 5, 8, and 10, respectively. When a quiz is due, remove the appropriate quiz from the packet, perform the calculations that are required, clearly showing the work that you perform so that your instructor can locate and review your work. Then, select and mark the correct answers on the answer sheet that is provided and, finally, submit the completed quiz as noted previously.
There are 10 course lessons. The lesson titles and corresponding sections of the textbook are listed below:
Copyrights and Acknowledgements
Submitting Assignments
All assignments are listed under the "Reading Assignment" box and in the "Assessing Your Learning" section.
The due date listed in your course calendar is the last date on which an assignment can be delivered to the Course Support Office, or postmarked.
The Drop Box is conveniently located along the curb in front of the Rio Salado building at 2323 W. 14th Street in Tempe.
Mailed Assignments
All mailed assignments must be properly addressed and mailed with adequate postage. Please remember all correspondence to Rio Salado College must have a return address, an addressee, and the correct postage. The U.S. Postal Service may refuse delivery if any of these three are missing. All items placed in the Rio drop box must have a return address and an addressee. Please keep a copy of all work turned in to your instructor. Assignments will not be accepted if postage is due. If you are unsure of the postage required, take the item to the post office and have it weighed.
Include the course section number and assignment identifier on the envelope below your name and return address. Envelopes that are labeled incorrectly can cause a delay in processing your work. Address your envelope as shown in this example:
The Course Support staff cannot answer questions about the receipt of specific mail-in assignments. Only your instructor can do so.
Note to students: Please submit only one assignment in each envelope. The special envelopes provided to you by Rio Salado are only for computer answer sheets. Please mail all other assignments in separate envelopes.
Note to students: The U.S. Post Office no longer offers Sunday or holiday mail posting, and pick-up does not automatically mean that your envelope will be posted the same day. To be safe, allow extra time: mail early.
Faxed Assignments
Assignments may be faxed to (480) 377-4728 for print and mixed media courses. Your name, your instructor's name, and the course name and section numbers must appear at the top of every page. When the Course Support Office receives assignments, they are sent to your instructor for evaluation. Once your instructor has graded your assignment, he or she will return it to you.
Protect your hard work. Again, clearly label every page of your assignment with your name, the course and section numbers, your instructors name, and the name of the assignment as it appears in the syllabus.
Course Completion Policy
A student who registers for a Print or Multimedia course is assigned a start date and an end date. It is the student's responsibility to note due dates for assignments and to keep up with the course work.
Students may request an extension because of illness or other extenuating circumstances, if they have been doing acceptable work. The instructor will define the requirements and timelines to complete the course.
Please Note: It is the prerogative of the instructor to decide whether or not to grant the request You can access all library services at Change of Address
Please notify Course Support at (480) 517-8243 1-800-729-1197 or by email at course.support@riosalado.edu. Please include your name, student number, phone number, and new address including city, state, and zip code.
Disability Statement
Contact Rio Salado College
The RSC Bookstore does not accept credit cards over the phone. If you want to purchase textbooks with a credit card, including a Citi Prepaid Visa Card, you must either order your books online ( or visit the store in person. The bookstore is located in the Conference Center at 2323 W. 14th St., Tempe, AZ 85281. (Major cross streets are Broadway and Priest).
Information about Rio Salado College computer labs located throughout the valley. The computer labs are open to registered students and have a variety of software available. Computer courses can also be taken from your home or office if you have the appropriate hardware and software. Some RSC locations have either Knowledge Commons or staff-supported and monitored Computer Labs.
Grants and scholarships are available to assist eligible students with college expenses. To be eligible for federal financial aid, students must meet application criteria and select a program of study. Applying for financial aid will take at least eight weeks, so begin early!
Available to answer questions about your course, help you contact your instructor or your faculty chair, provide Successful Start information, and to help you work through instructional issues that may arise during your course. | 677.169 | 1 |
Effectively write mathematical solutions in a clear and con cise manner. This will be assessed through class assignments and exams.
Effectively locate and use the information needed to prove theorems and establish mathematical results. This will be assessed through assignments and exams.
Demonstrate the ability to
integrate knowledge and ideas of complex differentiation and complex integration in a coherent and meaningful manner and use appropriate techniques for solving related problems and for establishing theoretical results. This will be assessed through assign ments and exams.
Demonstrate ability to think critically by proving mathematical conjectures and establishing theorems from complex analysis. This will be assessed through tests and a final exam.
In addition, students will be able to: Operate with complex numbers , u se the complex derivatives function , u se and operate analytic functions , d emonstrate knowledge of integration in the complex plane , u se the Cauchy integral theorem and Cauchy integral formula , m anipulate and use power series , understand residues and their u se in integration , d emonstrate the understanding of conformal mappings . | 677.169 | 1 |
Thursday, August 18, 2016
The first chapter of this book prepares the way for quite a full treatment of simple integral equations with one unknown number. In the first two chapters only positive numbers are involved, and the beginner is led to see the practical advantages of Algebra before he encounters the difficulties of negative numbers.
The definitions and explanations contained in these chapters should be carefully read at first; after the learner has become familiar with algebraic operations, special attention should be given to the principal definitions.
Where to begin?
First, let's ignore the dated and politically incorrect use of the male pronoun as this was published well before women had the vote in the US or Eleanor Roosevelt published "It's Up To The Women." Then, the text is four hundred seven pages (not counting a whopping six pages of front matter) published in a four and a half by seven inch format starting with definitions and simple equations and covering multivariate equations, imaginary numbers, quadratics and simultaneous equations, properties of series and the binomial theorem. On average the book is more than fifty percent exercises (you know, where the learner does the work of learning by actually solving problems) with Chapter XII comprising fourteen pages with less than a page and a half of text and the remaining space dedicated to 66 exercises. Today's student might wonder what happened to all the pictures, the visual pop-outs of definitions and "further study," and the multi-cultural-correct photos of children having fun doing something that must be related to math if for no other reason than it is in a math book.
Today's pedagogical theorists would dismiss this as antiquated "drill and kill." Obsolete. Ineffective. Out of step with today's students. Nothing could be further from the truth. This is actually "skill and thrill." By progressively working thru exercises that demonstrate and elucidate the principles explained in the text the student learns--masters--techniques and concepts necessary for a deep understanding of and proficiency in more advanced mathematics.
This one book can take a learner from colours and counting to pre-calc. Yet you'll not see this in any modern school today. If you have a child you wish to see as a tiger-cub you don't need to subscribe to modernity in mathematics. Instead you should go to a used book sale and buy a text no less than fifty years old. Have your child learn alongside the minds that put a man on the moon. | 677.169 | 1 |
$251Calculus teachers recognize Calculus as the leading resource among the reform projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The fifth edition uses all strands of the Rule of Four - graphical, numeric, symbolic/algebraic, and verbal/applied presentations - to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique. Readers will also gain access to WileyPLUS, an online tool that allows for extensive drills and practice. Calculus teachers will build on their understanding in the field and discover new ways to present concepts to their students. | 677.169 | 1 |
General Description
Classical Conversations endorses Saxon math as a complete K-12 Curriculum. No curriculum is ever perfect, but Saxon has the history and statistics to prove that it can take a home schooled student through Algebra II and even beyond without the guidance of an expert math teacher.
Math 5/4 is an introduction to basic, mid-level math concepts such as whole numbers, computation algorithms, geometry, patterns, and sequences.
What does the Math 5/4 Kit contain?
1) Student Book -Customized for homeschooling, 12 Investigations and an Illustrated Glossary, 120 Lessons. Each daily lesson includes warm-up activities, teaching of the new concept, and practice of new and previous material, two-color format, 627 pages.
2) Tests and Worksheets Booklet -Testing schedule and 23 cumulative tests, Worksheets for one student for one year, including Facts Practice Tests and Activity Sheets, Various recording forms for tracking student progress on assignments and tests. | 677.169 | 1 |
Calculator use is prohibited on any portion of The Mandelbrot Competition
or Mandelbrot Team Play, including wristwatch calculators, slide rules,
or any other computational device. Students need only bring an adequate
supply of pencils, pens, and erasers with them. Proctors will provide
blank paper and all contest materials. For more information see the official
rules for the Mandelbrot Competition
and rules for the Mandelbrot Team Play.
Without question the advent of calculators and mathematical software
has opened up many new and exciting avenues of exploration into the world
of mathematics. These tools rightly belong in the modern mathematics curriculum,
although implementing them effectively certainly requires as much thought
and effort as previous methods did. In adopting the above calculator policy,
Greater Testing Concepts is choosing to emphasize traditional mathematical
skills such as numerical operations, algebraic manipulations, and problem
solving techniques. Questions are generally designed to challenge students'
ability to reason or test their knowledge of a particular mathematical
topic, rather than requiring unwieldy computations by hand. | 677.169 | 1 |
7th Grade Algebra, Accelerated Algebra, and Math Lab
Student's username should be their school email address and id should be ACMS followed by their school id number (no spaces).
This year in Algebra 7, we will be covering the following topics: Real numbers and operations with real numbers; Ratios and Proportions; 2-D and 3-D spaces and figures; Linear Equations; and Statistics and Probability. We will be using Connected Mathematics 3 textbooks throughout the year.
Grades are based upon mastery of the material.
For Semester 1, here is the break-down of the grades:
Assignments/classwork: 5% of total grade. Assignments are graded on completion only. Generally a 2 means that is was completely done. 1 means only partially complete. 0 means that it was not handed in. Assignments are generally due the next class day. Late work is only accepted up to the assessment (quiz)., study guides and practice. Tests can only be revised for up to 70% using the pink correction sheet. Mastery work is required for students to earn a higher grade. | 677.169 | 1 |
7th Grade Algebra Reference Sheet
Be sure that you have an application to open
this file type before downloading and/or purchasing.
179 KB|1 page
Product Description
This reference sheet is used for my special education students who receive this accommodation for assignments, assessments, and homework. This reference sheet is useful for the concepts of:
- Multi-step equations
- Multi-step equations with fractions
- Consecutive integers
- Solving for a variable
- Unit price
- Word problems
- Area (polygons and circles)
- Surface Area (spheres and prisms)
- Distance, rate, and time formula
- Volume | 677.169 | 1 |
Quantitative Aptitude for Competitive Examinations is a comprehensive book for candidates preparing for various competitive examinations. The book comprises of chapters on number system, HCF and LCM, fractions and decimals, percentage, profit and loss, ratio and proportion, time, work and wages, time and distance, linear equations, geometry and trigonometry. In addition, the book consists of several solved and unsolved questions and model test papers for thorough revision and final practice. This book is essential for candidates appearing for exams like IBPS PO, Railway Recruitment examination, CTET, MAT and GRE.
About McGraw-Hill Education
McGraw-Hill Education is an Indian academic publishing company involved in releasing expertly authored books for students studying in India. The books present material which goes beyond traditional books and offer students an edge so that they can excel in their educational endeavours. The company has also released: NTSE Practice Papers Class-X and Study Package for NTSE Class VIII.
