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Mathematics A Discrete Introduction
9780534398989
ISBN:
0534398987
Edition: 2 Pub Date: 2005 Publisher: Thomson Learning
Summary: With a wealth of learning aids and a clear presentation, this book teaches students not only how to write proofs, but how to think clearly and present cases logically beyond this course. All the material is directly applicable to computer science and engineering, but it is presented from a mathematician's perspective.
Scheinerman, Edward R. is the author of Mathematics A Discrete Introduction, published 2005... under ISBN 9780534398989 and 0534398987. One hundred thirty two Mathematics A Discrete Introduction textbooks are available for sale on ValoreBooks.com, four used from the cheapest price of $23.81, or buy new starting at $60.00.[read more]
Ships From:Salem, ORShipping:Standard, ExpeditedComments:Has minor wear and/or markings. SKU:9780534398989-3-0-3 Orders ship the same or next business day... [more] | 677.169 | 1 |
Beginning Algebra: Connecting Concepts Through Applications
9780534419387
ISBN:
0534419380
Edition: 1 Pub Date: 2011 Publisher: Brooks Cole
Summary: BEGINNING ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master algebraic concepts, problem solving, and communication skills. Students learn how to solve problems generated from realistic applications, instead of learning techniques without conceptual underst...anding. The authors have developed several key ideas to make concepts real and vivid for students. First, they emphasize strong algebra skills. These skills support the applications and enhance student comprehension. Second, the authors integrate applications, drawing on realistic data to show students why they need to know and how to apply math. The applications help students develop the skills needed to explain the meaning of answers in the context of the application. Third, the authors develop key concepts as students progress through the course. For example, the distributive property is introduced in real numbers, covered when students are learning how to multiply a polynomial by a constant, and finally when students learn how to multiply a polynomial by a monomial. These concepts are reinforced through applications in the text. Last, the authors' approach prepares students for intermediate algebra by including an introduction to material such as functions and interval notation as well as the last chapter that covers linear and quadratic modeling.
Clark, Mark is the author of Beginning Algebra: Connecting Concepts Through Applications, published 2011 under ISBN 9780534419387 and 0534419380. Four hundred forty nine Beginning Algebra: Connecting Concepts Through Applications textbooks are available for sale on ValoreBooks.com, sixty four used from the cheapest price of $93.91, or buy new starting at $158 [more. Expedited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less] | 677.169 | 1 |
Geometry Workbook For Dummies
9780471799405
ISBN:
0471799408
Pub Date: 2006 Publisher: Wiley & Sons, Incorporated, John
Summary: From proofs to polygons -- solve geometry problems with ease Got a grasp on the terms and concepts you need to know, but get lost halfway through a problem or worse yet, not know where to begin? No fear -- this hands-on guide focuses on helping you solve the many types of geometry problems you encounter in a focused, step-by-step manner. With just enough refresher explanations before each set of problems, you'll shar...pen your skills and improve your performance. You'll see how to work with proofs, theorems, triangles, circles, formulas, 3-D figures, and more! 100s of Problems! Step-by-step answer sets clearly identify where you went wrong (or right) with a problem Get the inside scoop on geometry shortcuts and strategies Know where to begin and how to solve the most common problems Use geometry in practical applications with confidence
Ryan, Mark is the author of Geometry Workbook For Dummies, published 2006 under ISBN 9780471799405 and 0471799408. One hundred sixty one Geometry Workbook For Dummies textbooks are available for sale on ValoreBooks.com, sixty three used from the cheapest price of $1.67, or buy new starting at $10.90 | 677.169 | 1 |
Core Plus Course 1 (9th grade) contains about a dozen simultaneous equations problems, none involving more than two variables, and all with one of the variables isolated on the left side of the two equations as above. Thus, one variable is already "solved for," and the other one, appearing in two expressions that are equal to one another, can be solved for in a few easy steps.
Wentworth's New School Algebra contains many hundreds of simultaneous equations, many involving three variables, some with the variables in the denominators. Solving them involves multiple algebraic manipulations.
Relate this contrast to the amount of explanation given by the Core-Plus textbook (the entirety of which you see here) to the amount of explanation given by Wentworth above for just one of several algebraic methods.
3 comments:
Funny, i have most of my g-grandfathers school books from the mid 1870s, among them a copy of Frenchs Common Arithmetic. Our district uses TERC Investiigations (trying to get rid of). Not only is the currciulum in the book published in 1869 clearer--my ggrandfather had a habit of working problems in the margins and end pages.
Finally took it into a Board of Ed meeting one night and actually showed them how an 11 year old kid who went ot a one room school house on the Illinois prairie actually had better math fluency at the same age as his gg grandaughter, who attends a supposedly first class Westchester County NY public school. Were the problem sets not geared to a farmers offspring--lots in rods, furlongs, bushels etc--I'd just teach her from the old book.
The newer problems are an example of what I see in my kids public middle school algebra: they take as much of the algebra out as they can. There is almost no manipulation of expressions except for the simplest equation solving. They introduce 2x2 systems like this, with both lines already in point-slope form and lots of questions about what you would do with a table? a graph? etc? It gets really depressing when they get to exponentials. Instead of algebra (manipulating expressions) they make tables and graphs, tables and graphs. They eliminate the handicraft aspect of algebra | 677.169 | 1 |
Provides a concise overview of the core undergraduate physics and applied mathematics curriculum for students and practitioners of science and engineering Fundamental Math and Physics for Scientists and Engineers summarizes college and university level physics together with the mathematics frequently encountered in engineering and physics calculations.... more...
Applied Finite Mathematics, Second Edition presents the fundamentals of finite mathematics in a style tailored for beginners, but at the same time covers the subject matter in sufficient depth so that the student can see a rich variety of realistic and relevant applications. Some applications of probability, game theory, and Markov chains are given.... more...
This new addition to the bestselling 20 Minutes a Day series helps students master the math essentials found on all levels of the COMPASS, ASSET, and ACCUPLACER exams. These exams, given by colleges country-wide, are taken by students to place them into the appropriate courses. Placing out of courses with a high score can mean credits (and money)... more...
An introduction to the subject of index numbers for statisticians, economists and numerate members of the public. The ideal accompanying text for students taking the Royal Statistical Society?s Ordinary and Higher examinations and for members of the Government Statistical Service. As well as covering the essential basics of the subject, it will describe... more...
3rd Edition provides new content and expanded coverage of key topics New section discusses the fixed point index and its many applications Concise presentation and clear exposition make it an ideal resource for classroom use or self study more...
The qualitative theory of dynamic equations is a rapidly developing area of research. In the last 50 years, the Oscillation Theory of ordinary, functional, neutral, partial and impulsive differential equations, and their discrete versions, has inspired many scholars. Hundreds of research papers have been published in every major mathematical journal.... more...
This volume deals with first- and second-order complex equations of hyperbolic and mixed types. The authors investigate in detail general boundary value problems for linear and quasilinear complex equations and present some discontinuous boundary value problems for elliptic complex equations. Mixed complex equations are included in the quasilinear... more... | 677.169 | 1 |
Algebra for College Students
9780495105107
ISBN:
0495105104
Edition: 8 Pub Date: 2006 Publisher: Thomson Learning
Summary: Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; use the skill to help solve equations; and then apply what you have learned to solve application problems. This simple, straightforward approach has helped many students grasp and apply fundam...ental problem solving skills necessary for future mathematics courses in an easy-to-read format. The new Eighth Edition of ALGEBRA FOR COLLEGE STUDENTS includes new and updated problems, revised content based on reviewer feedback and a new function in iLrn. This enhanced iLrn homework functionality was designed specifically for Kaufmann/Schwitters' users. Textbook-specific practice problems have been added to iLrn to provide additional, algorithmically-generated practice problems, along with useful support and assistance to solve the problems for students.
Kaufmann Schwitters Staff is the author of Algebra for College Students, published 2006 under ISBN 9780495105107 and 0495105104. Fifteen Algebra for College Students textbooks are available for sale on ValoreBooks.com, twelve used from the cheapest price of $0.45, or buy new starting at $96.94 | 677.169 | 1 |
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About the book:
Few beginning graduate students in mathematics and other quantitative subjects possess the daunting breadth of mathematical knowledge expected of them when they begin their studies. This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundationsCBR via United States
Softcover, ISBN 0521797071 Publisher: Cambridge University Press This book is BRAND NEW Soft cover International edition with black and white printing. ISBN number & cover page may be different but contents identical to the US edition word by word. Book is in English language.
Softcover, ISBN 0521797071 Publisher: Cambridge University Press, 2001521797071 Publisher: Cambridge University Press, 2001 New Softcover International Edition, Printed in Black and White, Different ISBN, Same Content As US edition, Book Cover may be Different, in English Language
Softcover, ISBN 0521797071 Publisher: Cambridge University Press, 2001 1st. Softcover. . Brand New Softcover International Edition, Black and White Printing, Have Identical Content as US edition, ISBN or Book Cover may be Different. 1st
Softcover, ISBN 0521797071 Publisher: Cambridge University Press, 2001 Paperback. New. Brand New Softcover International Edition, Have same content as US Edition. ISBN is different. Never Used, in English Language. Printed in Black and White. 100% return and refund.
Softcover, ISBN 0521797071 Publisher: Cambridge University Press, 2001521797071 Publisher: Cambridge University Press, 2001 Softcover, International. Brand New Softcover International Edition, Printed in Black and White, Have same content as US Edition. ISBN is different. Never Used, in English Language..
Softcover, ISBN 0521797071 Publisher: Cambridge University Press1797071 Publisher: Cambridge University Press, 2001
Softcover, ISBN 0521797071 Publisher: Cambridge University Press, 2001 brand new softcover international edition. different ISBN and front cover, have same contents as US Edition, Edition,Perfect Condition.fast shipping
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Softcover, ISBN 0521797071 Publisher: Cambridge University Press, 2001 Used - Good, Usually ships in 1-2 business days, Fast shipping! In great shape. All proceeds benefit Habitat for Humanity, unable to ship to prisons/correctional facilities.
Softcover, ISBN 0521797071 Publisher: Cambridge University Press, 2001 Used - Very Good, Usually ships in 1-2 business days, Slight cover and page wear. Slight markings on outside page edges. Text appears unmarked. Ships the next business day with tracking.
Softcover, ISBN 0521797071 Publisher: Cambridge University Press, 2001 Used - Very Good, Usually ships in 1-2 business days, VERY GOOD SOFT COVER BOOK WITH JUST SOME LIGHT NORMAL READING USAGE. NO MARKS OR HIGHLIGHTS. FAST SHIPPING FROM COLORADO
Softcover, ISBN 0521797071 Publisher: Cambridge University1797071 Publisher: Cambridge University Press, 2001Softcover, ISBN 0521797071 Publisher: Cambridge University Press, 2001 | 677.169 | 1 |
tried-and-true text from Allyn Washington preserves the author's highly regarded approach to technical math, while enhancing the integration of technology. Appropriate for a three- to four- semester course, BASIC TECHNICAL MATHEMATICS WITH CALCULUSshows how algebra, trigonometry, and basic calculus are used on the job. It addresses a vast number of technical and pre-engineering fields, including computer design, electronics, solar energy, lasers fiber optics, and the environment. Known for its exceptional problem sets and applied material, the book offers practice exercises, writing exercises, word problems, and practice tests. This edition features more technical applications, over 2300 new exercises, additional graphing calculator screens and the innovative MyLab websites. | 677.169 | 1 |
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2,500 fully worked problems of varying difficulty
Clear, concise explanations of arithmetic, algebra, and geometry
Outline format supplies a concise guide to the standard college courses in elementary mathematics
Appropriate for the following courses: Basic Mathematics, Elementary Mathematics, Introduction to Mathematics, Review of Arithmetic, Elementary Algebra, Review of Algebra, Business Mathematics I, Math for the GED
Detailed explanations and practice problems in arithmetic, algebra, and geometry
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Review of Elementary Mathematics is students' #1 choice for mastering math. This easy-to-follow study guide can help anyone succeed in mathematics. Assuming no knowledge of math, it explains simply and clearly every important concept you need to know in a straightforward, uncomplicated way. It doesn't waste your time with things you don't need to know.
Thousands of sample problems show you step-by-step how to solve the kind of problems you will find on your exams. Hundreds more practice problems (with answers supplied) let you test your skills. Whether you use this excellent study guide to help you ace your math course, study it alone as a complete program in elementary mathematics, or use it for review before a standardized test, this Schaum's guide will save you study time and move you quickly from the definition of a number through the elements of algebra.
This edition of one of Schaum's most popular Outlines features added material on calculations both with and without a calculator. You've found the study guide that makes math comprehensiblethe one that's been chosen by generations of grateful students! Chapters include:
Fundamentals of Arithmetic
Numbers
Fundamentals of Arithmetic and Introduction to Calculators
Fractions
Decimals
Per Cents
Signed Numbers
Fundamentals of Algebra
Laws and Operations
Fundamentals of Algebra
Equations and Formulas
Ratios, Proportions, and Rates
Fundamentals of Geometry
--This text refers to an out of print or unavailable edition of this title.
About the Author
Dr. Philip A. Schmidt is a professor of secondary education at SUNY College at New Paltz. He is the coauthor of Schaum's Outline of Mathematics for Physics Students.
Dr. Barnett Rich (deceased) taught at CUNY and Columbia University and was the author of Schaum's Outline of Elementary Algebra, Schaum's Outline of Modern Elementary Algebra, and Schaum's Outline of Geometry found this book to be a great supplement for my review of Math. Just the way it is presented makes it a joy to review. Straight and to the point. I plan on using the others in this line of books to hopefully get up to pre-calc for college.
However, I gave it four stars because of the unbelievably amount of errors found within. Where was the proof reader before publishing? Im at chapter 6 and have found approx 30+ errors. Ive lost count, something like one every other page or so.
I said above that I value these books, the errors have got to stop... if and when one reaches a level that he/she is not sure what it is they're doing, how will they know the right answer? They won't and will be misled, unfortunately.
To sum up, I definately approve of Schaums methods of supplementing mathematics but there needs to be some higher level of accuracy. Luckily, they are cheap and one would be wise to purchase additional material as well.
My son needs some real education in math (he is 7.5 years old in second grade). I use this book to set the curriculum and scope of teaching him math. This book serves as the basis to learn algebra. So far he loves it and understands math is not all about just addition/subtraction/multiplication and division.
Schaum's Review of Elementary Mahematics,Second Edition, by Barnett Rich and revised by Philip Schmidt is a survey of pre-college mathematics and provides assistance well beyond the regular book in elementary mathematics.
Each rule, formula and principle is given in simple language and immediately applied to solved problems Each procedure is developed step by step, each step applied to problems. Each set of solved problems illustrates a rule.
2 500 fully solved problems.
It even introduces the reader to Trigonometry(Law of Pythagoras). The calculator is introduced throughout. A 5-page index concludes the book.
Let me draw the attention to the completeness of the following chapters :chap.2 Fundamentals of Arithmetic, chap.8 Fundamentals of Algebra on Equations and Formulas,chap.10 Fundamentals of Geometry.
5/13: One of the very first math books I started with for my self-study was Schaum's Outlines: Review of Elementary Mathematics. Pedagogically, it is a very good book that effortlessly guides the reader throughout the basics of mathematics. There is nothing dry in the language. It simply explains and explains as much of details as possible how and why one does the procedure for a certain type of problems. Schaum's Outlines: Review of Elementary Mathematics will address the terminology from ground up. Every problem there is in the book, the solutions are provided, and half of them are fully worked out before the supplementary problems. All in all, I highly recommend Schaum's Outlines: Review of Elementary Mathematics as the very first mathematics book and follow it up with Schaum's Outline of Elementary Algebra, 3ed (Schaum's Outline Series).
I bought this book for one of my adult students. She is from a country in eastern Africa that does not emphasize women's education. Once I had her started with chapter 1, she was able to understand how to complete the rest of the book on her own.
excellent condition, great use for my school ager especially on those days he is without home work. I definitely recommend using supplements in addition to the material they use @ school for superior grades | 677.169 | 1 |
A practical introduction to the core mathematics required for engineering study and practice
Now in its seventh edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams.
John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for a range of Level 2 and 3 engineering courses.
This title is supported by a companion website with resources for both students and lecturers, including lists of essential formulae, multiple choice tests, full solutions for all 1,800 further questions contained within the practice exercises, and biographical information on the 24 famous mathematicians and engineers referenced throughout the book.
The companion website for this title can be accessed from
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Most Helpful Customer Reviews
Bought this to support someone working through the BTec in Engineering as a mature student. Nice clear processes and explanations with lots of examples to follow and work through, A real godsend for catching up and moving forward. It is a large book, which surprised me, don't know why! | 677.169 | 1 |
Abstract: Asha Habib
Mentor:Dr. Cheng
My summer research will focus on applications of Fourier analysis. Fourier analysis, developed by Jean Baptiste Joseph Fourier, allows one to take complicated mathematical objects and decompose them as a sum of sines and cosines, making them more manageable. Further research of Fourier analysis allowed for future developments so that signals could be compressed and be sent quickly and efficiently. This had led to much advancement in technology over the past decades. In particular, I will study applications to telecommunication. Also, I will learn how to write in LaTex. This program allows writers to create large and complex projects. Unlike Microsoft Word, the writer is not distracted with the presentation of his or her work. In LaTex, the writer simply writes a command in order to format the project to his or her desire. Also, LaTex is very user friendly for mathematics because of its options to code equations and graphs into one's paper. In all, learning how to use LaTex and gaining an understating of Fourier analysis will provide exposure to mathematical research and prepare me for future research. | 677.169 | 1 |
Calculus students are presented with a write-pair-share activity that leads them to a practical understanding of the...
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Calculus students are presented with a write-pair-share activity that leads them to a practical understanding of the Fundamental Theorem of Calculus. The activity involves analyzing a function that describes eating speed in a hypothetical dinner table experience. Suitable for either Calculus I or Calculus II students.Note: This project has a prequel entitled Calculus of the Dinner Table: Mathematical Modeling (listed under Interactive Lectures) in which students construct the mathematical model for the king's eating speed. This prequel provides an excellent and engaging prelude to this Theorem of Calculus: An Investigation to your Bookmark Collection or Course ePortfolio
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Gauss elimination is a method of solving a system of linear equations. This site contains an interactive tool that performs...
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Gauss elimination is a method of solving a system of linear equations. This site contains an interactive tool that performs Gauss elimination procedure one step at a time. The result is displayed after each step. A user can also use this tool to invert a matrix Gaussian Elimination to your Bookmark Collection or Course ePortfolio
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Matrix Calculator is a site containing an interactive applet that let a user to input a square matrix and then with a press...
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Matrix Calculator is a site containing an interactive applet that let a user to input a square matrix and then with a press of a button compute a power of this matrix, determinant, inverse, characteristic polynomials and other useful matrix characteristics calculator to your Bookmark Collection or Course ePortfolio
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A collection of puzzles ranging over geometry, probability, number theory, algebra, calculus, and logic. Hints are provided,...
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A collection of puzzles ranging over geometry, probability, number theory, algebra, calculus, and logic. Hints are provided, along with fully worked solutions, and links to related mathematical Nick's Mathematical Puzzles to your Bookmark Collection or Course ePortfolio
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This site contains reference material in Matrix Algebra. Topics covered include matrix operations, linear equations,...
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This site contains reference material in Matrix Algebra. Topics covered include matrix operations, linear equations, determinants, eigenvectors and eigenvalues. S.O.S. Mathematics--Matrix Algebra is a part of an independent, commercial site that offers straightforward technical assistance primarily to high school and college this {0}
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Atherton SAT MathLewis H.
...The questions are all multiple choice. A third of the test covers pre-algebra and elementary algebra. A third covers intermediate algebra and coordinate geometry (graphing). A quarter covers regular geometryJianzhong L.
...The subject matter of linear algebra was studied when I was in college and then used throughout my graduate studies and career as a research scientist. In general, I teach students how to solve problems, and then lead students through understanding why the subject is introduced and what is the c... | 677.169 | 1 |
Learning homological algebra is a two-stage affair. Firstly, one must learn the language of Ext and Tor, and what this describes. Secondly, one must be able to compute these things using a separate language. This title provides a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology.
Students learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely reading about mathematics is no substitute for doing mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and | 677.169 | 1 |
Elementary and Intermediate Algebra for College Students (3rd Edition)
9780132337229
ISBN:
0132337223
Edition: 3 Pub Date: 2007 Publisher: Prentice Hall
Summary: Angel's texts are a proven favorite among students and instructors alike. The Angel texts consistently receive praise for their readability - short, clear sentences are used to ensure the text is readable even for those with weak reading skills- and for the abundance of detailed, worked-out examples... more than any other text! In this revised, 3rd edition of Elementary and Intermediate Algebra for College Students, ...Angel continues to focus on the needs of the students taking this class and the instructors teaching them.
Allen R. Angel is the author of Elementary and Intermediate Algebra for College Students (3rd Edition), published 2007 under ISBN 9780132337229 and 0132337223. One hundred eighty seven Elementary and Intermediate Algebra for College Students (3rd Edition) textbooks are available for sale on ValoreBooks.com, fifty four used from the cheapest price of $1.44, or buy new starting at $43 ***Please Read***Annotated Instructor's Edition. Brand new except for a sticker on the front cover, hardcover 3rd edition. Same as student with additional notes and answers de [more]
ALTERNATE EDITION: ***Please Read***Annotated Instructor's Edition. Brand new except for a sticker on the front cover, hardcover 3rd edition. Same as student with additional notes and answers designed to assist the instructor.Shipping from California.[less] | 677.169 | 1 |
Description
Taking pre-algebra? Then you need the Wolfram Pre-Algebra Course Assistant. This definitive app for pre-algebra—from the world leader in math software—will help you work through your homework problems, ace your tests, and learn pre-algebra concepts. Forget canned examples! The Wolfram Pre-Algebra Course Assistant solves your specific pre-algebra problems on the fly.
This app covers the following pre-algebra topics:
- Find the divisors and prime factorization of a number - Calculate the GCD and LCM of two numbers - Determine the percent change - Reduce and round numbers - Evaluate expressions - Solve equations and simplify expressions - Convert units of length, area, volume, and weight - Compute the mean, median, and mode of a dataset - Plot equations on the coordinate plane - Graph inequalities on a number line - Calculate the area, surface area, or volume of a geometric figure - Find the midpoint, slope, and distance between two points
The Wolfram Pre-Algebra Course Assistant is powered by the Wolfram|Alpha computational knowledge engine and is created by Wolfram Research, makers of Mathematica—the world's leading software system for mathematical research and education.
The Wolfram Pre-Algebra | 677.169 | 1 |
La Honda StatisticsAaron K.
...In this course I got an A. AsideAlgebra is continually reviewed and used throughout the course. Prealgebra is a very important subject since it is the foundation for a new language, the language of algebra. Since algebra simply imitates your knowledge or how to use and apply numbers, the next step is simply using "x" instead of the number. | 677.169 | 1 |
Better student preparation needed for university maths: UK study
August 1, 2012
Moving from sixth form, or college, into higher education (HE) can be a challenge for many students, especially those who start mathematically demanding courses. Life prior to university focuses on achieving maximum examination success to be sure of a place. Faced with this pressure, school and college maths courses pay little attention to preparing students to use maths in other areas of study according to a project funded by the Economic and Social Research Council (ESRC).
A student's ability to apply mathematical reasoning is critical to their success, especially in HE courses like science, technology, engineering and medicine. The study, undertaken by Professor Julian Williams, Dr Pauline Davis, Dr Laura Black, Dr Birgit Pepin of the University of Manchester and Associate Professor Geoffrey Wake from the University of Nottingham, shows that it is important to understand how students can prepare for the 'shock to the system' they face and how they can be given support at school, college and university to help in the transition.
The researchers found that students were not fully aware of the importance of the mathematical content in the courses they had joined at university, and particularly how to apply maths in practice.