Read More
Specifications
Book Details
Publication Year
2014 June
Edition Type
Revised
Book Type
Entrance Exam Book
Table of Contents
1. Number System
2. Number Series
3. HCF and LCM of Numbers
4. Fractions and Decimals
5. Square Root and Cube Roots
6. Indices and Surds
7. Vedic Mathematics
8. Simplification and Approximation
9. Problems on Ages and Numbers
The book is brilliant as a reference text book and has formulae along with shortcuts and special results. There is a much needed chapter on vedic maths as well. Although there are not as many examples and practice sums, as a text book for the reference of formulae and in general it is perfect for Banking and SSC exams.
It is good but so many mistakes are there.Solutions aren't so good. But the good thing about this book is this book is contained so many chapters & they are well organized.Each & every chapters questions are divided into two parts--1.Regular problems & 2.challenging problems.There are so many solved examples, formulas & lots of shortcuts which helps at a good account.So, I'll suggest you to buy this book. | 677.169 | 1 |
Other Titles by Sy M. Blinder
This book reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly) which is needed to succeed in science courses. The focus is on math actually used in physics, chemistry and engineering, and the approach to mathematics begins with 12 examples of increasing complexity, designed to hone the student's ability to think in mathematical terms and to apply quantitative methods to scientific problems. By the author's design, no problems are included in the text, to allow the students to focus on their science course assignments.- Highly accessible presentation of fundamental mathematical techniques needed in science and engineering courses- Use of proven pedagogical techniques develolped during the author's 40 years of teaching experience- illustrations and links to reference material on World-Wide-Web- Coverage of fairly advanced topics, including vector and matrix algebra, partial differential equations, special functions and complex variables | 677.169 | 1 |
Synopses & Reviews
Publisher Comments
This newly revised book provides a strong foundation in the essential math processes that are employed by health occupations workers in all areas of health care. Exercises are presented in a word problem format with concrete examples of how the math process is used in different health care careers. Problems start with simple examples and progress to complex paradigms that induce readers to tackle difficult situations. In addition to basic applications with whole numbers, fractions, and decimals, information is also featured on common graphs, charts, and gauges that are likely to be encountered in the health care field. This edition includes a large portion of coverage that is devoted to problems involving medications, intravenous solutions, and other emulsions.
About the Author
Louise Simmers received a Bachelor of Science Degree in Nursing from the University of Maryland and a Masters degree in Education from Kent State University. She has worked as a public health nurse, a medical-surgical nurse, coronary care nurse and an instructor of Practical Nursing and Diversified Health Occupations. Louise has received the Vocational Educator of the Year award and the Diversified Health Occupations Instructor of the Year Award for the state of Ohio. | 677.169 | 1 |
Consolidate the fundamental math knowledge and challenge the complicated problems. By teaching in a logical, detailed and accurate way, we help to develop the students' ability to analyze and calculate, enabling them to solve Mathematical problems of medium difficulty or above and get ready for both ProvincialExams and higher grade learning. | 677.169 | 1 |
Primary functions our resources that can be used for revision with classes, small groups or individually.
Includes matching pairs memory games, worksheets, assessment ladders. Topics covered include quadratics, completing the square, sequences, rounding, surds, prime factors, simultaneous equations.
Over £50 Pounds worth of Resources for a crazy price, SPECIAL OFFER TODAY ONLY.
20 Resources.
Over 40 Lessons worth of resources.
Each lesson being 50 minutes worth.
Great for whole lesson or quick fire revision.
You are guaranteed to be happy with what you are buying. Great bargain !!!
Please look at each resource individually for details.
SPECIAL PRICE ONLY TODAY!! 95% off original prices. Buy whilst you can before the price goes up.This Bundle Contains 16 of the best Algebra Resources. Ideal for whole lessons or revision. Very well planned so ideal for either mode.
Solving Quadratic Equations (Factorising, Completing Square and Formula),
Great for whole lesson or quick fire revision as questions contain in depth answers.
Solving Simultaneous Equations (Elimination, Substitution, Linear and Quadratics) comes with Questions and Solutions. Bonus Hexagon Puzzle for Indices.
It also now includes Inequalities.
Great for Revision or Whole Lessons.
Read on for full details.
Quadratic Equations:
Written by an Outstanding practitioner from an Outstanding School.
This resource contains:
1) A 23 slide power point containing explanation, questions and in depth answers/solutions on: great for you and your students to check answers and use as a guide to support and differentiate.
There is 3 hours worth of lesson resources.
Simultaneous Equations:
Written by an Outstanding practitioner from an Outstanding School.
This resource contains:
1) A 17 slide power point containing explanation, questions and in depth answers/solutions on:2) 3 Exercises/questions on the below 3 points: The exercises are on the power point and on a word document for you to choose how to use them.3) Full in depth answers to the above 3 exercises, this is fantastic tool for support and extension. The answers are on a word document, great for you and your students to check answers and use as a guide to support and differentiate.
4) 3 Exam Questions with Mark Scheme.
There is minimum 2 hours worth of lesson resources.
Kindly review after purchasing. Thanks.
All Quadratics covered, written by an Outstanding practitioner from an Outstanding School.
Great for whole lesson or quick fire revision. As it is very detailed it can be used for revision lessons or whole lessons. Can be printed and used to provide revision material to students.
This resource contains:
1) A 23 slide power point containing explanation, questions and in depth answers/solutions on:
a) Drawing quadratic graphs.
b) Factorising and solving quadratic Equations.
c) Completing the square
d) Solving quadratic equation after completing the square.
e) Solving quadratic equationgreat for you and your students to check answers and use as a guide to support and differentiate.
There is 3 hours worth of lesson resources.
As it is in depth can be used for revision or whole lessons.
Kindly review after purchasing. Thanks.
A bundle of algebraic assignments from the two collections of Topic Homework assignments that I have published; this bundle contains a wealth of practice that includes understanding of coordinate geometry, forming and solving equations, factorisation and other aspects of algebraic manipulation, transformation of functions, solving and interpreting inequalities, solving simultaneous equations and quadratics. The papers each comprise 4 pages of increasing complexity, and each assignment comprises a total of 60 marks. Answer booklets are available. I have also included an example from my 'Pure' homework series (comprising 12 papers at both Foundation and Higher level and forming part of my 36 GCSE assignment pack), and a couple of additional free algebra resources that you may find useful. | 677.169 | 1 |
The history of algebra essay
Pearson Course Content. Pearson is the world leader in publishing, education and learning. Pearson Prentice Hall, along with our other respected imprints, provides. Varsity Tutors College Scholarship Contest. Enter this monthly essay contest for a chance to win a $1,000 scholarship. A Time-line for the History of Mathematics (Many of the early dates are approximates) This work is under constant revision, so come back later. Please report any. If you're working on NaNoWriMo this month, remember that short, simple words are often best, so if you have a thesaurus nearby, cross out "Thesaurus" and write "Other.
AP Exams are in May, but there are other dates to keep in mind. Jul 28, 2012 · A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high …
The history of algebra essay
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Find the perfect online Algebra tutor for you. Search for Algebra tutors online now or schedule a session for later. Welcome to the Oswego City School District Regents Exam Prep Center! The goal of this nonprofit site is to help high school students meet the New York. The Problem With History Classes. Single-perspective narratives do students a gross disservice. ClassZone Book Finder. Follow these simple steps to find online resources for your book.
AP Exams are in May, but there are other dates to keep in mind. Pearson Prentice Hall and our other respected imprints provide educational materials, technologies, assessments and related services across the secondary curriculum. The School of Athens represents all the greatest mathematicians, philosophers and scientists from classical antiquity gathered together sharing their ideas and.
Mar 26, 2016 · This essay is an original work by several authors. Please comment only on the talk page. Andrew Schlafly has several times stated that most - if not all. Varsity Tutors College Scholarship Contest. Enter this monthly essay contest for a chance to win a $1,000 scholarship. In the next few pages I will talk about a famous mathematician I decided to choose and write an essay about. I chose probably the most well known mathematician. If you have decided to let us perform your request "do my algebra, math or physics homework for me", let us do our job and enjoy your time. Affordable homework help. One page US History outlines of the topics below. These topic outlines, along with the US History outlines, unit notes, practice quizzes, vocabulary terms, court.
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Calculus
With the technical preliminaries out of the way, the two fundamental aspects of calculus may be examined:
a. Finding the instantaneous rate of change of a variable quantity.
b. Calculating areas, volumes, and related "totals" by adding together many small parts.
Although it is not immediately obvious, each process is the inverse of the other, and this is why the two are brought together under the same overall heading. The first process is called differentiation, the second integration. Following a discussion of each, the relationship between them will be examined.
Differentiation
Differentiation is about rates of change; for geometric curves and figures, this means determining the slope, or tangent, along a given direction. Being able to calculate rates of change also allows one to determine where maximum and minimum values occur—the title of Leibniz's first calculus publication was "Nova Methodus pro Maximis et Minimis, Itemque Tangentibus, qua nec Fractas nec Irrationales Quantitates Moratur, et Singulare pro illi Calculi Genus" (1684; "A New Method for Maxima and Minima, as Well as Tangents, Which Is Impeded Neither by Fractional nor by Irrational Quantities, and a Remarkable Type of Calculus for This"). Early applications for calculus included the study of gravity and planetary motion, fluid flow and ship design, and geometric curves and bridge engineering.
Average rates of change
A simple illustrative example of rates of change is the speed of a moving object. An object moving at a constant speed travels a distance that is proportional to the time. For example, a car moving at 50 kilometres per hour (km/hr) travels 50 km in 1 hr, 100 km in 2 hr, 150 km in 3 hr, and so on. A graph of the distance traveled against the time elapsed looks like a straight line whose slope, or gradient, yields the speed (seefigure).
Constant speeds pose no particular problems—in the example above, any time interval yields the same speed—but variable speeds are less straightforward. Nevertheless, a similar approach can be used to calculate the average speed of an object traveling at varying speeds: simply divide the total distance traveled by the time taken to traverse it. Thus, a car that takes 2 hr to travel 100 km moves with an average speed of 50 km/hr. However, it may not travel at the same speed for the entire period. It may slow down, stop, or even go backward for parts of the time, provided that during other parts it speeds up enough to cover the total distance of 100 km. Thus, average speeds—certainly if the average is taken over long intervals of time—do not tell us the actual speed at any given moment.
Instantaneous rates of change
In fact, it is not so easy to make sense of the concept of "speed at a given moment." How long is a moment? Zeno of Elea, a Greek philosopher who flourished about 450 bce, pointed out in one of his celebrated paradoxes that a moving arrow, at any instant of time, is fixed. During zero time it must travel zero distance. Another way to say this is that the instantaneous speed of a moving object cannot be calculated by dividing the distance that it travels in zero time by the time that it takes to travel that distance. This calculation leads to a fraction, 0/0, that does not possess any well-defined meaning. Normally, a fraction indicates a specific quotient. For example, 6/3 means 2, the number that, when multiplied by 3, yields 6. Similarly, 0/0 should mean the number that, when multiplied by 0, yields 0. But any number multiplied by 0 yields 0. In principle, then, 0/0 can take any value whatsoever, and in practice it is best considered meaningless.