Associate Professor Geoffrey Wake states, "Different teaching styles of university lecturers and the need for autonomously-managed learning, where students need to learn some mathematical content of their courses on their own without input from lecturers, also came as a bit of a shock for many students. On the other hand, some of the lecturers had limited knowledge of the exam-driven priorities of A-level maths courses and were not aware of the techniques students had been taught prior to attending their university courses."
The researchers also found significant problems in motivating students to engage with the mathematics within their chosen university coursewhere mathematics was not their main area of study. Generally, schools and colleges were found not to be preparing students for university learning practices, and the level of learning-skills support was variable once students arrived at university.
"Many students felt that they would benefit from student-centred learning and greater opportunity for dialogue with their lecturers," says Associate Professor Wake. "Unfortunately, the efficiencies required of university teaching resulting in lecturing of large numbers of students makes developing such a learning culture unlikely."
The findings led the researchers to consider the implications for the policies and practices of schools, colleges and universities recommending a better two-way flow of information between schools and colleges and universities to address the issues of preparation and expectation.
They concluded that the sixth-form curriculum should provide 'learning to learn' skills and mathematical modelling for students following A-level maths coursesA recent study reports that high school students who study fewer science topics, but study them in greater depth, have an advantage in college science classes over their peers who study more topics and spend less time on ...
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1
00:00:00,000 --> 00:00:25,690
2
00:00:25,690 --> 00:00:27,660
PROFESSOR: OK, hi.
3
00:00:27,660 --> 00:00:33,780
This is the second in my videos
about the main ideas,
4
00:00:33,780 --> 00:00:36,090
the big picture of calculus.
5
00:00:36,090 --> 00:00:40,180
And this is an important one,
because I want to introduce
6
00:00:40,180 --> 00:00:44,480
and compute some derivatives.
7
00:00:44,480 --> 00:00:50,500
And you'll remember the overall
situation is we have
8
00:00:50,500 --> 00:00:55,270
pairs of functions, distance
and speed, function 1 and
9
00:00:55,270 --> 00:01:00,570
function 2, height of a graph,
slope of the graph, height of
10
00:01:00,570 --> 00:01:03,000
a mountain, slope
of a mountain.
11
00:01:03,000 --> 00:01:06,650
And it's the connection
between those two that
12
00:01:06,650 --> 00:01:08,220
calculus is about.
13
00:01:08,220 --> 00:01:16,770
And so our problem today is, you
could imagine we have an
14
00:01:16,770 --> 00:01:19,880
airplane climbing.
15
00:01:19,880 --> 00:01:27,160
Its height is y as it
covers a distance x.
16
00:01:27,160 --> 00:01:30,640
And its flight recorder will--
17
00:01:30,640 --> 00:01:33,000
Well, probably it has two
flight recorders.
18
00:01:33,000 --> 00:01:34,890
Let's suppose it has.
19
00:01:34,890 --> 00:01:40,120
Or your car has two recorders.
20
00:01:40,120 --> 00:01:44,330
One records the distance, the
height, the total amount
21
00:01:44,330 --> 00:01:48,430
achieved up to that moment,
up to that time, t,
22
00:01:48,430 --> 00:01:50,990
or that point, x.
23
00:01:50,990 --> 00:01:56,400
The second recorder would tell
you at every instant
24
00:01:56,400 --> 00:01:57,640
what the speed is.
25
00:01:57,640 --> 00:02:00,050
So it would tell you the
speed at all times.
26
00:02:00,050 --> 00:02:01,040
Do you see the difference?
27
00:02:01,040 --> 00:02:05,732
The speed is like what's
happening at an instant.
28
00:02:05,732 --> 00:02:11,400
The distance or the height, y,
is the total accumulation of
29
00:02:11,400 --> 00:02:14,540
how far you've gone, how
high you've gone.
30
00:02:14,540 --> 00:02:17,750
And now I'm going to suppose
that this speed, this second
31
00:02:17,750 --> 00:02:22,930
function, the recorder is lost.
But the information is
32
00:02:22,930 --> 00:02:24,480
there, and how to recover it.
33
00:02:24,480 --> 00:02:25,970
So that's the question.
34
00:02:25,970 --> 00:02:29,130
How, if I have a total record,
say of height--
35
00:02:29,130 --> 00:02:32,940
I'll say mostly with y of x.
36
00:02:32,940 --> 00:02:36,350
I write these two so that you
realize that letters are not
37
00:02:36,350 --> 00:02:37,660
what calculus is about.
38
00:02:37,660 --> 00:02:39,020
It's ideas.
39
00:02:39,020 --> 00:02:42,150
And here is a central idea.
40
00:02:42,150 --> 00:02:44,660
if I know the height--
41
00:02:44,660 --> 00:02:47,780
as I go along, I know the
height, it could go down--
42
00:02:47,780 --> 00:02:50,780
43
00:02:50,780 --> 00:02:55,390
how can I recover from that
height what the slope is at
44
00:02:55,390 --> 00:02:57,970
each point?
45
00:02:57,970 --> 00:03:04,330
So here's something rather
important, that's the notation
46
00:03:04,330 --> 00:03:08,740
that Leibniz created, and it was
a good, good idea for the
47
00:03:08,740 --> 00:03:09,330
derivative.
48
00:03:09,330 --> 00:03:11,790
And you'll see where
it comes from.
49
00:03:11,790 --> 00:03:19,190
But somehow I'm dividing
distance up by distance
50
00:03:19,190 --> 00:03:26,760
across, and that ratio of
up to across is a slope.
51
00:03:26,760 --> 00:03:32,770
So let me develop what
we're doing.
52
00:03:32,770 --> 00:03:41,930
So the one thing we can do and
now will do is, for the great
53
00:03:41,930 --> 00:03:46,250
functions of calculus,
a few very special,
54
00:03:46,250 --> 00:03:48,060
very important functions.
55
00:03:48,060 --> 00:03:53,360
We will actually figure
out what the slope is.
56
00:03:53,360 --> 00:03:57,260
These are given by formulas,
and I'll find a formula for
57
00:03:57,260 --> 00:04:01,120
the slope, dy/dx equals.
58
00:04:01,120 --> 00:04:04,750
And I won't write it in yet.
59
00:04:04,750 --> 00:04:06,290
Let me keep a little suspense.
60
00:04:06,290 --> 00:04:11,640
But this short list of the
great functions is
61
00:04:11,640 --> 00:04:14,800
tremendously valuable.
62
00:04:14,800 --> 00:04:17,620
The process that we go through
takes a little time, but once
63
00:04:17,620 --> 00:04:20,240
we do it it's done.
64
00:04:20,240 --> 00:04:23,640
Once we write in the answer
here, we know it.
65
00:04:23,640 --> 00:04:31,420
And the point is that other
functions of science, of
66
00:04:31,420 --> 00:04:37,380
engineering, of economics,
of life, come from these
67
00:04:37,380 --> 00:04:42,410
functions by multiplying--
68
00:04:42,410 --> 00:04:44,750
I could multiply that
times that--
69
00:04:44,750 --> 00:04:47,330
and then I need a product
rule, the rule for the
70
00:04:47,330 --> 00:04:49,760
derivative, the slope
of a product.
71
00:04:49,760 --> 00:04:51,490
I could divide that by that.
72
00:04:51,490 --> 00:04:54,070
73
00:04:54,070 --> 00:04:56,090
So I need a quotient rule.
74
00:04:56,090 --> 00:04:58,050
I could do a chain.
75
00:04:58,050 --> 00:05:02,490
And you'll see that's maybe the
best and most valuable.
76
00:05:02,490 --> 00:05:07,360
e to the sine x, so I'm putting
e to the x together
77
00:05:07,360 --> 00:05:13,700
with sine x in a chain of
functions, e to the sine of x.
78
00:05:13,700 --> 00:05:15,230
Then we need a chain rule.
79
00:05:15,230 --> 00:05:17,620
That's all coming.
80
00:05:17,620 --> 00:05:18,460
Let me start--
81
00:05:18,460 --> 00:05:23,680
Well, let me even start by
giving away the main facts for
82
00:05:23,680 --> 00:05:26,930
these three examples, because
they're three you want to
83
00:05:26,930 --> 00:05:31,350
remember, and might
as well start now.
84
00:05:31,350 --> 00:05:35,120
The x to the nth, so that's
something if n is positive.
85
00:05:35,120 --> 00:05:36,680
x to the nth climbs up.
86
00:05:36,680 --> 00:05:42,920
Let me draw a graph here of y
equals x squared, because
87
00:05:42,920 --> 00:05:47,940
that's one we'll work out in
detail, y equals x squared.
88
00:05:47,940 --> 00:05:50,370
So this direction is x.
89
00:05:50,370 --> 00:05:52,520
This direction is y.
90
00:05:52,520 --> 00:05:54,610
And I want to know the slope.
91
00:05:54,610 --> 00:05:58,680
And the point is that that slope
is changing as I go up.
92
00:05:58,680 --> 00:06:01,090
So the slope depends on x.
93
00:06:01,090 --> 00:06:03,220
The slope will be
different here.
94
00:06:03,220 --> 00:06:06,330
So it's getting steeper
and steeper.
95
00:06:06,330 --> 00:06:08,400
I'll figure out that slope.
96
00:06:08,400 --> 00:06:10,520
For this example, x
squared went in
97
00:06:10,520 --> 00:06:12,690
as 2, and it's climbing.
98
00:06:12,690 --> 00:06:20,520
If n was minus 2, just because
that's also on our list, n
99
00:06:20,520 --> 00:06:26,120
could be negative, the function
would be dropping.
100
00:06:26,120 --> 00:06:31,400
You remember x to the minus 2,
that negative exponent means
101
00:06:31,400 --> 00:06:34,550
divide by x squared.
102
00:06:34,550 --> 00:06:37,630
x to the minus 2 is 1 divided
by x squared,
103
00:06:37,630 --> 00:06:39,730
and it'll be dropping.
104
00:06:39,730 --> 00:06:43,030
So n could be positive
or negative here.
105
00:06:43,030 --> 00:06:45,220
So I tell you the derivative.
106
00:06:45,220 --> 00:06:49,830
The derivative is easy to
remember, the set number n.
107
00:06:49,830 --> 00:06:53,020
It's another power of
x, and that power is
108
00:06:53,020 --> 00:06:55,610
one less, one down.
109
00:06:55,610 --> 00:06:58,030
You lose one power.
110
00:06:58,030 --> 00:07:01,470
I'm going to go through the
steps here for n is equal to
111
00:07:01,470 --> 00:07:07,850
2, so I hope to get the answer
2 times x to the 2 minus 1
112
00:07:07,850 --> 00:07:11,280
will just be 1, 2x.
113
00:07:11,280 --> 00:07:13,860
But what does the slope mean?
114
00:07:13,860 --> 00:07:17,450
That's what this lecture
is really telling you.
115
00:07:17,450 --> 00:07:22,830
I'll tell you the answer for
if it's sine x going in,
116
00:07:22,830 --> 00:07:29,990
beautifully, the derivative of
sine x is cos x, the cosine.
117
00:07:29,990 --> 00:07:33,260
The derivative of the sine curve
is the cosine curve.
118
00:07:33,260 --> 00:07:37,860
You couldn't hope for
more than that.
119
00:07:37,860 --> 00:07:42,470
And then we'll also, at the same
time, find the derivative
120
00:07:42,470 --> 00:07:45,940
of the cosine curve, which
is minus the sine curve.
121
00:07:45,940 --> 00:07:49,380
It turns out a minus sine comes
in because the cosine
122
00:07:49,380 --> 00:07:52,280
curve drops at the start.
123
00:07:52,280 --> 00:07:55,640
And would you like
to know this one?
124
00:07:55,640 --> 00:08:01,480
e to the x, which I will
introduce in a lecture coming
125
00:08:01,480 --> 00:08:05,220
very soon, because it's the
function of calculus.
126
00:08:05,220 --> 00:08:09,230
And the reason it's so terrific
is, the connection
127
00:08:09,230 --> 00:08:15,220
between the function, whatever
it is, whatever this number e
128
00:08:15,220 --> 00:08:19,900
is to whatever the xth power
means, the slope is the same
129
00:08:19,900 --> 00:08:22,200
as the function, e to the x.
130
00:08:22,200 --> 00:08:25,810
131
00:08:25,810 --> 00:08:28,750
That's amazing.
132
00:08:28,750 --> 00:08:31,300
As the function changes,
the slope changes
133
00:08:31,300 --> 00:08:32,550
and they stay equal.
134
00:08:32,550 --> 00:08:35,210
135
00:08:35,210 --> 00:08:39,059
Really, my help is just to say,
if you know those three,
136
00:08:39,059 --> 00:08:41,950
you're really off to a
good start, plus the
137
00:08:41,950 --> 00:08:43,500
rules that you need.
138
00:08:43,500 --> 00:08:47,000
All right, now I'll tackle this
particular one and say,
139
00:08:47,000 --> 00:08:50,690
what does slope mean?
140
00:08:50,690 --> 00:08:56,500
So I'm given the recorder
that I have. This
141
00:08:56,500 --> 00:08:57,850
is function 1 here.
142
00:08:57,850 --> 00:09:01,910
This is function 1,
the one I know.
143
00:09:01,910 --> 00:09:05,700
And I know it at every point.
144
00:09:05,700 --> 00:09:09,710
If I only had the trip meter
after an hour or two hours or
145
00:09:09,710 --> 00:09:15,810
three hours, well, calculus
can't do the impossible.
146
00:09:15,810 --> 00:09:20,440
It can't know, if I only knew
the distance reached after
147
00:09:20,440 --> 00:09:26,560
each hour, I couldn't tell what
it did over that hour,
148
00:09:26,560 --> 00:09:29,500
how often you had to break,
how often you accelerated.
149
00:09:29,500 --> 00:09:33,360
I could only find an average
speed over that hour.
150
00:09:33,360 --> 00:09:34,820
That would be easy.
151
00:09:34,820 --> 00:09:38,890
So averages don't
need calculus.
152
00:09:38,890 --> 00:09:43,140
It's instant stuff, what happens
at a moment, what is
153
00:09:43,140 --> 00:09:48,630
that speedometer reading at the
moment x, say, x equal 1.
154
00:09:48,630 --> 00:09:50,280
What is the slope?
155
00:09:50,280 --> 00:09:58,600
Yeah, let me put in x equals 1
on this graph and x equals 2.
156
00:09:58,600 --> 00:10:02,720
And now x squared is going
to be at height 1.
157
00:10:02,720 --> 00:10:08,320
If x is 1, then x squared
is also 1.
158
00:10:08,320 --> 00:10:13,160
If x is 2, x squared
will be 4.
159
00:10:13,160 --> 00:10:14,150
What's the average?
160
00:10:14,150 --> 00:10:15,970
Let me just come back
one second to
161
00:10:15,970 --> 00:10:17,810
that average business.
162
00:10:17,810 --> 00:10:24,410
The average slope there would
be, in a distance across of 1,
163
00:10:24,410 --> 00:10:27,840
I went up by how much?
164
00:10:27,840 --> 00:10:29,590
3.
165
00:10:29,590 --> 00:10:31,680
I went up from 1 to 4.
166
00:10:31,680 --> 00:10:33,650
I have to do a subtraction.
167
00:10:33,650 --> 00:10:39,480
Differences, derivatives, that's
the connection here.
168
00:10:39,480 --> 00:10:41,510
So it's 4 minus 1.
169
00:10:41,510 --> 00:10:42,830
That is 3.
170
00:10:42,830 --> 00:10:50,125
So I would say the
average is 3/1.
171
00:10:50,125 --> 00:10:54,120
172
00:10:54,120 --> 00:10:56,620
But that's not calculus.
173
00:10:56,620 --> 00:11:00,160
Calculus is looking at
the instant thing.
174
00:11:00,160 --> 00:11:03,633
And let me begin at this
instant, at that point.
175
00:11:03,633 --> 00:11:07,090
176
00:11:07,090 --> 00:11:11,750
What does the slope look like
to you at that point?
177
00:11:11,750 --> 00:11:14,840
At at x equals 0, here's
x equals 0, and
178
00:11:14,840 --> 00:11:16,120
here's y equals 0.
179
00:11:16,120 --> 00:11:19,380
We're very much 0.
180
00:11:19,380 --> 00:11:26,600
You see it's climbing, but at
that moment, it's like it just
181
00:11:26,600 --> 00:11:30,300
started from a red
light, whatever.
182
00:11:30,300 --> 00:11:32,940
The speed is 0 at that point.
183
00:11:32,940 --> 00:11:37,130
And I want to say
the slope is 0.
184
00:11:37,130 --> 00:11:38,860
That's flat right there.
185
00:11:38,860 --> 00:11:39,800
That's flat.
186
00:11:39,800 --> 00:11:44,350
If I continued the curve, if I
continued the x squared curve
187
00:11:44,350 --> 00:11:47,030
for x negative, it would be the
same as for x positive.
188
00:11:47,030 --> 00:11:49,620
Well, it doesn't look
very the same.
189
00:11:49,620 --> 00:11:51,680
Let me improve that.
190
00:11:51,680 --> 00:11:55,440
It would start up the same way
and be completely symmetric.
191
00:11:55,440 --> 00:12:00,650
Everybody sees that, at
that 0 position, the
192
00:12:00,650 --> 00:12:04,050
curve has hit bottom.
193
00:12:04,050 --> 00:12:06,710
Actually, this will
be a major, major
194
00:12:06,710 --> 00:12:08,420
application of calculus.
195
00:12:08,420 --> 00:12:12,960
You identify the bottom of a
curve by the fact that the
196
00:12:12,960 --> 00:12:14,600
slope is 0.
197
00:12:14,600 --> 00:12:15,540
It's not going up.
198
00:12:15,540 --> 00:12:17,470
It's not going down.
199
00:12:17,470 --> 00:12:19,250
It's 0 at that point.
200
00:12:19,250 --> 00:12:23,830
But now, what do I mean
by slope at a point?
201
00:12:23,830 --> 00:12:27,000
Here comes the new idea.
202
00:12:27,000 --> 00:12:30,570
If I go way over to 1,
that's too much.
203
00:12:30,570 --> 00:12:32,540
I just want to stay
near this point.
204
00:12:32,540 --> 00:12:36,140
I'll go over a little
bit, and I call that
205
00:12:36,140 --> 00:12:39,030
little bit delta x.
206
00:12:39,030 --> 00:12:44,300
So that letter, delta,
signals to our
207
00:12:44,300 --> 00:12:48,660
minds small, some small.
208
00:12:48,660 --> 00:12:52,230
And actually, probably smaller
than I drew it there.
209
00:12:52,230 --> 00:12:54,620
And then, so what's
the average?
210
00:12:54,620 --> 00:12:56,780
I'd like to just find
the average
211
00:12:56,780 --> 00:13:00,310
speed, or average slope.
212
00:13:00,310 --> 00:13:06,040
If I go over by delta x, and
then how high do I go up?
213
00:13:06,040 --> 00:13:08,240
Well, the curve is y
equals x squared.
214
00:13:08,240 --> 00:13:10,420
So how high is this?
215
00:13:10,420 --> 00:13:20,120
So the average is up first,
divided by across.
216
00:13:20,120 --> 00:13:22,750
Across is our usual delta x.
217
00:13:22,750 --> 00:13:25,830
How far did it go up?
218
00:13:25,830 --> 00:13:30,530
Well, if our curve is x squared
and I'm at the point,
219
00:13:30,530 --> 00:13:32,830
delta x, then it's
delta x squared.
220
00:13:32,830 --> 00:13:35,360
221
00:13:35,360 --> 00:13:42,011
That's the average over the
first piece, over short, over
222
00:13:42,011 --> 00:13:46,760
the first piece of the curve.
223
00:13:46,760 --> 00:13:49,342
Out is-- from here
out to delta x.
224
00:13:49,342 --> 00:13:50,592
OK.
225
00:13:50,592 --> 00:13:52,160
226
00:13:52,160 --> 00:13:57,920
Now, again, that's still only
an average, because delta x
227
00:13:57,920 --> 00:13:59,480
might have been short.
228
00:13:59,480 --> 00:14:01,370
I want to push it to 0.
229
00:14:01,370 --> 00:14:06,680
That's where calculus comes
in, taking the limit of
230
00:14:06,680 --> 00:14:09,930
shorter and shorter and shorter
pieces in order to
231
00:14:09,930 --> 00:14:17,120
zoom in on that instant, that
moment, that spot where we're
232
00:14:17,120 --> 00:14:19,630
looking at the slope, and where
we're expecting the
233
00:14:19,630 --> 00:14:22,500
answer is 0, in this case.
234
00:14:22,500 --> 00:14:26,270
And you see that the average,
it happens to
235
00:14:26,270 --> 00:14:28,300
be especially simple.
236
00:14:28,300 --> 00:14:31,180
Delta x squared over delta
x is just delta x.
237
00:14:31,180 --> 00:14:38,710
So the average slope
is extremely small.
238
00:14:38,710 --> 00:14:43,140
And I'll just complete
that thought.
239
00:14:43,140 --> 00:14:55,040
So the instant slope-- instant
slope at 0, at x equals 0, I
240
00:14:55,040 --> 00:14:56,860
let this delta x get smaller
and smaller.
241
00:14:56,860 --> 00:15:01,440
I get the answer is 0, which
is just what I expected it.
242
00:15:01,440 --> 00:15:04,520
And you could say, well,
not too exciting.
243
00:15:04,520 --> 00:15:07,110
But it was an easy one to do.
244
00:15:07,110 --> 00:15:10,400
It was the first time that we
actually went through the
245
00:15:10,400 --> 00:15:12,260
steps of computing.
246
00:15:12,260 --> 00:15:15,180
This is a, like, a delta y.
247
00:15:15,180 --> 00:15:18,440
This is the delta x.
248
00:15:18,440 --> 00:15:23,140
Instead of 3/1, starting
here I had delta x
249
00:15:23,140 --> 00:15:24,290
squared over delta x.
250
00:15:24,290 --> 00:15:25,520
That was easy to see.
251
00:15:25,520 --> 00:15:26,730
It was delta x.
252
00:15:26,730 --> 00:15:31,180
And if I move in closer, that
average slope is smaller and
253
00:15:31,180 --> 00:15:35,670
smaller, and the slope
at that instant is 0.
254
00:15:35,670 --> 00:15:37,970
No problem.
255
00:15:37,970 --> 00:15:43,340
The travel, the climbing
began from rest, but
256
00:15:43,340 --> 00:15:45,220
it picked up speed.
257
00:15:45,220 --> 00:15:48,300
The slope here is
certainly not 0.
258
00:15:48,300 --> 00:15:50,200
We'll find that slope.
259
00:15:50,200 --> 00:15:52,740
We need now to find the
slope at every point.
260
00:15:52,740 --> 00:15:55,210
OK.
261
00:15:55,210 --> 00:15:57,810
That's a good start.
262
00:15:57,810 --> 00:16:04,170
Now I'm ready to find the
slope at any point.
263
00:16:04,170 --> 00:16:09,890
Instead of just x equals 0,
which we've now done, I better
264
00:16:09,890 --> 00:16:18,920
draw a new graph of the same
picture, climbing up.
265
00:16:18,920 --> 00:16:23,900
Now I'm putting in a little
climb at some point x here.
266
00:16:23,900 --> 00:16:26,085
I'm up at a height, x squared.
267
00:16:26,085 --> 00:16:30,590
268
00:16:30,590 --> 00:16:33,310
I'm at that point
on the climb.
269
00:16:33,310 --> 00:16:37,410
I'd like to know the slope
there, at that point.
270
00:16:37,410 --> 00:16:40,110
How am I going to do it?
271
00:16:40,110 --> 00:16:45,880
I will follow this as the
central dogma of calculus, of
272
00:16:45,880 --> 00:16:50,810
differential calculus, function
1 to function 2.