Despite these arguments, there is a strong feeling that a moving object does move at a well-defined speed at each instant. Passengers know when a car is traveling faster or slower. So the meaninglessness of 0/0 is by no means the end of the story. Various mathematicians—both before and after Newton and Leibniz—argued that good approximations to the instantaneous speed can be obtained by finding the average speed over short intervals of time. If a car travels 5 metres in one second, then its average speed is 18 km/hr, and, unless the speed is varying wildly, its instantaneous speed must be close to 18 km/hr. A shorter time period can be used to refine the estimate further.
If a mathematical formula is available for the total distance traveled in a given time, then this idea can be turned into a formal calculation. For example, suppose that after time t seconds an object travels a distance t2 metres. (Similar formulas occur for bodies falling freely under gravity, so this is a reasonable choice.) To determine the object's instantaneous speed after precisely one second, its average speed over successively shorter time intervals will be calculated.
To start the calculation, observe that between time t = 1 and t = 1.1 the distance traveled is 1.12 − 1 = 0.21. The average speed over that interval is therefore 0.21/0.1 = 2.1 metres per second. For a finer approximation, the distance traveled between times t = 1 and t = 1.01 is 1.012 − 1 = 0.0201, and the average speed is 0.0201/0.01 = 2.01 metres per second.
The table displays successively finer approximations to the average speed after one second. It is clear that the smaller the interval of time, the closer the average speed is to 2 metres per second. The structure of the entire table points very compellingly to an exact value for the instantaneous speed—namely, 2 metres per second. Unfortunately, 2 cannot be found anywhere in the table. However far it is extended, every entry in the table looks like 2.000…0001, with perhaps a huge number of zeros, but always with a 1 on the end. Neither is there the option of choosing a time interval of 0, because then the distance traveled is also 0, which leads back to the meaningless fraction 0/0.
More generally, suppose an arbitrary time interval h starts from the time t = 1. Then the distance traveled is (1 + h)2 −12, which simplifies to give 2h + h2. The time taken is h. Therefore, the average speed over that time interval is (2h + h2)/h, which equals 2 + h, provided h ≠ 0. Obviously, as h approaches zero, this average speed approaches 2. Therefore, the definition of instantaneous speed is satisfied by the value 2 and only that value. What has not been done here—indeed, what the whole procedure deliberately avoids—is to set h equal to 0. As Bishop George Berkeley pointed out in the 18th century, to replace (2h + h2)/h by 2 + h, one must assume h is not zero, and that is what the rigorous definition of a limit achieves.
Even more generally, suppose the calculation starts from an arbitrary time t instead of a fixed t = 1. Then the distance traveled is (t + h)2 − t2, which simplifies to 2th + h2. The time taken is again h. Therefore, the average speed over that time interval is (2th + h2)/h, or 2t + h. Obviously, as h approaches zero, this average speed approaches the limit 2t.
This procedure is so important that it is given a special name: the derivative of t2 is 2t, and this result is obtained by differentiatingt2 with respect to t.
One can now go even further and replace t2 by any other function f of time. The distance traveled between times t and t + h is f(t + h) − f(t). The time taken is h. So the average speed is(f(t + h) − f(t))/h. (3) If (3) tends to a limit as h tends to zero, then that limit is defined as the derivative of f(t), written f′(t). Another common notation for the derivative isdf/dt, symbolizing small change in f divided by small change in t. A function is differentiable at t if its derivative exists for that specific value of t. It is differentiable if the derivative exists for all t for which f(t) is defined. A differentiable function must be continuous, but the converse is false. (Indeed, in 1872 Weierstrass produced the first example of a continuous function that cannot be differentiated at any point—a function now known as a nowhere differentiable function.)
Graphical interpretation
The above ideas have a graphical interpretation. Associated with any function f(t) is a graph in which the horizontal axis represents the variable t and the vertical axis represents the value of the function. Choose a value for t, calculate f(t), and draw the corresponding point; now repeat for all appropriate t. The result is a curve, the graph of f (see part A of the figure). For example, if f(t) = t2, then f(t) = 0 when t = 0, f(t) = 1 when t = 1, f(t) = 4 when t = 2, f(t) = 9 when t = 3, and so on, leading to the curve known as a parabola.
Expression (3), the numerical calculation of the average speed traveled between times t and t + h, also can be represented graphically. The two times can be plotted as two points on the curve, as shown in the figure, and a line can be drawn joining the two points. This line is called a secant, or chord, of the curve, and its slope corresponds to the change in distance with respect to time—that is, the average speed traveled between t and t + h. If, as h becomes smaller and smaller, this slope tends to a limiting value, then the direction of the chord stabilizes and the chord approximates more and more closely the tangent to the graph at t. Thus, the numerical notion of instantaneous rate of change of f(t) with respect to t corresponds to the geometric notion of the slope of the tangent to the graph.
The graphical interpretation suggests a number of useful problem-solving techniques. An example is finding the maximum value of a continuously differentiable function f(x) defined in some interval a ≤ x ≤ b. Either f attains its maximum at an endpoint, x = a or x = b, or it attains a maximum for some x inside this interval. In the latter case, as x approaches the maximum value, the curve defined by f rises more and more slowly, levels out, and then starts to fall. In other words, as x increases from a to b, the derivative f′(x) is positive while the function f(x) rises to its maximum value, f′(x) is zero at the value of x for which f(x) has a maximum value, and f′(x) is negative while f(x) declines from its maximum value. Simply stated, maximum values can be located by solving the equationf′(x) = 0.
It is necessary to check whether the resulting value genuinely is a maximum, however. First, all of the above reasoning applies at any local maximum—a place where f(x) is larger than all values of f(x) for nearby values of x. A function can have several local maxima, not all of which are overall ("global") maxima. Moreover, the derivative f′(x) vanishes at any (local) minimum value inside the interval. Indeed, it can sometimes vanish at places where the value is neither a maximum nor a minimum. An example is f(x) = x3 for −1 ≤ x ≤1. Here f′(x) = 3x2 so f′(0) = 0, but 0 is neither a maximum nor a minimum. For x < 0 the value of f(x) gets smaller than the value f(0) = 0, but for x > 0 it gets larger. Such a point is called a point of inflection. In general, solutions of f′(x) = 0 are called critical points of f.
Local maxima, local minima, and points of inflection are useful features of a function f that can aid in sketching its graph. Solving the equation f′(x) = 0 provides a list of critical values of x near which the shape of the curve is determined—concave up near a local minimum, concave down near a local maximum, and changing concavity at an inflection point. Moreover, between any two adjacent critical points of f, the values of f either increase steadily or decrease steadily—that is, the direction of the slope cannot change. By combining such information, the general qualitative shape of the graph of f can often be determined.
For example, suppose that f(x) = x3 − 3x + 2 is defined for −3 ≤ x ≤ 3. The critical points are solutions x of 0 = f′(x) = 3x2 − 3; that is, x = −1 and x = 1. When x < −1 the slope is positive; for −1 < x < 1 the slope is negative; for x > 1 the slope is positive again. Thus, x = −1 is a local maximum, and x = 1 is a local minimum. Therefore, the graph of f slopes upward from left to right as x runs from −3 to −1, then slopes downward as x runs from −1 to 1, and finally slopes upward again as x runs from 1 to 3. In addition, the value of f at some representative points within these intervals can be calculated to obtain the graph shown in the figure.
Higher-order derivatives
The process of differentiation can be applied several times in succession, leading in particular to the second derivative f″ of the function f, which is just the derivative of the derivative f′. The second derivative often has a useful physical interpretation. For example, if f(t) is the position of an object at time t, then f′(t) is its speed at time t and f″(t) is its acceleration at time t. Newton's laws of motion state that the acceleration of an object is proportional to the total force acting on it; so second derivatives are of central importance in dynamics. The second derivative is also useful for graphing functions, because it can quickly determine whether each critical point, c, corresponds to a local maximum (f″(c) < 0), a local minimum (f″(c) > 0), or a change in concavity (f″(c) = 0). Third derivatives occur in such concepts as curvature; and even fourth derivatives have their uses, notably in elasticity. The nth derivative of f(x) is denoted byf(n)(x) or dnf/dxn and has important applications in power series.
An infinite series of the forma0 + a1x + a2x2 +⋯, where x and the aj are real numbers, is called a power series. The aj are the coefficients. The series has a legitimate meaning, provided the series converges. In general, there exists a real number R such that the series converges when −R < x < R but diverges if x < −R or x > R. The range of values −R < x < R is called the interval of convergence. The behaviour of the series at x = R or x = −R is more delicate and depends on the coefficients. If R = 0 the series has little utility, but when R > 0 the sum of the infinite series defines a function f(x). Any function f that can be defined by a convergent power series is said to be real-analytic.
The coefficients of the power series of a real-analytic function can be expressed in terms of derivatives of that function. For values of x inside the interval of convergence, the series can be differentiated term by term; that is,f′(x) = a1 + 2a2x + 3a3x2 +⋯, and this series also converges. Repeating this procedure and then setting x = 0 in the resulting expressions shows that a0 = f(0), a1 = f′(0), a2 = f″(0)/2, a3 = f′′′(0)/6, and, in general, aj = f(j)(0)/j!. That is, within the interval of convergence of f,
This expression is the Maclaurin series of f, otherwise known as the Taylor series of f about 0. A slight generalization leads to the Taylor series of f about a general value x: All these series are meaningful only if they converge.
Integration
Like differentiation, integration has its roots in ancient problems—particularly, finding the area or volume of irregular objects and finding their centre of mass. Essentially, integration generalizes the process of summing up many small factors to determine some whole.
Also like differentiation, integration has a geometric interpretation. The (definite) integral of the function f, between initial and final values t = a and t = b, is the area of the region enclosed by the graph of f, the horizontal axis, and the vertical lines t = a and t = b, as shown in the figure. It is denoted by the symbol
∫abf(t)dt.Here the symbol ∫ is an elongated s, for sum, because the integral is the limit of a particular kind of sum. The values a and b are often, confusingly, called the limits of the integral; this terminology is unrelated to the limit concept introduced in the section Technical preliminaries.
The fundamental theorem of calculus
The process of calculating integrals is called integration. Integration is related to differentiation by the fundamental theorem of calculus, which states that (subject to the mild technical condition that the function be continuous) the derivative of the integral is the original function. In symbols, the fundamental theorem is stated asd/dt(
∫atf(u)du) = f(t).
The reasoning behind this theorem (seefigure) can be demonstrated in a logical progression, as follows: Let A(t) be the integral of f from a to t. Then the derivative of A(t) is very closely approximated by the quotient (A(t + h) − A(t))/h. This is 1/h times the area under the graph of f between t and t + h. For continuous functions f the value of f(t), for t in the interval, changes only slightly, so it must be very close to f(t). The area is therefore close to hf(t), so the quotient is close to hf(t)/h = f(t). Taking the limit as h tends to zero, the result follows.