273
00:16:50,810 --> 00:16:56,990
Take a little delta x, go as
far as x plus delta x.
274
00:16:56,990 --> 00:16:59,860
That will take you to a higher
point on the curve.
275
00:16:59,860 --> 00:17:05,230
That's now the point x plus
delta x squared, because our
276
00:17:05,230 --> 00:17:09,730
curve is still y equals
x squared in this
277
00:17:09,730 --> 00:17:11,919
nice, simple parabola.
278
00:17:11,919 --> 00:17:13,810
OK.
279
00:17:13,810 --> 00:17:19,829
So now I you look at distance
across and distance up.
280
00:17:19,829 --> 00:17:25,210
So delta y is the change up.
281
00:17:25,210 --> 00:17:30,360
Delta x is the across.
282
00:17:30,360 --> 00:17:35,500
And I have to put
what is delta y.
283
00:17:35,500 --> 00:17:38,310
I have to write in,
what is delta y?
284
00:17:38,310 --> 00:17:40,280
It's this distance up.
285
00:17:40,280 --> 00:17:44,700
It's x plus delta x squared.
286
00:17:44,700 --> 00:17:49,120
That's this height minus
this height.
287
00:17:49,120 --> 00:17:51,610
I'm not counting this
bit, of course.
288
00:17:51,610 --> 00:17:53,190
It's that that I want.
289
00:17:53,190 --> 00:17:58,040
That's the delta y,
is this piece.
290
00:17:58,040 --> 00:18:03,600
So it's up to this, subtract
x squared.
291
00:18:03,600 --> 00:18:05,780
That's delta y.
292
00:18:05,780 --> 00:18:07,470
That's important.
293
00:18:07,470 --> 00:18:11,520
Now I divide by delta x.
294
00:18:11,520 --> 00:18:13,820
This is all algebra now.
295
00:18:13,820 --> 00:18:18,320
Calculus is going to come in
a moment, but not yet.
296
00:18:18,320 --> 00:18:20,160
For algebra, what do I do?
297
00:18:20,160 --> 00:18:21,870
I multiply this out.
298
00:18:21,870 --> 00:18:23,520
I see that thing squared.
299
00:18:23,520 --> 00:18:26,160
I remember that x is squared.
300
00:18:26,160 --> 00:18:29,190
And then I have this
times this twice.
301
00:18:29,190 --> 00:18:34,133
2x delta x's, and then I
have delta x squared.
302
00:18:34,133 --> 00:18:36,750
303
00:18:36,750 --> 00:18:38,820
And then I'm subtracting
x squared.
304
00:18:38,820 --> 00:18:47,080
So that's delta y written
out in full glory.
305
00:18:47,080 --> 00:18:53,080
I wrote it out because
now I can simplify by
306
00:18:53,080 --> 00:18:55,400
canceling the x squared.
307
00:18:55,400 --> 00:18:58,200
I'm not surprised.
308
00:18:58,200 --> 00:19:01,840
Now, in this case, I can
actually do the division.
309
00:19:01,840 --> 00:19:04,420
Delta x is just there.
310
00:19:04,420 --> 00:19:06,520
So it leaves me with a 2x.
311
00:19:06,520 --> 00:19:08,810
Delta x over delta x is 1.
312
00:19:08,810 --> 00:19:11,810
And then here's a delta x
squared over a delta x, so
313
00:19:11,810 --> 00:19:13,940
that leaves me with
one delta x.
314
00:19:13,940 --> 00:19:17,930
315
00:19:17,930 --> 00:19:21,400
As you get the hang of
calculus, you see the
316
00:19:21,400 --> 00:19:27,590
important things is like this
first order, delta x to the
317
00:19:27,590 --> 00:19:28,680
first power.
318
00:19:28,680 --> 00:19:34,370
Delta x squared, that, when
divided by delta x, gives us
319
00:19:34,370 --> 00:19:38,130
this, which is going
to disappear.
320
00:19:38,130 --> 00:19:39,490
That's the point.
321
00:19:39,490 --> 00:19:48,940
This was the average over a
short but still not instant
322
00:19:48,940 --> 00:19:52,080
range, distance.
323
00:19:52,080 --> 00:19:54,870
Now, what happens?
324
00:19:54,870 --> 00:19:56,130
Now dy/dx.
325
00:19:56,130 --> 00:20:00,180
326
00:20:00,180 --> 00:20:09,470
So if this is short, short over
short, this is darn short
327
00:20:09,470 --> 00:20:11,160
over darn short.
328
00:20:11,160 --> 00:20:18,610
That d is, well, it's
too short to see.
329
00:20:18,610 --> 00:20:23,880
So I don't actually now try
to separate a distance dy.
330
00:20:23,880 --> 00:20:31,350
This isn't a true division,
because it's effectively 0/0.
331
00:20:31,350 --> 00:20:35,360
And you might say, well, 0/0,
what's the meaning?
332
00:20:35,360 --> 00:20:40,620
Well, the meaning of 0/0, in
this situation, is, I take the
333
00:20:40,620 --> 00:20:54,140
limit of this one, which does
have a meaning, because those
334
00:20:54,140 --> 00:20:55,070
are true numbers.
335
00:20:55,070 --> 00:20:58,320
They're little numbers
but they're numbers.
336
00:20:58,320 --> 00:21:07,440
And this was this, so now here's
the big step, leaving
337
00:21:07,440 --> 00:21:11,380
algebra behind, going to
calculus in order to get
338
00:21:11,380 --> 00:21:13,780
what's happening at a point.
339
00:21:13,780 --> 00:21:16,230
I let delta x go to 0.
340
00:21:16,230 --> 00:21:17,510
And what is that?
341
00:21:17,510 --> 00:21:19,900
So delta y over delta
x is this.
342
00:21:19,900 --> 00:21:22,380
What is the dy/dx?
343
00:21:22,380 --> 00:21:28,960
So in the limit, ah,
it's not hard.
344
00:21:28,960 --> 00:21:31,270
Here's the 2x.
345
00:21:31,270 --> 00:21:34,030
It's there.
346
00:21:34,030 --> 00:21:35,570
Here's the delta x.
347
00:21:35,570 --> 00:21:39,280
In the limit, it disappears.
348
00:21:39,280 --> 00:21:44,460
So the conclusion is that
the derivative is 2x.
349
00:21:44,460 --> 00:21:48,330
350
00:21:48,330 --> 00:21:50,000
So that's function two.
351
00:21:50,000 --> 00:21:51,660
That's function two here.
352
00:21:51,660 --> 00:21:53,450
That's the slope function.
353
00:21:53,450 --> 00:21:55,060
That's the speed function.
354
00:21:55,060 --> 00:21:56,390
Maybe I should draw it.
355
00:21:56,390 --> 00:21:59,370
Can I draw it above and then
I'll put the board back up?
356
00:21:59,370 --> 00:22:06,740
So here's a picture of function
2, the derivative, or
357
00:22:06,740 --> 00:22:08,910
the slope, which I
was calling s.
358
00:22:08,910 --> 00:22:12,070
So that's the s function,
against x.
359
00:22:12,070 --> 00:22:16,320
x is still the thing that's
varying, or it could be t, or
360
00:22:16,320 --> 00:22:20,270
it could be whatever
letter we've got.
361
00:22:20,270 --> 00:22:23,710
And the answer was 2x
for this function.
362
00:22:23,710 --> 00:22:28,970
So if I graph it, it starts
at 0, and it climbs
363
00:22:28,970 --> 00:22:32,540
steadily with slope 2.
364
00:22:32,540 --> 00:22:37,184
So that's a graph of s of x.
365
00:22:37,184 --> 00:22:40,460
And for example--
366
00:22:40,460 --> 00:22:45,490
yeah, so take a couple of
points on that graph--
367
00:22:45,490 --> 00:22:50,520
at x equals 0, the slope is 0.
368
00:22:50,520 --> 00:22:55,520
And we did that first. And
we actually got it right.
369
00:22:55,520 --> 00:22:59,680
The slope is 0 at the start,
at the bottom of the curve.
370
00:22:59,680 --> 00:23:04,430
At some other point on the
curve, what's the slope here?
371
00:23:04,430 --> 00:23:08,240
Ha, yeah, tell me
the slope there.
372
00:23:08,240 --> 00:23:12,100
At that point on the curve, an
average slope was 3/1, but
373
00:23:12,100 --> 00:23:15,180
that was the slope of this,
like, you know--
374
00:23:15,180 --> 00:23:19,490
375
00:23:19,490 --> 00:23:21,660
sometimes called a chord.
376
00:23:21,660 --> 00:23:26,040
That's over a big jump of 1.
377
00:23:26,040 --> 00:23:29,190
Then I did it over a small jump
of delta x, and then I
378
00:23:29,190 --> 00:23:34,790
let delta x go to 0, so it was
an instant infinitesimal jump.
379
00:23:34,790 --> 00:23:39,630
So the actual slope, the way to
visualize it is that it's
380
00:23:39,630 --> 00:23:41,560
more like that.
381
00:23:41,560 --> 00:23:45,170
That's the line that's
really giving the
382
00:23:45,170 --> 00:23:47,860
slope at that point.
383
00:23:47,860 --> 00:23:49,240
That's my best picture.
384
00:23:49,240 --> 00:23:54,920
It's not Rembrandt,
but it's got it.
385
00:23:54,920 --> 00:23:57,040
And what is the slope
at that point?
386
00:23:57,040 --> 00:24:00,540
Well, that's what our
calculation was.
387
00:24:00,540 --> 00:24:02,410
It found the slope
at that point.
388
00:24:02,410 --> 00:24:11,250
And at the particular point, x
equals 1, the height was 2.
389
00:24:11,250 --> 00:24:12,570
The slope is 2.
390
00:24:12,570 --> 00:24:17,720
The actual tangent line
is only-- is there.
391
00:24:17,720 --> 00:24:18,400
You see?
392
00:24:18,400 --> 00:24:20,730
It's up.
393
00:24:20,730 --> 00:24:24,350
Oh, wait a minute.
394
00:24:24,350 --> 00:24:27,950
Yeah, well, the slope is 2.
395
00:24:27,950 --> 00:24:31,230
I don't know.
396
00:24:31,230 --> 00:24:34,510
This goes up to 3.
397
00:24:34,510 --> 00:24:41,300
It's not Rembrandt, but
the math is OK.
398
00:24:41,300 --> 00:24:43,070
So what have we done?
399
00:24:43,070 --> 00:24:49,130
We've taken the first small step
and literally I could say
400
00:24:49,130 --> 00:24:52,290
small step, almost a play on
words because that's the
401
00:24:52,290 --> 00:24:55,180
point, the step is so small--
402
00:24:55,180 --> 00:24:59,170
to getting these great
functions.
403
00:24:59,170 --> 00:25:06,110
Before I close this lecture, can
I draw this pair, function
404
00:25:06,110 --> 00:25:14,630
1 and function 2, and just see
that the movement of the
405
00:25:14,630 --> 00:25:16,650
curves is what we
would expect.
406
00:25:16,650 --> 00:25:23,710
So let me, just for one more
good example, great example,
407
00:25:23,710 --> 00:25:26,510
actually, is let me draw.
408
00:25:26,510 --> 00:25:28,990
Here goes x.
409
00:25:28,990 --> 00:25:32,830
In fact, maybe I already drew
in the first letter, lecture
410
00:25:32,830 --> 00:25:37,890
that bit out to 90 degrees.
411
00:25:37,890 --> 00:25:41,140
Only if we want a nice formula,
we better call that
412
00:25:41,140 --> 00:25:45,000
pi over 2 radians.
413
00:25:45,000 --> 00:25:46,870
And here's a graph of sine x.
414
00:25:46,870 --> 00:25:48,450
This is y.
415
00:25:48,450 --> 00:25:52,380
This is the function
1, sine x.
416
00:25:52,380 --> 00:25:54,530
And what's function 2?
417
00:25:54,530 --> 00:25:57,210
What can we see about
function 2?
418
00:25:57,210 --> 00:26:00,400
419
00:26:00,400 --> 00:26:01,650
Again, x.
420
00:26:01,650 --> 00:26:04,560
421
00:26:04,560 --> 00:26:06,410
We see a slope.
422
00:26:06,410 --> 00:26:09,160
This is not the same
as x squared.
423
00:26:09,160 --> 00:26:12,230
This starts with a
definite slope.
424
00:26:12,230 --> 00:26:17,690
And it turns out this will be
one of the most important
425
00:26:17,690 --> 00:26:19,480
limits we'll find.
426
00:26:19,480 --> 00:26:24,760
We'll discover that the first
little delta x, which goes up
427
00:26:24,760 --> 00:26:30,610
by sine of delta x, has a slope
that gets closer and
428
00:26:30,610 --> 00:26:34,120
closer to 1.
429
00:26:34,120 --> 00:26:36,440
Good.
430
00:26:36,440 --> 00:26:42,210
Luckily, cosine does start
at 1, so we're OK so far.
431
00:26:42,210 --> 00:26:45,120
Now the slope is dropping.
432
00:26:45,120 --> 00:26:49,330
And what's the slope at the
top of the sine curve?
433
00:26:49,330 --> 00:26:51,810
It's a maximum.
434
00:26:51,810 --> 00:26:56,710
But we identify that by the
fact that the slope is 0,
435
00:26:56,710 --> 00:27:01,690
because we know the thing is
going to go down here and go
436
00:27:01,690 --> 00:27:02,780
somewhere else.
437
00:27:02,780 --> 00:27:04,410
The slope there is 0.
438
00:27:04,410 --> 00:27:07,400
The tangent line
is horizontal.
439
00:27:07,400 --> 00:27:12,980
And that is that point.
440
00:27:12,980 --> 00:27:14,260
It passes through 0.
441
00:27:14,260 --> 00:27:15,980
The slope is dropping.
442
00:27:15,980 --> 00:27:18,030
So this is the slope curve.
443
00:27:18,030 --> 00:27:22,200
And the great thing is that
it's the cosine of x.
444
00:27:22,200 --> 00:27:26,090
And what I'm doing now is
not proving this fact.
445
00:27:26,090 --> 00:27:28,610
I'm not doing my delta x's.
446
00:27:28,610 --> 00:27:33,160
That's the job I have to do
once, and it won't be today,
447
00:27:33,160 --> 00:27:34,445
but I only have to do it once.
448
00:27:34,445 --> 00:27:37,820
449
00:27:37,820 --> 00:27:40,330
But today, I'm just saying
it makes sense
450
00:27:40,330 --> 00:27:42,630
the slope is dropping.
451
00:27:42,630 --> 00:27:46,700
In that first part, I'm going
up, so the slope is positive
452
00:27:46,700 --> 00:27:49,910
but the slope is dropping.
453
00:27:49,910 --> 00:27:52,650
And then, at this point,
it hits 0.
454
00:27:52,650 --> 00:27:54,500
And that's this point.
455
00:27:54,500 --> 00:27:58,730
And then the slope
turns negative.
456
00:27:58,730 --> 00:28:00,110
I'm falling.
457
00:28:00,110 --> 00:28:02,830
So the slope goes negative,
and actually
458
00:28:02,830 --> 00:28:04,420
it follows the cosine.
459
00:28:04,420 --> 00:28:09,240
So I go along here to that
point, and then I can continue
460
00:28:09,240 --> 00:28:13,840
on to this point where
it bottoms out again
461
00:28:13,840 --> 00:28:16,760
and then starts up.
462
00:28:16,760 --> 00:28:19,140
So where is that
on this curve?
463
00:28:19,140 --> 00:28:23,300
Well, I'd better draw a
little further out.
464
00:28:23,300 --> 00:28:27,730
This bottom here
would be the--
465
00:28:27,730 --> 00:28:28,980
This is our pi/2.
466
00:28:28,980 --> 00:28:31,220
467
00:28:31,220 --> 00:28:36,270
This is our pi, 180 degrees,
everybody would say.
468
00:28:36,270 --> 00:28:39,280
469
00:28:39,280 --> 00:28:41,510
So what's happening
on that curve?
470
00:28:41,510 --> 00:28:47,760
The function is dropping, and
actually it's dropping its
471
00:28:47,760 --> 00:28:51,510
fastest. It's dropping its
fastest at that point, which
472
00:28:51,510 --> 00:28:53,640
is the slope is minus 1.
473
00:28:53,640 --> 00:28:57,180
And then the slope is still
negative, but it's not so
474
00:28:57,180 --> 00:29:02,670
negative, and it comes back up
to 0 at 3 pi/2 So this is the
475
00:29:02,670 --> 00:29:05,500
point, 3 pi/2.
476
00:29:05,500 --> 00:29:10,530
And this has come back
to 0 at that point.
477
00:29:10,530 --> 00:29:14,500
And then it finishes the
whole thing at 2 pi.
478
00:29:14,500 --> 00:29:17,920
This finishes up here
back at 1 again.
479
00:29:17,920 --> 00:29:19,170
It's climbing.
480
00:29:19,170 --> 00:29:22,050
481
00:29:22,050 --> 00:29:26,850
All right, climbing, dropping,
faster, slower, maximum,
482
00:29:26,850 --> 00:29:33,070
minimum, those are the words
that make derivatives
483
00:29:33,070 --> 00:29:36,150
important and useful to learn.
484
00:29:36,150 --> 00:29:40,930
And we've done, in detail,
the first of our
485
00:29:40,930 --> 00:29:45,580
great list of functions.
486
00:29:45,580 --> 00:29:46,720
Thanks.
487
00:29:46,720 --> 00:29:48,480
FEMALE SPEAKER: This has been
a production of MIT
488
00:29:48,480 --> 00:29:50,870
OpenCourseWare and
Gilbert Strang.
489
00:29:50,870 --> 00:29:53,140
Funding for this video was
provided by the Lord
490
00:29:53,140 --> 00:29:54,360
Foundation.
491
00:29:54,360 --> 00:29:57,490
To help OCW continue to provide
free and open access
492
00:29:57,490 --> 00:30:00,570
to MIT courses, please
make a donation at
493
00:30:00,570 --> 00:30:02,130
ocw.mit.edu/donate.
494
00:30:02,130 --> 00:30:04,223 | 677.169 | 1 |
Summary of Contents for Texas Instruments TI-85
ALCULATORS Setup When using this Guide, you should always, unless instructed otherwise, use the calculator setup specified below for both the TI-85 and TI-86. ) . Use the following instructions to choose the settings shown in Figure 1. Check MORE...
TI-86 Note: Because appropriate TI-86 computer linking software had not yet been perfected at the time this material was written, TI-86 screens in this Guide appear smaller than the TI- 85 screens. Screens that appear the same on both calculators are shown for the TI-85. Basic Operation You should be familiar with the basic operation of your calculator.
æ ö ç ÷ Calculate ç ÷ 4*15 + 895 è ø (If you wish to clear the home screen, press 3. ANSWER DISPLAY When the denominator of a fraction has no more than three digits, your calculator can provide the answer in fraction form. When an answer is very large or very small, the calculator displays the result in scientific notation.
Chapter 1 Ingredients of Change: Functions and Linear Models & 1.1 Fundamentals of Modeling There are many uses for a function that is entered in the graphing list. Graphing the function in an appropriate viewing window is one of these. Because you must enter all functions on one line (that is, you cannot write fractions and exponents the same way you do on paper) it is very important to have a good understanding of the calculatorÕs order of operations and to use parentheses whenever they are needed.
TI-85/TI-86 Graphing Calculators Remove the lower menu with ZOOM MORE Notice that the graphics screen is blank. TI-85 Press EXIT by ZDECM. TI-86 Press EXIT by ZDECM. ¥ Both xMin and xMax are the settings of the left and right edges of the viewing screen, and yMin and yMax are the settings for the lower and upper edges of the viewing screen.
(Delete all other functions that may be entered in other locations.) Before doing what follows, access the graphics menu with To access the range on the TI-85 (called the window on the TI-86), press . Set xMin to 0 and xMax to 10. (It does not matter what values are set in the yMin and yMax positions.) Press...
TI-86: Evaluating outputs from the home screen indicated above works on the TI-86, advances in the TI-86 technology give you a way to evaluate functions from the home screen using fewer keystrokes than for the TI-85. Type ALPHA...
1.1.7. You can also evaluate functions using the calculatorÕs TABLE. (On the TI-85, the table is accessed with program TABLE.) When you use the table, you can ask for specific output values corresponding to the inputs you enter or generate a list of input values that begin with TblMin and differ by DTbl and their corresponding outputs.
B-12 TI-85/TI-86 Graphing Calculators The message that appears tells you to press to see the output. The output is in the form [ t, v(t) ]. We see that v(85) » $6945. If you had wanted to generate a list of values, starting at a value called TblMin and differing by DTbl, use the AUTO option in the program.
Press ) , type in the x-value(s) at which TABLE the function is to be evaluated, and press You can scroll through the table with , and/or . Unwanted input entries can be cleared with 1.2.2 SOLVING FOR INPUT VALUES equation that you enter in the SOLVER.
TI-85 and with GRAPH RANGE is at the top of the TI-85 screen and the word WINDOW is at the top of the TI-86 screen. Because the only difference in the calculators in this situation is the name that is used, we from this point forward refer to this key for both calculators as ) .
B-16 TI-85/TI-86 Graphing Calculators To graphically find an x-intercept, i.e., a value of x at which the graph crosses the horizontal axis, first press to return the menu to the bottom of the screen. EXIT TI-85 Press MATH TI-86 Press...
On the TI-85, ¥ The TI-85 interprets y composite function f(g(x)), you should substitute g(x) everywhere an x appears in f(x). For instance, if f(x) = x composite function (f On the TI-86, ¥ Enter y ) in y to obtain the composite function (f Both Your calculator will evaluate and graph these constructed functions.
ENTER TI-85 You can find function values by evaluating out- puts on the home screen or using the table. Do not forget to change the calculatorÕs FORMAT setting back to DrawLine when you finish graphing the piecewise function.
After setting the proper horizontal view, you can now use ZFIT to draw a graph of the piecewise function. You can find function values by evaluating outputs on the home screen or using the table. & 1.4 Linear Functions and Models Actual real-world data is used throughout Calculus Concepts.
There are several ways to do this, and the most convenient method is illustrated below. TI-85 Whenever you enter new data in your calculator, you should first delete any previously-entered data using one of the following methods: ¥...
(The boxes may appear a slightly different size with different screen settings.) ¥ Even though the TI-85 generally allows you to call lists by any names you want, you must enter the input data in the list named L using program STPLT.
To graph data on the TI-86: The TI-86 has a built-in command to graph data and autoscale the data window. Press STAT PLOTS screen. (Your screen may not look exactly like this one.) Note: When drawing a graph from the y(x)= list, you may get an error message or see a scatter plot of ÒoldÓ...
B-24 TI-85/TI-86 Graphing Calculators output values are constant. indication that a linear model may be appropriate. Program DIFF is given in the TI-85/TI-86 Appendix. To run the program, press then the -key under the name of the program. Press . If you have not entered the data, stop the...
TI-85 It is possible to enter data while in the statis- tics mode of your calculator. However, the examples in this Guide assume that input data is already en- tered in list L and output data is in list L...
1.4.9 GRAPHING A MODEL scatter plot of the data to verify that the model provides a good fit to the data. TI-85 After you have copied the model to the y(x)= list, run program STPLT to graph the model and the scatter plot on the same screen.
B-28 TI-85/TI-86 Graphing Calculators process with this program, it is better to use data that is not perfectly linear and data for which you do not know the best-fitting line. Before using program LSLINE, clear the y(x)= list and enter your data in lists L Next, draw a scatter plot. | 677.169 | 1 |
Using and Understanding Mathematics A Quantitative Reasoning Approach
9780321227737
ISBN:
0321227735
Edition: 3 Pub Date: 2004 Publisher: Addison-Wesley
Summary: Most students taking this course do so to fulfill a requirement, but the true benefit of the course is learning how to use and understand mathematics in daily life. This quantitative reasoning text is written expressly for those students, providing them with the mathematical reasoning and quantitative literacy skills they' ll need to make good decisions throughout their lives. Common-sense applications of mathematics... engage students while underscoring the practical, essential uses of math.