Antidifferentiation
Strict mathematical logic aside, the importance of the fundamental theorem of calculus is that it allows one to find areas by antidifferentiation—the reverse process to differentiation. To integrate a given function f, just find a function F whose derivative F′ is equal to f. Then the value of the integral is the difference F(b) − F(a) between the value of F at the two limits. For example, since the derivative of t3 is 3t2, take the antiderivative of 3t2 to be t3. The area of the region enclosed by the graph of the function y = 3t2, the horizontal axis, and the vertical lines t = 1 and t = 2, for example, is given by the integral
∫12 3t2dt. By the fundamental theorem of calculus, this is the difference between the values of t3 when t = 2 and t = 1; that is, 23 − 13 = 7.
All the basic techniques of calculus for finding integrals work in this manner. They provide a repertoire of tricks for finding a function whose derivative is a given function. Most of what is taught in schools and colleges under the name calculus consists of rules for calculating the derivatives and integrals of functions of various forms and of particular applications of those techniques, such as finding the length of a curve or the surface area of a solid of revolution.
Table 2 lists the integrals of a small number of elementary functions. In the table, the symbol c denotes an arbitrary constant. (Because the derivative of a constant is zero, the antiderivative of a function is not unique: adding a constant makes no difference. When an integral is evaluated between two specific limits, this constant is subtracted from itself and thus cancels out. In the indefinite integral, another name for the antiderivative, the constant must be included.)
The Riemann integral
The task of analysis is to provide not a computational method but a sound logical foundation for limiting processes. Oddly enough, when it comes to formalizing the integral, the most difficult part is to define the term area. It is easy to define the area of a shape whose edges are straight; for example, the area of a rectangle is just the product of the lengths of two adjoining sides. But the area of a shape with curved edges can be more elusive. The answer, again, is to set up a suitable limiting process that approximates the desired area with simpler regions whose areas can be calculated.
The first successful general method for accomplishing this is usually credited to the German mathematician Bernhard Riemann in 1853, although it has many precursors (both in ancient Greece and in China). Given some function f(t), consider the area of the region enclosed by the graph of f, the horizontal axis, and the vertical lines t = a and t = b. Riemann's approach is to slice this region into thin vertical strips (see part A of the figure) and to approximate its area by sums of areas of rectangles, both from the inside and from the outside. If both of these sums converge to the same limiting value as the thickness of the slices tends to zero, then their common value is defined to be the Riemann integral of f between the limits a and b. If this limit exists for all a, b, then f is said to be (Riemann) integrable. Every continuous function is integrable. | 677.169 | 1 |
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68 ABILENE CHRISTIAN COLLEGE LATIN Latin 1.-Beginner's Latin. Vocabulary, declensions, and conjugations; the simpler rules for composition; and the derivation of words. Syntax of cases and the verbs is included with structure of the sentences in general, particular attention being given to conditional sentences, indirect discourse, and the subjunctive. Translation of easy selections into Latin continues throughout the year. Text, Smith's Latin Lessons. Latin 2.-Caesar. This course includes a rapid review of declensions and conjugations, a careful review of principles of syntax, structure of the sentence with stress on indirect discourse, and uses of the subjunctive. The reading is four books of Caesar's Gallic War. The historical facts are brought out and attention is given to the character and personality of the writer. Twenty lessons in prose composition. Text, D'Ooge and Eastman. Latin 3.-Cicero and Virgil. Orations of Cicero against Catiline and the Manilian Law are taken. Book I of the Aeneid is covered. The historical facts which called forth the orations will be noticed. Attention will be given to how the age is reflected in the writings. Twenty lessons in prose composition. Text, Bennett. MATHEMATICS Course 1.-This is a course of arithmetic and algebra combined. The work will be made as practical as possible. Text, Wentworth and Smith, Junior High School Mathematics, Book II. Course 2.-Algebra and arithmetic will be compared. Their similarity and differences will be 'emphasized. The fundamental operations are drilled on thoroughly, special rules in multiplication and division with corresponding cases in factoring and fractions. Factoring and the solution of equations will be stressed. Text, Wentworth and Smith, School Algebra, Book I. Course 3.-(1) A rapid review of Algebra and a close study of radicals and quadratics. Text, Wentworth and Smith, School Algebra, Book I. (2) The remainder of the year will be devoted to arithmetic. Com-- mercial and rapid methods will be stressed. Text, (to be selected). Course 4.-This course will be a close study of plane Geometry. A great deal of time will be devoted to original problems. Text, Wentworth and Smith. Course 5.-This course is intended for those students who have completed two or three books of plane geometry. Text, Wentworth and Smith, Plane and Solid Geometry. SCIENCE Course 1.-Snyder's General Science, completed. Course 2.-Descriptive Chemistry: (Brownlee, Fuller and others). The facts, laws, theories, and application of Chemistry are to be emphasized through exercises, problems and experiments. | 677.169 | 1 |
MAC 1140
Module 6 Nonlinear Functions and Equations II
Learning Objectives
Upon completing this module, you should be able to 1. 2. 3. 4. 5. 6. 7. 8. identify a rational function and state its domain. find and interpret vertical asymptotes. find and
MAC 1140
Module 1 Introduction to Function and Graphs
Learning Objectives
Upon completing this module, you should be able to 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. recognize common sets of numbers. understand scientific notation and use it in applications.
MAC 1140
Module 9 System of Equations and Inequalities I
Rev.S08
Learning Objectives
Upon completing this module, you should be able to 1. 2. 3. 4. 5. 6. 7. evaluate functions of two variables. apply the method of substitution. apply graphical and n
PRECALCULUS ALGEBRA Advice
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Matrix Operations - PowerPoint PPT Presentation
Matrix Operations. Chapter 4: Matrices Lesson 1: using Matrices to Represent Data. Objectives: Represent mathematical and real-world data in a matrix. Find sums and differences of matrices and the scalar product of a number and a matrix Matrix Operations' - pep | 677.169 | 1 |
Math Problems and Solutions Guide
Practice for math comprehension
Provides extra math practice for students in all levels, from Foundations to Challenge IV. Great for summer review!
Accessibility
Mature reading level but clearly written.
Preparation
Recommended to accompany Understanding Mathematics: From Counting to Calculus.
Ease of use
Lessons are found in Understanding Mathematics. Students will need to flip between the two books to review concepts while they work the problems in the first half of the book. Solutions are included in the second half of the book.
Author
David Scheinker & Keith Kressin
Page Count
305
Format
Softcover
Publication Date
2009
General Description
Written to complement the explanations provided in Understanding Mathematics: From Counting to Calculus, the books may be used as a supplement or independent core curriculum. This textbook provides problem sets that are aligned with the sections explained in From Counting to Calculus; over 10,000 problems and solutions provided. | 677.169 | 1 |
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Scientific Calulator is a powerful, programmable, scientific calculator.Some of its features include: Supports variables, constants, and custom functions; Save scripts online so you can access them anywhere or in a local library; Complex numbers, arbitrary precision integers, and exact fractions; Algebraic pretty-printed display; Full functional programming language; Supports matrix and vector operations; Calculation history lets you refer to previous results.
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Solving Logarithmic Equations learning guide
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This 16-problem, segmented learning guide supports a lesson helping students learn the various methods of solving logarithmic equations. Led by the instructor, students will connect logarithmic solving to exponential solving, including the use of logarithmic properties. The guide also provides scaffolding for problems involving quadratic and rational equations so that students can focus on the new material separate from the review. The most complex problem requires distributing a log and then factoring a variable. | 677.169 | 1 |
Download and read online Introduction to Technical Mathematics in PDF and EPUB #This text is designed for a first course in technical mathematics; problem solving sections are designed to help students apply basic mathematical principles to a multitude of situations; each problem-solving tactic is introduced with a sample problem & step-by-step solution.
Download and read online Introduction to Technical Mathematics in PDF and EPUB Designed for a first course in technical mathematics, this comprehensive, easy-to-read text is ideal for students with minimal mathematics training who wish to prepare for further study in technical areas. The newly revised Third Edition builds on the success of the first two editions, featuring a new chapter on using the quadratic formula to solve quadratic equations. Moreover, extra problem sets that feature technical applications have been added to several chapters. Introduction to Technical Mathematics, 3/E has a versatile format that can be used in many instructional settings. Its user-friendly approach includes problem-solving chapters designed to help students apply basic mathematical principles to a multitude of situations. Students also will benefit from the wealth of applications contained in the worked-out examples and problem sets.
Download and read online Basic Mathematics for Technical Programs in PDF and EPUB An easy-to-use mathematics book designed along a practical, hands-on format that provides a unified approach to problem-solving by linking topics and their corresponding computational techniques. Mathematics for Technical Programs devotes special attention to mental activities involving elementary computations, fraction-decimal-percent conversions, and estimations to aid reader in achieving mathematical literacy. It assumes the use of scientific calculators to enable the reader to focus on concepts and problem-solving skills rather than time-consuming computations. The book also provides a unified approach to problem-solving not found with traditional arithmetic methods. A valuable book for any reader who wishes to improve his "mathematical literacy."
Download and read online Introductory Technical Mathematics in PDF and EPUB With an emphasis on real-world math applications, the Sixth Edition of INTRODUCTORY TECHNICAL MATHEMATICS provides readers with current and practical technical math applications for today's sophisticated trade and technical work environments. Straightforward and easy to understand, this hands-on book helps readers build a solid understanding of math concepts through step-by-step examples and problems drawn from various occupations. Updated to include the most current information in the field, the sixth edition includes expanded coverage of topics such as estimation usage, spreadsheets, and energy-efficient electrical applications. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Download and read online Fundamentals of Technical Mathematics in PDF and EPUB Fundamentals of Technical Mathematics introduces key, applied mathematics for engineering technologists and technicians. Through a simple, engaging approach, the book reviews basic mathematics, including whole numbers, fractions, mixed numbers, decimals, percentages, ratios, and proportions. The book covers conversions to different units of measure (standard and/or metric) and other topics as required by specific businesses and industries, providing a go-to resource on the topic. Building on these foundations, it then explores concepts in arithmetic, introductory algebra, equations, inequalities, and modeling, graphs and functions, measurement, geometry, and trigonometry, all the while supporting these concepts with practical applications in a variety of technical and career vocations, including automotive, allied health, welding, plumbing, machine tool, carpentry, auto mechanics, HVAC, and many other fields. In addition, the book provides practical examples from a vast number of technologies. Presents foundational math concepts in a concise, engaging way Covers conversions to different units of measure (standard and/or metric) and other topics as required by specific businesses and industries Reviews basic mathematics, including whole numbers, fractions, mixed numbers, decimals, percentages, ratios, and proportions Connects concepts with recent applications in technology, engineering, manufacturing, and science Includes many practice and review problems
Download and read online Introduction to Insurance Mathematics in PDF and EPUB This second edition expands the first chapters, which focus on the approach to risk management issues discussed in the first edition, to offer readers a better understanding of the risk management process and the relevant quantitative phases. In the following chapters the book examines life insurance, non-life insurance and pension plans, presenting the technical and financial aspects of risk transfers and insurance without the use of complex mathematical tools. The book is written in a comprehensible style making it easily accessible to advanced undergraduate and graduate students in Economics, Business and Finance, as well as undergraduate students in Mathematics who intend starting on an actuarial qualification path. With the systematic inclusion of practical topics, professionals will find this text useful when working in insurance and pension related areas, where investments, risk analysis and financial reporting play a major role.