Bennett, Jeffrey O. is the author of Using and Understanding Mathematics A Quantitative Reasoning Approach, published 2004 under ISBN 9780321227737 and 0321227735. One hundred thirty five Using and Understanding Mathematics A Quantitative Reasoning Approach textbooks are available for sale on ValoreBooks.com, twenty four used from the cheapest price of $1.86, or buy new starting at $21.62
Purchased as new and in great condition. We cannot guarantee the availability of CD/DVD or other resource materials such as access code etc if the book is so described by the [more]
Purch | 677.169 | 1 |
Publications Waiting to be Reviewed/New Publications
The 'Working with Maths' DVD has five x 5-minute clips with young interviewees all filmed in the workplace. They talk about their work, career paths and the relevance of chemistry across a broad range of careers. Interviews include an equity analyst, payroll assistant, chartered accountant, stone mason and computer games software engineer.
Eyes on Math is a unique teaching resource that provides engaging, full-color graphics and pictures with text showing teachers how to use each image to stimulate mathematical teaching conversations around key K-8 concepts. Teachers using the book can download images for projection onto classroom whiteboards or screens. the questions and asnwers will help both students and teachers look more deeply and see the math behind the math!
Curious about quarks, quasers and the fantastic universe around you? Ever wanted to explore mathematical proof? Need some trigonometry fast? Want to swap up physics, chemistry, or learn some new biology? Ever wondered why your scratches itch before you go to sleep? Beautifully illustrated and packed with fascinating and useful information, SCIENCIA is the ultimate one-stop science reference book for inquisitive readers for all ages. Whether you just want to bursh up on what you learnt at school, still are at school, or never went to school, these pages will test you, stretch you, and make you brainier.
Essential Statistics, Regression, and Econometrics aims to help students in an introductory statistics course develop the statistical reasoning they need for econometric. Many students mistakenly believe that statistics courses are too abstract, mathematical, and tedious to be useful or interesting. To demonstrate the power, elegance, and even beauty of statistical reasoning, this textbook provides hundreds of interesting and relevant examples, and discusses not only the uses but also the abuses of statistics. these examples show how statistical reasoning can be used to answer important questions and also to expose the errors-accidental or intentional-that people often make.
Mathematics is everywhere, and this is the secind book Derek Holtin shows how the ordinary can become the extraordinary when viewed through a mathematical prim. be prepared to slice through cubes, lick stamps and fill jugs of water - along the way spot the patterns, make conjectures and see it through to a mathematical result and its proof. here are everyday problems to taunt, delight - and to solve.
Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique.
Each teacher and student brings many identities to the classroom. What is their impact on the student's learning and the teacher's teaching of mathematics? this book invites K-8 teachers to reflect on their own and their studnets' multiple identities. Rich possibilities for learning result when teachers draw on these identities to offer high-quality, equity-based teaching to all studnets.
One Equals Zero! Every number is greater than itself! All triangles are isosceles! Suprised? Welcome to the world of One Equals Zero and Other Mathematical Supirses. In this engaging book of blackline activity masters, all men are bald, mistakes are lucky, and teachers can never spring suprise tests on their students!
The transition from classroom teacher to elementary mathematics specialist is challenging, but the principal can smooth specialist's path by reassuring teachers that the new specialist is there to support them, not judge them the specialised pedagogical content knowledge that you need to teach multiplication and division effectively in grades 3-5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with these computations - not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of multiplication and division. Use the oppertunities that these and similar tasks provide to build on their own understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning.
The wonder of recreational mathematics.... This book is a compilation of 30 articles originally issued as a series entitled "enjoying maths" for the japanese magazine Rikeieno Sugaku (Mathematics for Science).
The book is a collection of 50 original essays contributed by a wide variety of authors. It contains articles by some of the best expositors of the subject (du Sautoy, Singh and Stewart for example) together with entertaining biographical pieces and articles of relevance to our everyday lives (such as Spiegelhalter on risk and Elwes on medical imaging).
This Practical book provides primary teachers and secondary with advice and resources to develop a visual and active approach to teaching mathematics. Our exciting new edition comes with a helpful CD, offering resources and practical activities that make it easy for readers to try out the ideas in the book for themselves. The new edition has: New resource materials, PowerPoint presentions for each chapter, to use in the classroom, a new section in time, specific examples of teaching strategies and lots more ideas for lesson activities.
"Help Children to learn to love the subject...Make mathematics more the mathematics that people need out there in the world" BBC Radio 4's Woman's Hour Why do millions struggle with mathematics and what can teachers do to change that? Jo Boaler has followed the progress of thousands of pupils in two countries ( the UK adn USA), monitoring how they learn maths through their school carers and then following them into adult life. This remarkable research is the foundation of her investigations into the impact that differing maths experiences can have on an enitre generation. Jo Boaler outlines what has gone wrong, identifying the problems facing children in mathematics classrooms today and offers concrete solutions for parents and teachers that will revolutionise children's experiences with maths. "A very interesting book which addresses some common problems found in the maths classroom which have been well researched adn provides positive solutions and practical activities for those interested in trying to encourage students of today to become mathematicians of tomorrow" Times Educational Supplement Online The Elephant in the classroom offers concrete suggestions on ways to teach maths well, and ways to help children in the home, that will offer new and more effective ways of learning maths. This is an exciting way forward, a new approach that teaches children to reason and problem solve; helping all children, even those who think that they are maths failures and that they could never enjoy maths. An indispensable guide and resource for parents, teachers and educationalists, that inspires and enthuses as much as it teaches.
The Essential Guide to Navigating Your First Years of Teaching Secondary Mathematics "Too much advcice for teachers is either to abstract to be useful or consists of cute ideas for tomorrow that offer no lasting support. Wieman and Arbaugh hit the coveted middle ground - practical ideas for teachers drawn from sound principles of learning and teachin. Because their focus is directly on middle and secondary school mathematics, thye have produced a rare practical guide for upper-grade teachers that is easily accessible and rewardingly substantive. Middle and high school math teachers who want to improve their teaching, with the Common Core State Standards in mind, cannot go wrong by reading this book, cover to cover." - James Hiebert University of Delaware Based on classroom observations and interviews with seasoned and beginning teachers, Success from the Start: Your First Years Teaching Secondary Mathematics offers valuable suggestions to improve your teaching and your studnets oppertunities to learn.
In the 1970's Professor Sir Roger Penrose Discovered some amazing tiles. They could fill vast surface to produce beautiful pentagonal patterns at every scale which never repeated. Altair Design is proud to present the world's first Penrose Tilings colouring book. Choose a design. Relax, and look without staring. Slowly, faces, animals, scenes and patterns will appear. Every aperiodic pattern in this pad perfectly overlays every other! Fire up your creativity and enhance your visual imagination!
MyMaths for Key Stage 3
MyMaths for KeyStage 3 is a brand new series that fully addresses the new National Curriculum for KeyStage 3 Mathematics in England. Student Book 1B is for students starting KS3 that already have a secure understanding of upper KS2 topics, allowing them to consolidate their knowledge and progress to KS3 maths standards. MyMaths for Key Stage 3 is the only course to provide: - Coherent progression through KS3, with a 'learn it once and learn it well' philosophy leading to secure knowledge. - A truly differentiated structure so that all levels of ability can access the new curriculum, including all the new topics. - A Clear Approach to attainment with the emphasis on visible progress.
Written by a highly experienced and respected author team, the third edition of STP Mathematics provides complete andcomprehensive coverage of the 2014 Key Stage 3 programme of Study. Maintaining its rigorous and authoritative approach, this fully updated textbook also develops students' problem-solving skills, preparing them for a high level of achievement at key stage 3 leading onto the higher tier at GCSE.
The subject of the Calculus seems a mystery to all but the most numerate of people, but J F Riley writes with a dry humour tat engages the general reader in an informed acquantance with its history. The book describes the trials and tribulations that the topic of motion and therefore variability and change encountered from its beginnings in ancient Greece up to its discovery in the 17th century and the subsequent period of development. It is is a story behind the evolution of the 'algebra of change and shape' we call the Calculus, and about what it is, why we needed it and who made it happen.
It is not the ugly sister that it is often presented as being; it can be the 'Belle of the Ball' if the correct make-up is applied. This book will show you what 'make-up' ypu can slap on the subject to make it alluring for young people, and will hopefully encourage you to dress maths up in the way that best suits you and your pupils. By picking up this little collection of ramblings you have made the first step: you are clearly interested in what you do and want to be better at it. This was exactly how I felt about teaching maths. I realised I had a deficiency, and that only thinking positively about it would start me on the road to being good at it.See if it wors for you too.
The development of children's language and their mathematical understanding takes place from the earliest years. Research evidence suggests that teacher-facilitated 'mathematical talk' in the early years has the potential to stimulate growth in children's understanding of mathematics. It is argued that acquiring the language of mathematics is important to the acquisition of mathematical concepts and to the use and application of mathematics in a variety of situations.
City of Zombies builds speed and confidence with number play and rewards players as their maths improve. Co-operative gameplay encourages players to work together and help each other to win. Players of mixed abilities share learning through a positive play. | 677.169 | 1 |
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic...
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In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also very useful for college students who studied Calculus I, and other students who want to review some linear algebra concepts before studying a second course in linear algebra Course in Linear Algebra: Study Guide for the Undergraduate Linear Algebra Course to your Bookmark Collection or Course ePortfolio
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Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a...
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Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs. The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds mathematical analysis to your Bookmark Collection or Course ePortfolio
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'In this book you find the basic mathematics that is needed by engineers and university students . The author will help you...
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'In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.Topics as Elementary probability calculus, density functions and stochastic processes are illustrated.This book requires knowledge of Calculus 1 and Calculus 2 Introduction to Probability - Probability Examples c-1 to your Bookmark Collection or Course ePortfolio
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This is a free textbook from Bookboon.'This tutorial textbook has been organized into 4 chapters (units) with several...
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This is a free textbook from Bookboon.'This tutorial textbook has been organized into 4 chapters (units) with several individual tutorial lessons within each chapter. As presented in the table of contents, each of the tutorials has been listed separately with its objective and its starting page. For coding purposes: "Tutorial N.M" means that the tutorial is the Mth lesson in chapter N.I attempted to present each of the tutorials as if a person (teacher, tutor) was sitting next to the reader talking each of the concepts through. My goal was to make sure that each of the lessons was fully explained but still fully understandable. Hopefully this goal was met.- description of whom I believe might be interested in using these tutorials…The purpose of this tutorial textbook is to present mathematical skills (algebraic concepts) and their various applications that may be important to students of management (business) science. The applications included should allow readers to view math in a practical setting relevant to their intended careers.'Topics include:Equations, Inequalities & Linear ProgrammingMatrices & Array OperationsQuadratic & Other Special FunctionsMathematics of FinanceAbout the Author Quantitative Analysis - Algebra with a Business Perspective to your Bookmark Collection or Course ePortfolio
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Scat Testing Questions For 4th Grade Math. Answer: All 4th grade students have the opportunity to take the GATE test and their scores are used to determine GATE eligibility. Students must score in the top 2-5% Updated: 2013-01-05 Field Trip Specialist Program include plant and animal species, water quality testing This plan was generated by the Fraction Games for 4th Graders
4th Grade FAQs - Welcome to the Hope.
STAAR UPDATE Score on EOC must be 15% FINAL grade. Quote: TEA does not have the authority to so cumulative could be modified to consist of only 2 tests (Geometry
simple algorithms SIMPLE [Semi-Implicit Method for Pressure-Linked Equations] If a steady-state problem is being solved iteratively, it is not necessary to fully resolve the linear Thanks to everyone replying with ideas and alternate solutions. More efficient ways of solving problems are always welcome, as well as reminders to question my In an earlier post we discussed brute-force attacks on SSH servers, and that got me thinking: why not have a go at implementing our own brute-force search?