Download and read online Basic Technical Mathematics in PDF and EPUB For courses in technical and pre-engineering technical programs or other programs for which coverage of basic mathematics is required. The best-seller in technical mathematics gets an "Oh, wow!" update The 11th Edition of Basic Technical Mathematics is a bold revision of this classic best-seller. The text now sports an engaging full-color design, and new co-author Rich Evans has introduced a wealth of relevant applications and improvements, many based on user feedback. The text is supported by an all-new online graphing calculator manual, accessible at point-of-use via short URLs. The MyLab™ Math course features hundreds of new algorithmic exercises, tutorial videos, and PowerPoint slides. The text continues to feature a vast number of applications from technical and pre-engineering fields—including computer design, electronics, solar energy, lasers fiber optics, and the environment—and aims to develop students' understanding of mathematical methods without simply providing a collection of formulas. The authors start the text by establishing a solid background in algebra and trigonometry, recognizing the importance of these topics for success in solving applied problems. Also available with MyLab Math My MyLab Math course features hundreds of new algorithmic exercises, tutorial videos, and PowerPoint slides. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. If you would like to purchase both the physical text and MyLab Math, search for: 0134465407 / 9780134465401 Basic Technical Mathematics plus MyLab Math with Pearson eText -- Access Card Package Package consists of: 0134437705 / 9780134437705 Basic Technical Mathematics 0321431308 / 9780321431301 MyLab Math -- Glue-in Access Card 0321654064 / 9780321654069 MyLab Math Inside Star Sticker MyLab Math should only be purchased when required by an instructor. | 677.169 | 1 |
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This text introduces the vast and fascinating area of computational number theory. It treats algorithms for common number-theoretic problems in an elementary fashion, eliminating the need for an extensive prerequisite of algebra and analysis. The GP/PARI calculator is used throughout to demonstrate the working of arithmetic algorithms. The book contains detailed examples illustrating almost every algorithmic concept discussed. It also includes practical applications of arithmetic algorithms in public-key cryptography. Every chapter ends with many exercises and partial solutions are given in the appendix. | 677.169 | 1 |
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Overview
geometry; measurement; data analysis; probability; problem solving; and the following algebra 1 topics: operations with real numbers, linear equations and inequalities, relations and functions, graphing linear equations and inequalities, pairs of linear equations and inequalities, polynomials, algebraic fractions, algebraic proportions, and quadratic, cubic, and radical equations. Students will also find a helpful glossary of math terms.
Related Subjects
Meet the Author
Donna Osborn has taught math for 34 years. She has won the Presidential Award for Excellence in the Teaching of Mathematics for Indiana, the Albert Einstein Distinguished Educator Fellowship, the Purdue University Distinguished Alumna Award, and the Christa McAuliffe Award for Indiana. | 677.169 | 1 |
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AP Physics 2
Section
AP Physics 2
AP Physics 2: Algebra-Based is a second-year
physics course designed for high school students in grade 12 who
have completed AP Physics 1. The course covers topics and
concepts typically included in the second semester of an
algebra-based, introductory college-level physics course. Topics
include fluid statics & fluid dynamics, thermal physics &
thermodynamics, electricity & magnetism (including RC circuits
and electromagnetic induction), light & optics, and modern
(quantum, atomic & nuclear) physics. The course focuses on
high-level understanding of concepts, experimental design and
critical thinking, and prepares students for the AP Physics 2 exam
in May.
Resources
Mathematics
- Toggle
Mathematics
Notes pp. 43-78
The purpose of this chapter is to familiarize you with mathematical concepts and skills that will be needed in physics.
Standard Assumptions in Physics discusses what you can and cannot assume to be true in order to be able to solve the problems you will encounter in this class.
Assigning & Substituting Variables discusses how to determine which quantity and which variable apply to a number given in a problem based on the units, and how to choose which formula applies to a problem.
The Metric System and Scientific Notation briefly review skills that you are expected to remember from your middle school math and science classes.
Trigonometry, Vectors, Vectors vs. Scalars in Physics, and Vector Multiplication discuss important mathematical concepts that are widely used in physics, but may be unfamiliar to you.
Depending on your math background, some of the topics, such as trigonometry and vectors, may be unfamiliar. These topics will be taught, but in a cursory manner.
Skills learned & applied in this chapter:
Estimating uncertainty in measurements
Propagating uncertainty through calculations
Identifying quantities in word problems and assigning them to variables
Choosing a formula based on the quantities represented in a problem
Using trigonometry to calculate the lengths of sides and angles of triangles
Representing quantities as vectors
Adding and subtracting vectors
Multiplying vectors using the dot product and cross product
Standards
Massachusetts Frameworks (2006):
No MA curriculum frameworks are specifically addressed in this chapter. However, this chapter addresses the following mathematical understandings explicitly listed in the MA Curriculum Frameworks as prerequisites for this course:
Construct and use tables and graphs to interpret data sets.
Solve simple algebraic expressions.
Perform basic statistical procedures to analyze the center and spread of data.
In addition, this chapter addresses the following mathematical understandings. The MA frameworks state that "the following skills are not detailed in the Mathematics Framework, but are necessary for a solid understanding in this course."
Fluid Motion & Bernoulli's Law describes the effects of fluid motion on pressure.
This chapter focuses on real-world applications of fluids and pressure, including more demonstrations than most other topics. One of the challenges in this chapter is relating the equations to the behaviors seen in the demonstrations.
Thermal Expansion describes the calculation of the change in size of an object caused by heating or cooling.
New challenges specific to this chapter include looking up and working with constants that are different for different substances.
Skills learned & applied in this chapter:
Working with material-specific constants from a table.
Working with more than one instance of the same quantity in a problem.
Combining equations and graphs.
Standards
Next Generation Science Standards (NGSS):
HS-PS2-6. Communicate scientific and technical information about why the molecular-level structure is important in the functioning of designed materials.4. Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).
Massachusetts Curriculum Frameworks (2006):
3.1 Explain how heat energy is transferred by convection, conduction, and radiation.
3.2 Explain how heat energy will move from a higher temperature to a lower temperature until equilibrium is reached.
3.3 Describe the relationship between average molecular kinetic energy and temperature. Recognize that energy is absorbed when a substance changes from a solid to a liquid to a gas, and that energy is released when a substance changes from a gas to a liquid to a solid. Explain the relationships among evaporation, condensation, cooling, and warming.
3.4 Explain the relationships among temperature changes in a substance, the amount of heat transferred, the amount (mass) of the substance, and the specific heat of the substance.
Electrical Components, Series Circuits, Parallel Circuits, Mixed Series & Parallel Circuits, and Measuring Voltage, Current & Resistance describe the behavior of electrical components in a circuit and how to calculate quantities relating to the individual components and the entire circuit, based on the way the components are arranged.
Magnetism describes properties of magnets and what causes objects to be magnetic. Electricity & Magnetism describes how electricity and magnetism affect each other.
One of the new challenges encountered in this chapter is interpreting and simplifying circuit diagrams, in which different equations may apply to different parts of the circuit.
Skills learned & applied in this chapter:
Working with material-specific constants from a table.
Identifying electric circuit components.
Simplifying circuit diagrams.
Standards
Next Generation Science Standards (NGSS):-PS2-6. Communicate scientific and technical information about why the molecular-level structure is important in the functioning of designed materials-PS3-5. Develop and use a model of two objects interacting through electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction.
Massachusetts Curriculum Frameworks (2006):
5.1 Recognize that an electric charge tends to be static on insulators and can move on and in conductors. Explain that energy can produce a separation of charges.
5.2 Develop qualitative and quantitative understandings of current, voltage, resistance, and the connections among them (Ohm's law).
5.3 Analyze simple arrangements of electrical components in both series and parallel circuits. Recognize symbols and understand the functions of common circuit elements (battery, connecting wire, switch, fuse, resistance) in a schematic diagram.
5.4 Describe conceptually the attractive or repulsive forces between objects relative to their charges and the distance between them (Coulomb's law).
5.5 Explain how electric current is a flow of charge caused by a potential difference (voltage), and how power is equal to current multiplied by voltage.
5.6 Recognize that moving electric charges produce magnetic forces and moving magnets produce electric forces. Recognize that the interplay of electric and magnetic forces is the basis for electric motors, generators, and other technologies.
Topics from this chapter assessed on the SAT Physics Subject Test:
Electric Fields, Forces, and Potentials, such as Coulomb's law, induced charge, field and potential of groups of point charges, and charged particles in electric fields
Capacitance, such as parallel-plate capacitors and time-varying behavior in charging/ discharging
Circuit Elements and DC Circuits, such as resistors, light bulbs, series and parallel networks, Ohm's law, and Joule's law
Reflection, Refraction, Polarization, and Diffraction discuss specific properties of light, and the equations that relate these properties.
Mirrors and Lenses discuss what happens when the direction of a ray of light is changed by a mirror or a lens.
One of the new skills learned in this chapter is visualizing and drawing representations of how light is affected as it is reflected off a mirror or refracted by a lens. This can be challenging because the behavior of the light rays and the size and location of the image changes depending on the location of the object relative to the focal point of the mirror or lens. Another challenge is in drawing precise, to-scale ray tracing drawings such that you can use the drawings to accurately determine properties of the image, or of the mirror or lens.
Skills learned & applied in this chapter:
Drawing images from mirrors and through lenses.
Standards
Next Generation Science Standards (NGSS):
HS-PS4-2. Evaluate questions about the advantages of using a digital transmission and storage of information
Massachusetts Curriculum Frameworks (2006):
4.2 Distinguish between mechanical and electromagnetic waves.
6.1 Recognize that electromagnetic waves are transverse waves and travel at the speed of light through a vacuum.
6.2 Describe the electromagnetic spectrum in terms of frequency and wavelength, and identify the locations of radio waves, microwaves, infrared radiation, visible light (red, orange, yellow, green, blue, indigo, and violet), ultraviolet rays, x-rays, and gamma rays on the spectrum.
Topics from this chapter assessed on the SAT Physics Subject Test:
Reflection and Refraction, such as Snell's law and changes in wavelength and speed.
Ray Optics, such as image formation using pinholes, mirrors, and lenses.
Practice Problems & Tests
Modern Physics
- Toggle
Modern Physics
Notes pp. 317-362
This chapter discusses the particles that atoms and other matter are made of, how those particles interact, and the process by which radioactive decay can change the composition of a substance from one element into another.
The Bohr Model of the Hydrogen Atom describes the first attempts to use quantum mechanics to describe the behavior of the electrons in an atom. The Quantum Mechanical Model of the Atom describes the evolution of atomic theory from the Bohr model to the present day.
Fundamental Forces describes the four natural forces that affect everything in the universe. The strong nuclear force and the weak nuclear force are particularly relevant to this chapter.
The Standard Model and Particle Interactions describe properties of and interactions between the particles that all matter is made of.
One of the challenging aspects of this chapter is that it describes process that happen on a scale that is much too small to observe directly. Another challenge is the fact that the Standard Model continues to evolve. Many of the connections between concepts that make other topics easier to understand have yet to be made in the realm of atomic & particle physics.
Standards
Next Generation Science Standards (NGSS):
HS-PS1-8: Develop models to illustrate the changes in the composition of the nucleus of the atom and the energy released during the processes of fission, fusion, and radioactive decayMassachusetts Curriculum Frameworks (2006):
No MA physics standards are addressed in this chapter. However, this chapter addresses the following standards from the chemistry frameworks:
2.5 Identify the three main types of radioactive decay (alpha, beta, and gamma) and compare their properties (composition, mass, charge, and penetrating power).
2.6 Describe the process of radioactive decay by using nuclear equations, and explain the concept of half-life for an isotope (for example, C-14 is a powerful tool in determining the age of objects).
2.7 Compare and contrast nuclear fission and nuclear fusion.
Topics from this chapter assessed on the SAT Physics Subject Test:
Quantum Phenomena, such as photons and the photoelectric effect.
Atomic Physics, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra.
Nuclear and Particle Physics, such as radioactivity, nuclear reactions, and fundamental particles.
Practice Problems & Tests
Special Relativity
- Toggle
Special Relativity
Notes pp. 199-221
This chapter describes changes to the properties of objects when they are moving at speeds near the speed of light.
Relative Motion and Relative Velocities describes relationships between objects that are moving with different velocities.
The Speed of Light describes some familiar assumptions we have about our universe that do not apply at speeds near the speed of light.
Length Contraction & Time Dilation and the Energy-Momentum Relation describe calculations involving changes in the length, time, mass, and momentum of objects as their speeds approach the speed of light.
New challenges in this chapter involve determining and understanding the changing relationships between two objects, both of which are moving in different directions and at different speeds.
Standards
Next Generation Science Standards (NGSS):
No NGSS standards are addressed in this chapter.
Massachusetts Curriculum Frameworks (2006):
No MA curriculum standards are addressed in this chapter.
Topics from this chapter assessed on the SAT Physics Subject Test:
Relativity, such as time dilation, length contraction, and mass-energy equivalence. | 677.169 | 1 |
Omtale
Calculus Workbook for Dummies Second Edition
Your light-hearted, practical approach to conquering calculus Does the thought of calculus give you a coronary? You aren't alone. Thankfully, this new edition of Calculus Workbook For Dummies makes it infinitely easier. Focusing "beyond the classroom," it contains calculus exercises you can work on that will help to increase your confidence and improve your skills. This hands-on, friendly guide gives you hundreds of practice problems on limits, vectors, continuity, differentiation, integration, curve-sketching, conic sections, natural logarithms, and infinite series. Calculus is a gateway and potential stumbling block for students interested in pursuing a career in math, science, engineering, finance, and technology. Calculus students, along with math students in nearly all disciplines, benefit greatly from opportunities to practice different types of problems in the classroom and out. Calculus Workbook For Dummies takes you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English, rather than math-speak.
Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be. * Master differentiation and integration * Use the calculus microscope: limits * Analyze common functions * Score your highest in calculus Complete with tips for problem-solving and traps to avoid, Calculus Workbook For Dummies is your sure-fire weapon for conquering calculus! | 677.169 | 1 |
2 TEACHERS' GUIDE COURSE DESCRIPTION: The Anywhere Learning System (ALS) Math Foundations IIB full semester course is the second semester of Math Foundations II. It is designed to guide students through foundational math skills typically found in sixth to eighth grade instruction. It is appropriate for use as remediation at the high school level, as a bridge to high school, or as middle school curriculum. Carefully paced, guided instruction is accompanied by interactive practice. When used in combination with Math Foundations I (addressing skills typically found in grade 3 to 5), the course effectively remediates the computational skills and conceptual understanding needed to undertake high school-level math courses with confidence. COURSE FEATURES: Math Foundations IIB is presented as a full semester course. All fifty-two lessons contain a study guide, a practice test, and a mastery test. A math unit review assignment is presented at the end of each unit. Answer keys are available to assist teachers in grading the unit assignments. This course is split into seven units: Operations and Real Numbers; Ratio, Proportion, and Probability; Concepts in Algebra; Geometric Concepts; Expressions and Equations; Elements of Algebra; and Geometry. All lessons contain introduction and reinforcement of mathematical skills and concepts. 2
3 TEACHERS' GUIDE COURSE OBJECTIVES: The content in this course is based on Common Core Standards. Students learn about absolute value and how to add, subtract, multiply, and divide integers. Students will understand numbers, ways of representing numbers, relationships among numbers, and number systems. Students review simplifying expression and solving multistep equations and inequalities. They also review plane and space figures and learn formulas for the area of plane figures and volume of space figures. Students use number lines to identify, locate, and compare integers, as well as determine absolute value. Students learn rules for solving equations by adding/subtracting/multiplying/dividing integers with the same or different sign. Students review the definitions of point, line, ray, line segment, and angle. Students find area of polygons and surface area of pyramids, prisms, and cones. COURSE CONTENT Course Name Number of Lessons Length of Course in Semesters Grade Levels Unit Assignments Math Foundations IIB
8 Unit 6: Elements of Algebra 6.01 Integers Integers and their opposites; using number lines to identify, locate, and compare integers; absolute value of integers; using integers in real life situations 6.02 Equations with Integers by Adding and Subtracting Rules for solving equations by adding and subtracting integers with the same sign or different signs; examples of strategies to solve equations 6.03 Equations with Integers by Multiplying and Dividing Rules for solving equations by multiplying and dividing integers with the same or different signs; examples of strategies to solve equations 6.04 Inequalities Definition and examples of inequalities; signs that indicate inequality 6.05 Solving Inequalities with Inverse Operations Solving inequalities by reversing signs Solving Inequalities with Multiplication and Division Factors and Exponents Other strategies for solving inequalities; checking for reasonability Identifying laws of exponents; writing numbers in exponential form; writing exponents and variables; rules for determining exponents when adding, subtracting, multiplying, and dividing 6.08 Rational Numbers Identifying parts of fractions; relating fractions to rational numbers; locating rational numbers on the number line; comparing rational numbers; writing rational numbers in decimal form; algebraic fractions 8
New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and The lessons that address each Performance Indicator are listed, and those in which the Performance Indicator
A Correlation of Prentice Hall Mathematics Courses 1-3 Common Core Edition 2013 to the Topics & Lessons of Pearson A Correlation of Courses 1, 2 and 3, Common Core Introduction This document demonstrates
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Grade 5 Math Content 1 Number and Operations: Whole Numbers Multiplication and Division In Grade 5, students consolidate their understanding of the computational strategies they use for multiplication.
Content Area: Mathematics Grade Level Expectations: High School Standard: Number Sense, Properties, and Operations Understand the structure and properties of our number system. At their most basic level | 677.169 | 1 |
Challenge
Professor John Tucker sought a solution to help students better engage with course materials and subject matter, especially mature students who had been away from academia for an extended period of time.
Solution
Maple T.A. was adopted for its advanced and instantaneous evaluation capabilities, to allow students to improve and refresh their math skills to prepare for government-level engineering exams. Maple T.A. was eventually extended to all of the applied math courses at the institution.
Result
Maple T.A. has helped foster a more interactive and cooperative learning environment at the school. With Maple T.A.'s unique algorithmic question generation, students receive different questions and thus work together to understand the underlying concepts, allowing them to solve their own unique set of problems.
In a world of innovative ideas and expanding technology, instructors are continually searching for new methods to more effectively engage their students and communicate complex concepts in a way that facilitates a deeper understanding of materials being taught. At the Fisheries and Marine Institute at Memorial University of Newfoundland, Maple T.A. was adopted to facilitate greater engagement between students and course subject matter through its instantaneous, algorithmic approach to administering tests in mathematics.
Maple T.A. is a testing and assessment software system designed specifically for courses involving mathematics, by providing an advanced evaluation environment that benefits both students and instructors. When first implemented at the Institute, Maple T.A. was used as a system to allow more mature students who had been away from academia for an extended period of time to brush up on their math skills in preparation for government-level engineering certification exams. Instructor John Tucker said these unique learners wanted many opportunities to practice the concepts they were learning. Maple T.A. was ideally suited for this because of its algorithmic question generation feature that lets students practice with different variations of the same question, giving them feedback each time so they learn better before moving on to the next question.
Each Maple T.A. assessment is unique and able to utilize both questions created by the instructors themselves, and those available through the Maple T.A. Cloud, which stores user-developed material for shared use. Whether the instructors choose to have each assessment available for retake or set to no time limits on submitting answers, Maple T.A. offers analysis of results almost instantaneously after every submission. Students can assess where they went wrong, get feedback on errors, and thus develop a stronger understanding of concepts and subject matter. "Maple T.A. is a superior tool for that," said Tucker. "This is how our students want to prepare themselves for the exam."
Based on the success of the initial program, Maple T.A. was extended to the Institute's applied math courses. Tucker said students were initially resistant to the move to digital testing from paper-based assessment, but eventually came to value the software. "Once they got through the initial learning period, students came to appreciate the program because it actually helped them understand the material better," Tucker said.
Maple T.A. provides ample opportunities for students to develop their skills before taking tests in class. Instructors rely heavily on Maple T.A. for assignments and to provide students with practice questions to gain a better understanding of the course material. Tucker develops his own questions to supplement his teaching, something to which his students respond positively. "They like going through questions just before a test and Maple T.A. provides them with similar questions to those at the end of each chapter in a textbook," he said. "The questions are authored by me. The solutions are tailored to look exactly like the solutions that I do on the chalkboard or with PowerPoint, so it all makes sense to them. It's a complete circle and my students really appreciate that. We see tangibly better results in marks for the courses where Maple T.A. has been implemented."
Using online testing and assessment technology has also challenged Tucker to improve as an instructor. Teaching engineering, Tucker said he often focused on the process his students used, rather than the final answer or outcome. Now, he uses Maple T.A. to emphasize that the result is often as important as the process. "For many years, we have rewarded students based on the process and not necessarily for getting the answer," he said. "I want to teach my students that the right answer matters and Maple T.A. is a great tool for this as it provides the option of using 'mission critical' type questions, where students have to get the right answer the first time, or adaptive style questions that teach and reinforce the process of getting to the right answer."
Tucker has been using Maple T.A. and other Maplesoft products for several years and expressed excitement about the fact that he is still discovering new features that allow him to incorporate and rework some of his existing content, and author new algorithms. He appreciates Maple T.A.'s "sharp" look and presentation of questions, as well as its easy-to-use interfaces that facilitate a user-friendly environment. He praised Maple T.A. for the ability it gives professors to create and customize questions and to tailor the material to the concepts being taught in class. "The power of Maple T.A.'s math engine is unparalleled," he said. "It opens the door to a more sophisticated online delivery in which my team and I can code our problems, create algorithmically generated questions, and customize the fully-worked out solution to look exactly the way it should from a student perspective."
Of all the benefits Maple T.A. offers, the greatest is the learning environment it fosters within the classroom, Tucker said. Maple T.A. allows him to encourage his students to work together. "I'm getting students to teach each other with Maple T.A.," Tucker said. "They're working together. You don't have one student just getting someone else's work and copying it; you're having them sit down with one another and actually work through the solutions, and that is worth its weight in gold."
Though the school currently has a small nucleus of users, Tucker sees greater potential and is pushing for Maple T.A. to be adopted for greater usage at the Institute. "We have adopted a policy where we're sharing our material freely with our peers and my hope is to see the use of Maple T.A. spread to all the knowledge-based instruction that goes on at the institution," Tucker concluded | 677.169 | 1 |
Honors Precalculus with Trigonometry Supplementary Notes
Chapter 5: The Trigonometric Functions
The Unit Circle
Preface:
This document introduces the unit circle as a tool for deeper understanding of the
trigonometric functions. Throughout the document th
The Area of a Triangle in Terms of Trigonometric Functions
Finding the area of a triangle can be tricky when we are not given the length of the height. As long as we
know any two sides of the triangle and the included angle (SAS) we can modify the traditi
UNDERSTANDING A STOCK TABLE
Column
Title
Description
Hint
52-WK
HI LO
52-Week
High and
Low
This column reports the highest and
lowest price of the stock in the most
recent 52-week period.
Study the difference represented by these two numbers.
If the diffe
Understanding Sequence Problems
A sequence is an ordered collection of numbers.
An inductive sequence uses a pattern based upon previous terms.
The Fibonacci sequence: a1 = 1, a 2 = 1, a n = a n 1 + a n 2 .
A sequence is just a collection of numbers
liste | 677.169 | 1 |
Algebra II, O. Mayes
Welcome to my Algebra 2 page. This year we will be using Eureka Math, and continuing skills that students learned in Algebra 1.
For this Class, it is required that you have a TI 83/84 Graphing Calculator. This not only will make the homework easier, but also help on EOC and PARCC testing.
Please note that homework should be done when assigned. Homework is given so that you can practice before an assessment. I will not accept late work after the assessment in which it was assigned. Please do not ask me to accept practice problems after the assessment.
"Email to be used by those with Hearing Difficulties for Attendance and Emergency messages only. General inquiry messages will not be answered. Please call the school if you require further assistance or information. Thank you." | 677.169 | 1 |
Precalculus, Enhanced Webassign Edition (Book Only) ...
Read More a customized resource that will better prepare your students for future courses in mathematics and sciences. In PRECALCULUS: MATHEMATICS FOR CALCULUS, Sixth Edition best-selling authors, James Stewart, Lothar Redlin and Saleem Watson refine their focus on problem solving and mathematical modeling to provide students with a solid foundation in the principles of mathematical thinking. The authors explain explains critical concepts simply and clearly, without glossing over difficult points to provide complete coverage of the function concept, and integrate a significant amount of graphing calculator material to help students develop insight into mathematical | 677.169 | 1 |
[ED: Hardcover], [PU: Springer, Berlin], This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity.
It Springer, Berlin], This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity. It über 4 Wochen, [SC: 0.00], Neuware, gewerbliches Angebot
De Bock, Dirk; Dooren, Wim van; Janssens, Dirk; Verschaffel, Lieven
The Illusion of Linearity
This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity.
It discusses: how the illusion of linearity appears in diverse domains of mathematics and science; what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon; and how the illusion of linearity can be remedied. | 677.169 | 1 |
Intermediate and High
SchoolMathSkills Learned First Degree Equations Linear Equations with One Variable Linear (CD in Printed Cardboard Sleeve)
Great for Collegiate Entrance Exam PrepProduct InformationHigh Achiever Algebra 2 for Grades 9-12 is curriculum based software foracademic success. It is for high school students currently enrolled inAlgebra 2 and is a great study aid for anyone preparing for his or her collegeentrance examinations. (CD in Printed Cardboard Sleeve)
Great for Collegiate Entrance Exam PrepProduct InformationHigh Achiever Geometry for Grades 10-12 is curriculum based software foracademic success. For high school students currently enrolled in Geometryand is a great study aid for anyone preparing for his or her college entranceexaminations. (CD in Printed Cardboard Sleeve)
Includes Over 40 Study LessonsProduct InformationHigh Achiever Middle School Mathematics 1 is curriculum based software foracademic success. Covers topics commonly taught in 6th grade math. It isalso suitable for high school students and adult learners who need to brush upon their basic math skills. Features include 43 standards based lessons over300 interactive quiz questions 43 skill-building animations and a searchabledatabase of over 500 key basic math terms. (CD in Printed Cardboard Sleeve)
Covers topics commonly taught in 7th grade math and some pre-algebra concepts. Also suitable for high school students and adult learners who need to brush up on their basic math skills. Features include 28 standards-based lessons, over 200 interactive quiz questions, 26 skill-building animations, and a searchable database of over 500 key basic math terms. (CD in Printed Cardboard Sleeve)
Covers topics commonly taught in 8th grade math and some pre-algebra concepts. Also suitable for high school students and adult learners who need to brush up on their basic math skills. Features include 25 standards-based lessons, over 300 interactive quiz questions, 25 skill-building animations, and a searchable database of over 500 key basic math terms. (CD in Printed Cardboard Sleeve) (CD in Printed Cardboard Sleeve)
High Achiever Trigonometry for Grades 10-12 is curriculum based software foracademic success. For high school students currently enrolled inTrigonometry, and a great study aid for anyone preparing for his or her collegeentrance examinations. (CD in Printed Cardboard Sleeve)
The world is losing math knowledge by the second, and all signs point to evil Dr. Dabble! Help Rave get to the root of this dastardly plot! Skills Covered: Computation using decimals, integers and rational numbers, Solving word problems, Ratios, proportions, and percents, Translating mathematical expressions, Applying order of operations, Creating equations, Graphing, Manipulating positive and negative numbers, Estimation, Logical thinking (CD in Gift Quality Jewel Case)
Hit the road with your cool new band and discover how much math plays a part in everyday life! Build key math skills as you manage money, buy food, use maps and more to help your band climb the charts. With Math for the Real World you can master all the math skills you need to succeed in real life! Skills Learned Addition and subtraction, money, time, fractions, decimals, percents, weight, measurement&patterns (CD in Gift Quality Jewel Case) | 677.169 | 1 |
Help With Math:
Purveyors of MathXpert
MathXpert: software to help you learn mathematics.
The student has used the mouse to select the term shown in the yellow selection rectangle.
MathXpert responded by displaying a list of mathematical operations--things that the student might do to the selected expression, or
in some cases, with the selected expression. The student will select an operation from this list--to see this, click
here. | 677.169 | 1 |
Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and problems.
This is a self-contained text on abstract algebra for senior undergraduate and senior graduate students, which gives complete and comprehensive coverage of the topics usually taught at this level. The book is divided into five parts. The first part contains fundamental information such as an informal introduction to sets, number systems, matrices, and determinants. The second part deals with groups. The third part treats rings and modules. The fourth part is concerned with field theory. Much of the material in parts II, III, and IV forms the core syllabus of a course in abstract algebra. The fifth part goes on to treat some additional topics not usually taught at the undergraduate level, such as the Wedderburn-Artin theorem for semisimple artinian rings, Noether-Lasker theorem, the Smith-Normal form over a PID, finitely generated modules over a PID and their applications to rational and Jordan canonical forms and the tensor products of modules. Throughout, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. In addition, the book contains many examples fully worked out and a variety of problems for practice and challenge. Solution to the odd-numbered problems are provided at the end of the book to encourage the student in problem solving. This new edition contains an introduction to categories and functors, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Noether-Lasker theorem. In addition, there are over 150 new problems and examples.
A completely reworked new edition of this superb textbook. This key work is geared to the needs of the graduate student. It covers, with proofs, the usual major branches of groups, rings, fields, and modules. Its inclusive approach means that all of the necessary areas are explored, while the level of detail is ideal for the intended readership. The text tries to promote the conceptual understanding of algebra as a whole, doing so with a masterful grasp of methodology. Despite the abstract subject matter, the author includes a careful selection of important examples, together with a detailed elaboration of the more sophisticated, abstract theoriesThis undergraduate text takes a novel approach to the standard introductory material on groups, rings, and fields. At the heart of the text is a semi-historical journey through the early decades of the subject as it emerged in the revolutionary work of Euler, Lagrange, Gauss, and Galois. Avoiding excessive abstraction whenever possible, the text focuses on the central problem of studying the solutions of polynomial equations. Highlights include a proof of the Fundamental Theorem of Algebra, essentially due to Euler, and a proof of the constructability of the regular 17-gon, in the manner of Gauss. Another novel feature is the introduction of groups through a meditation on the meaning of congruence in the work of Euclid. Everywhere in the text, the goal is to make clear the links connecting abstract algebra to Euclidean geometry, high school algebra, and trigonometry, in the hope that students pursuing a career as secondary mathematics educators will carry away a deeper and richer understanding of the high school mathematics curriculum. Another goal is to encourage students, insofar as possible in a textbook format, to build the course for themselves, with exercises integrally embedded in the text of each chapter.
This is the most current textbook in teaching the basic concepts of abstract algebra. The author finds that there are many students who just memorise a theorem without having the ability to apply it to a given problem. Therefore, this is a hands-on manual, where many typical algebraic problems are provided for students to be able to apply the theorems and to actually practice the methods they have learned. Each chapter begins with a statement of a major result in Group and Ring Theory, followed by problems and solutions. Contents: Tools and Major Results of Groups; Problems in Group Theory; Tools and Major Results of Ring Theory; Problems in Ring Theory; IndexAccessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields.
Geared toward upper-level undergraduates and graduate students, this text surveys fundamental algebraic structures and maps between these structures. Its techniques are used in many areas of mathematics, with applications to physics, engineering, and computer science as well. Author Robert B. Ash, a Professor of Mathematics at the University of Illinois, focuses on intuitive thinking. He also conveys the intrinsic beauty of abstract algebra while keeping the proofs as brief and clear as possible. The early chapters provide students with background by investigating the basic properties of groups, rings, fields, and modules. Later chapters examine the relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of algebraic number theory, algebraic geometry, noncommutative algebra, and homological algebra, including categories and functors. An extensive supplement to the text delves much further into homological algebra than most introductory texts, offering applications-oriented results. Solutions to all problems appear in the text.
CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory. | 677.169 | 1 |
Understanding precalculus often opens the door to learning more advanced and practical math subjects, and can also help satisfy college requisites. Precalculus Demystified, Second Edition, is your key to mastering this sometimes tricky subject.
This self-teaching guide presents general precalculus concepts first, so you'll ease into the basics. You'll gradually master functions, graphs of functions, logarithms, exponents, and more. As you progress, you'll also conquer topics such as absolute value, nonlinear inequalities, inverses, trigonometric functions, and conic sections. Clear, detailed examples make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key ideas.
It's a no-brainer! You'll learn about:
Linear questions
Functions
Polynomial division
The rational zero theorem
Logarithms
Matrix arithmetic
Basic trigonometry
Simple enough for a beginner but challenging enough for an advanced student, Precalculus Demystified, Second Edition, Second Edition, helps you master this essential subject.
"Sinopsis" puede pertenecer a otra edición de este libro.
About the Author:
Rhonda Huettenmueller has been teaching college mathematics for more than 20 years. She regularly teaches algebra, college algebra, and pre-calculus courses, along with more specialized versions of the classes for business students. Rhonda is the author of Algebra Demystified, McGraw-Hill's most successful Demystified book to date, College Algebra Demystified, and Business Calculus Demystified. Paperback. Estado de conservación: New. 2nd. Paperback. Your solution to mastering pre-calculus! Fully updated throughout, Pre-calculus DeMYSTiFieD, Second Edition features all-new quizzes and test questions, detailed explanations of the exerci.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 544 pages. 0.623. Nº de ref. de la librería 9780071778497 | 677.169 | 1 |
Direction-of-Arrival (DOA) estimation concerns the estimation of direction finding signals in the form of electromagnetic or acoustic waves, impinging on a sensor or antenna array. DOA estimation is used for locating and tracking signal sources in...
Facing Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately for you, there'apos;s Schaum'apos;s.More than 40 million students have trusted Schaum'apos;s to help them succeed in the classroom and on exams. Schaum'apos;s is the key to...
Six Sigma statistical methodology using Minitab Problem Solving and Data Analysis using Minitab presents example-based learning to aid readers in understanding how to use MINITAB 16 for statistical analysis and problem solving. Each example and...
Praise for the Third Edition '. . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . .'—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra...
This early work on chocolate manufacturing is both expensive and hard to find in its first edition. It details the many stages of chocolate production from the cocoa bean to the shelf. This is a fascinating work and is thoroughly recommended for...
A comprehensive and accessible guide to panel data analysis using EViews software This book explores the use of EViews software in creating panel data analysis using appropriate empirical models and real datasets. Guidance is given on developing...
Mathematics scares and depresses most of us, but politicians, journalists and everyone in power use numbers all the time to bamboozle us. Most maths is really simple - as easy as 2+2 in fact. Better still it can be understood without any jargon, any...
Features a practical approach to the analysis of biomedical data via mathematical methods and provides a MATLAB® toolbox for the collection, visualization, and evaluation of experimental and real-life data Applied Mathematics for the Analysis...
Exploring the scientific principles behind everyday recipes, this informative blend of lab book and cookbook reveals that cooks are actually chemists. Following or modifying recipes is shown to be an experiment with acids and bases, emulsions and...
This two-part treatment deals with foundations as well as models and applications. Topics include continuous multivariate distributions; regression and analysis of variance; factor analysis and latent structure analysis; and structuring multivariate...
Praise for the Second Edition 'This book is a systematic, well-written, well-organized text on multivariate analysis packed with intuition and insight . . . There is much practical wisdom in this book that is hard to find elsewhere.' —IIE...
Mathematical Tools for Applied Multivariate Analysis provides information pertinent to the aspects of transformational geometry, matrix algebra, and the calculus that are most relevant for the study of multivariate analysis. This book discusses the...
Electrons, Atoms, and Molecules in Inorganic Chemistry: A Worked Examples Approach builds from fundamental units into molecules, to provide the reader with a full understanding of inorganic chemistry concepts through worked examples and full color...
The book is intended for students of graduate and postgraduate level, researchers in mathematical sciences as well as those who want to apply the spectral theory of second order differential operators in exterior domains to their own field. In the...
Enzymes are currently used in various industries, most commonly in food, detergents, and pharmaceuticals production. Lipases are hydrolytic enzymes that demonstrate great potential as an alternative to conventional catalysts in a number of industrialJourney through the World of Numbers a onederful trek through the number sets Imagine that a digit dares himself to go traveling. And by digit we mean the plucky little number 1. What kind of adventures might the digit experience on such an odyssey?...
General Purpose Simulation System (GPSS) is a special computer programming language primarily used to simulate what can be classified as discrete systems. A discrete system is one where, at any given instant in time, a countable number of things can...
This third volume in a four-volume set offers new theories and applications for the diagnosis and treatment of mental disorders. Having laid the groundwork in the first two volumes, the authors now embark on significant, real-life scenarios that...
Forest Biometrics presents the methods of mathematical statistics and biometrics that are significant to forestry. This book explores other fields related to forestry, which are explained with the help of a large number of practical...
This monograph is the first and an initial introduction to the theory of bitopological spaces and its applications. In particular, different families of subsets of bitopological spaces are introduced and various relations between two topologies are...
The #1 New York Times bestsellerThe phenomenal true story of the black female mathematicians at NASA whose calculations helped fuel some of America's greatest achievements in space. Soon to be a major motion picture starring Taraji P. Henson, Octavia...
Praise for the Fourth Edition: 'This book is . . . an excellent source of examples for regression analysis. It has been and still is readily readable and understandable.' ?Journal of the American Statistical Association Regression analysis is a...
Steroid dimers are an important group of compounds produced by various marine organisms, and also synthesized in the laboratories. This group of compounds possesses various pharmacological and biological properties, and can also be used to create ...
An advanced discussion of linear models with mixed or random effects. In recent years a breakthrough has occurred in our ability to draw inferences from exact and optimum tests of variance component models, generating much research activity that...
Key Concepts in Environmental Chemistry provides a modern and concise introduction to environmental chemistry principles and the dynamic nature of environmental systems. It offers an intense, one-semester examination of selected concepts encountered...
This book provides an introduction to functional analysis for non-experts in mathematics. As such, it is distinct from most other books on the subject that are intended for mathematicians. Concepts are explained concisely with visual materials,...
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
A New Ecology presents an ecosystem theory based on the following ecosystem properties: physical openness, ontic openness, directionality, connectivity, a complex dynamic for growth and development, and a complex dynamic response to disturbances....
Right now, a group of scientists is working on ways to minimize the catastrophic impact of global warming. But they're not designing hybrids or fuel cells or wind turbines. They're trying to lower the temperature of the entire planet. And they're...
In this revolutionary work, the author sets the stage for the science ofthe 21st Century, pursuing an unprecedented synthesis of fields previouslyconsidered unrelated. Beginning with simple classical concepts, he endswith a complex multidisciplinary...
A fascinating and instructive guide to Markov chains for experienced users and newcomers alike This unique guide to Markov chains approaches the subject along the four convergent lines of mathematics, implementation, simulation, and experimentation....
Don't simply show your data—tell a story with it! Storytelling with Data teaches you the fundamentals of data visualization and how to communicate effectively with data. You'll discover the power of storytelling and the way to make data a pivotal... | 677.169 | 1 |
2
MATH 4500 PROJECTS
Wednesday 26 November. Project due. This is the day before Thanksgiving, so plan
ahead!
3. S UGGESTED TOPICS
You may pursue any of the following topics, or come up with one of your own,
provided you clear it with me.
Classication of s
MATH 4500 PROJECTS
REYER SJAMAAR
1. D ESCRIPTION
This project involves writing an expository paper on a topic of your own choice,
which is subject to my approval. The main criteria are that the project must be
related to Lie groups and that it must cover | 677.169 | 1 |
Get the confidence and the skills you need to master differential equations!
Need to know how to solve differential equations? This easy-to-follow, hands-on workbook helps you master the basic concepts and work through the types of problems you'll encounter in your coursework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every equation. You'll also memorize the most-common types of differential equations, see how to avoid common mistakes, get tips and tricks for advanced problems, improve your exam scores, and much more!
More than 100 Problems!
Detailed, fully worked-out solutions to problems The inside scoop on first, second, and higher order differential equations A wealth of advanced techniques, including power series
Steven Holzner, PhD, served on the faculty of Cornell University and Massachusetts Institute of Technology. He is an award-winning author who has written Physics For Dummies, Quantum Physics For Dummies, and more. This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. BZV9780470472019 | 677.169 | 1 |
Beginning Math and Physics for Game Programmers.pdf 2. ReadMe.Important!.txt 3. Beginning Math and Physics for Game Programmers.mobi 4. Beginning Math and Physics for Game Programmers.epub 5. Beginning Math and Physics for Game Programmers.doc | 677.169 | 1 |
Limit Quiz
Be sure that you have an application to open
this file type before downloading and/or purchasing.
55 KB
Product Description
Quiz on the following topics:
- Finding limits graphically
- Determine if a graph is continuous at a point
- Finding limits of piece wise functions
- Finding limits using direct substitution and factoring | 677.169 | 1 |
Further Maths
Specification
OCR MEI A Level Further Mathematics (H645)
Contact
Mr L Carne (Learning Director: Mathematics)
Entry Requirements
Potential students will need to have gained an grade 8 or 9 at GCSE to be equipped for the challenge of Further Mathematics. It will need to be taken as a separate option alongside a regular mathematics option.
Is this course for me?
If you are passionate about Mathematics, then Further Mathematics gives you the opportunity to gain a much wider and deeper understanding of advanced mathematics.
Where can it take me?
Further Mathematics is very favourably looked on by universities offering technical and engineering degrees, as well as being highly valuable for those who want to study Mathematics.
A Level Qualification Structure:
The three overarching themes of the New A Level Further Mathematics specification are:
Mathematical argument, language and proof
Mathematical problem-solving
Mathematical modelling
First Year
Second Year
You will expand your understanding of the number system and algebra through complex numbers and new forms of algebraic proof. You will learn about matrices and their vast and varied use in solving mathematical problems.
You will develop your understanding and application of complex numbers and matrices. You will also learn new types of functions and new ways of plotting coordinates which culminate in a true synthesis of the knowledge and techniques developed in A Level Further Mathematics.
Specification
OCR MEI A Level Mathematics (7895)
Contact
Mr L Carne (Learning Director: Mathematics)
Entry requirements
Students will need a B or higher at GCSE.
Specification
OCR MEI A Level Further Mathematics (7896)
Contact
Mr L Carne (Learning Director: Mathematics)
Entry requirements
Potential students will need to have gained an A* at GCSE to be equipped for the challenge of Further Mathematics. It will need to be taken as a separate option alongside a regular mathematics option | 677.169 | 1 |
Algebra Review
In this algebra review worksheet, 9th graders solve and complete 12 different problems. First, they use addition, subtraction, multiplication, and division properties of inequalities to solve the linear inequalities. They also write their responses in simplified terms. | 677.169 | 1 |
Description - From Calculus to Chaos by David Acheson
What is calculus really for? This book is a highly readable introduction to applications of calculus, from Newton's time to the present day. These often involve questions of dynamics, i.e. of how - and why - things change with time. Problems of this kind lie at the heart of much of applied mathematics, physics, and engineering. From Calculus to Chaos takes a fresh approach to the subject as a whole, by moving from first steps to the frontiers, and by highlighting only the most important and interesting ideas, which can get lost amid a snowstorm of detail in conventional texts. The book is aimed at a wide readership, and assumes only some knowledge of elementary calculus. There are exercises (with full solutions) and simple but powerful computer programs which are suitable even for readers with no previous computing experience. David Acheson's book will inspire new students by providing a foretaste of more advanced mathematics and showing just how interesting the subject can be.
Buy From Calculus to Chaos by David Acheson from Australia's Online Independent Bookstore, Boomerang Books. | 677.169 | 1 |
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