Algorithm - Wikipedia, the free.SIMPLE algorithm - Wikipedia, the free. Hi. This is a place to find information about some of the more fundamental algorithms used in computer science. This information is widely available on the net, but Algorithm - Wikipedia, the free.
Algorithm - Simple English Wikipedia, the.
In mathematics and computer science, an algorithm is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated An algorithm is a step-by-step list of directions that need to be followed to solve a problem. The instructions should be simple enough such that each step can be SIMPLE algorithm -- CFD-Wiki, the free.
simple search algorithm
algorithm - Complexity of finding all.
In computational fluid dynamics (CFD), SIMPLE algorithm is a widely used numerical procedure to solve the Navier-Stokes equations. SIMPLE is an acronym for Semi
In general, you will need to set up both auto reply messages for "Inside My Organization" and "Outside My Organization" in order to cover all staff, all students and
09.10.2011 · I didn't want to do this, but it's sort of come down to it. I am taking a little vacation and as such, I won't be able to post for awhile. Since I The Dangers of Out-of-Office Auto-Reply Messages You never know who you're replying to. By Andy O'Donnell, About.com Guide
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AT&T's DriveMode smartphone application can help prevent accidents caused by texting while driving. Sample business email auto reply messagesThe Dangers of Out-of-Office Auto-Reply. Name Name VPIEJ-L Discussion Archives June 1992 ===== Date: Fri, 29 May A client wanted to setup a rule to send an automatic reply to an email address that wasn't being used any longer. The solution was to create an Outlook rule
Atenolol User Reviews for Anxiety by Most. What Is Better Than Atenolol For Anxiety?. Anxiety is a type of mental health disorder involving excessive worry, panic and fear. Atenolol---a medication used to
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by N. A. Bobylev Review
"... the book is a valuable contribution to the literature. It is well-written, self-contained and it has an extensive bibliography, especially with regard to the literature in the Russian language." (Mathematical Reviews, 2001a | 677.169 | 1 |
This video was recorded at Summer School on Computational Topology and Topological Data Analysis, Ljubljana 2013. The main...
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This video was recorded at Summer School on Computational Topology and Topological Data Analysis, Ljubljana 2013. The main goal of the Summer school is to introduce the basics of new and attractive research fields in Computational Topology and Topological Data Analysis to students and young researchers in Mathematics and Computer Science. The school is aimed mainly at Master or early PhD level students, though all are welcome. The Summer school consist of a series of lectures by invited lecturers discussing various topics in Computational Topology. The general orientation of the summer school is towards applications of the methods of Computational Topology, like persistent homology, discrete Morse theory and topological robotics to the solution of specific problems from different areas, like Image Analysis and Bioinformatics, as well as on specific algorithms. For more information please visit Summer School for Ploting Basins of Attraction of Rational Maps and Calculating Their Areas to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Algorithms for Ploting Basins of Attraction of Rational Maps and Calculating Their Areas
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Select this link to open drop down to add material Angles on a ChordInteractive presentation for middle and high school students forming connections between the areas of two-dimensional...
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Interactive presentation for middle and high school students forming connections between the areas of two-dimensional figures. The main link is a PowerPoint show, but I have also included a link for the original ppt file so that others can modify as they see fit. The quiz section only has one question, for example, so that users can decide if, how much, and what type of questions they would like to ask. It would also be very easy for users to make their own worksheets and Google forms for student responses 2D Figures to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Area of 2D Figures
Select this link to open drop down to add material Area of 2D Figures to your Bookmark Collection or Course ePortfolio
The goal for this lesson is to provide students with an understanding of how to find the area of any regular polygon. This is...
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The goal for this lesson is to provide students with an understanding of how to find the area of any regular polygon. This is a discovery-based lesson in which students collaborate with their peers and test ideas using Regular Polygons to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Area of Regular Polygons
Select this link to open drop down to add material Area of Regular Polygons Triangle formed by Common Tangents to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Area of Triangle formed by Common Tangents
Select this link to open drop down to add material Area of Triangle formed by Common Tangents to your Bookmark Collection or Course ePortfolio
This video was recorded at Summer School on Computational Topology and Topological Data Analysis, Ljubljana 2013. For many...
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This video was recorded at Summer School on Computational Topology and Topological Data Analysis, Ljubljana 2013. For many classical algorithmic graph problems, faster algorithms are known for graphs that have additional structure. This short course will survey some important algorithmic techniques for graphs that can be drawn in the plane or other surfaces without crossing edges. The course will introduce several fundamental mathematical tools, including Euler's formula, rotation systems, duality, tree-cotree decompositions, the combinatorial Gauss-Bonnet theorem, homotopy, homology, covering spaces, balanced separators, and treewidth, as well as applications of these tools for computing minimum spanning trees, shortest paths, minimum cuts, and approximation solutions for several NP-hard prob algorithms for surface-embedded graphs to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Basic algorithms for surface-embedded graphs
Select this link to open drop down to add material Basic algorithms for surface-embedded graphs to your Bookmark Collection or Course ePortfolio
This video was recorded at Summer School on Computational Topology and Topological Data Analysis, Ljubljana 2013. Importance...
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This video was recorded at Summer School on Computational Topology and Topological Data Analysis, Ljubljana 2013. Importance of planar graphs and some more general classes of graphs in mathematics, computer science and applications will Beyond Planarity of Graphs to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Beyond Planarity of Graphs
Select this link to open drop down to add material Beyond Planarity of Graphs to your Bookmark Collection or Course ePortfolio
This is a lesson plan following the Instructional Design Template. It allows students the opportunity to explore the ideas...
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This is a lesson plan following the Instructional Design Template. It allows students the opportunity to explore the ideas and concepts of area, using their classroom dimensions as a real world experiment. Additionally, students view a short online video reiterating theating Area of Non-Standard Figures to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Calculating Area of Non-Standard Figures
Select this link to open drop down to add material Calculating Area of Non-Standard Figures to your Bookmark Collection or Course ePortfolio | 677.169 | 1 |
Practical Merchandising Math / Edition 1
Overview practical calculating procedures is indispensable. But don't worry, we're not talking algebra, trigonometry, or calculus—just simple arithmetic you can perform using a calculator.
Practical Merchandising Math helps you teach yourself all the math you need to succeed in the retail industry. You'll learn to calculate markon, markup, and markdown; plan net sales, purchases, and stock turnover; and determine expenses and gross margin. You'll also learn the meanings of important terms and discover how the four retail areas where math is required—buying, selling, expenses, and record-keeping—are interrelated. This easy-to-use guide
Covers all financial considerations relevant to costing and pricing merchandise | 677.169 | 1 |
007728111X
9780077281113
Details about Intermediate Algebra:
Intermediate Algebra offers a refreshing approach to the traditional content of the course. Presented in worktext format, Intermediate Algebra offers a review of problem solving, solving equations in two and three variables, a chapter devoted to functions, polynomials, radicals and complex numbers, factoring and quadratic functions, rational expressions, and inequalities. Other topics include exponential and logarithmic functions and conic sections. The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of developmental level students.
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Rent Intermediate Algebra 2nd edition today, or search our site for Julie textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by McGraw-Hill Science/Engineering/Math. | 677.169 | 1 |
A Friendly Mathematics Competition: Thirty-five Years of Teamwork in Indiana
Rick Gillman, Editor
A Friendly Mathematics Competition tells the story of the Indiana College Mathematics Competition (ICMC) by presenting the problems, solutions, and results of the first 35 years of the ICMC. The ICMC was organized in reaction to the Putnam Exam―its problems were to be more representative of the undergraduate curriculum, and students could work on them in teams. Originally participation was restricted to the small, private colleges and universities of the state, but was later opened up to students from all of the schools in Indiana. The competition was quickly nicknamed the "Friendly" Competition because of its focus on solving mathematical problems, which brought faculty and students together, rather than on the competitive nature of winning. Organized by year, the problems and solutions in this volume present an excellent archive of information about what has been expected of an undergraduate mathematics major over the past 35 years. With more than 245 problems and solutions, the book is also a must buy for faculty and students interested in problem-solving.
Table of Contents
Preface
The Indiana College Mathematics Competition: A Short History
An Update of the History of the ICMC
Exams
Solutions
Index by Problem Type
About the Editor
Rick Gillman is a native Hoosier. He was born in Batesville (near Cincinnati), grew up in Richmond, went to high school in Indianapolis, and to college in Muncie (Ball State University). After a four-year hiatus in Pocatello, Idaho, earning his Doctorate of Arts at Idaho State University, he returned to Indiana to work at Valparaiso University, where he's been for the past 17 years. He has been active in the Indiana Section of the MAA and has served as Student Activities Coordinator, Secretary-Treasurer, and Vice-Chair. In 2001, he received the section's Distinguished Service Award. A combinatorialist by training, he has published papers on a variety of topics, but his real interest is in helping undergraduates to become mathematicians. He mentors student research teams almost every year, resulting in some publications and many students going on to be successful in pure and applied mathematics. | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
This convenient volume offers a popular selection of 100 practice problems — with hints and solutions — for students preparing for undergraduate-level math competitions. The challenging brainteasers will also appeal to anyone interested in problems concerning real numbers, differential equations, integrals, polynomials, sets, and other mathematical topics.
The hints are very helpful and the solutions are easy to follow. Questions drawn from geometry, group theory and linear algebra involve subjects ranging from multivariate integration to finite series to infinite sums and classical analysis. The only prerequisite is a high school-level background in mathematics. Problem-solvers at varying degrees of proficiency will find this treasury of top-notch numerical puzzles an invitation to hone their mathematical skills as well as a source of stimulating entertainment.
Synopsis:
Synopsis:
Popular selection of 100 practice problems — with hints and solutions — for students preparing for undergraduate-level math competitions. Includes questions drawn from geometry, group theory, linear algebra, and other fields.
Synopsis:"Synopsis"
by Ingram,"Synopsis"
by Firebrand,
Popular selection of 100 practice problems — with hints and solutions — for students preparing for undergraduate-level math competitions. Includes questions drawn from geometry, group theory, linear algebra, and other fields.
"Synopsis"
by Firebrand, | 677.169 | 1 |
Synopses & Reviews
Please note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.
Publisher Comments:
This major revision prepares students to succeed on the New York State Math A Regents Exam as it is now given. The book places increased emphasis on use of the graphing calculator, and in line with New York State Regents core curriculum, it shows how given problems can be solved in several different ways. The author also includes new Regents question types dealing, for instance, with motion problems and mathematical systems defined by tables. New contextualized word problems further enhance the presentation. The totally rewritten chapter on problem-solving offers students a core set of strategies that apply to a variety of curriculum-related exercises. In addition to subject review, demonstration examples, and practice exercises with answers, the book includes several complete recent Math A Regents exams with answers.
Synopsis:
Barron's Review Course Series
An ideal companion to high school math textbooks, this major new revision covers all Math A topics prescribed by the New York State Board of Regents.
For Students:
Easy-to-follow topic summaries
Step-by-step demonstration examples
Examples of new Regents question types with answers
New contextualized word problems
Many practice exercises with answers
Helpful problem-solving and graphing calculator approaches
For Teachers:
A valuable lesson planning aid
A valuable source of practice and test questions
This book can be used with Barron's Regents Exam preparation web site | 677.169 | 1 |
Just the Essentials of Elementary Statistics
Succeed in statistics with ELEMENTARY STATISTICS! Including relevant examples, exercises, and applications, this textbook gives you the tools you need to get a good grade in your statistics course. Struggling with a specific concept? Log onto Personal Tutor with SMARTHINKING to get live, one-on-one online tutoring from a statistician who has a copy of the textbook. Video Skillbuilders and StatisticsNow (an online learning tool built around your individual progress that gives you a simple pre-test, and then focuses your learning experience on your studying needs) provide additional online support. Learning to use MINITAB, Excel, and the TI-83/84 graphing calculator is made easy with instructions included in relevant sections throughout the text.
This edition is the first 11 chapters of the parent book ELEMENTARY STATISTICS, 10THe | 677.169 | 1 |
You are here
Discrete Mathematics
Edition:
5
Publisher:
Prentice Hall
Number of Pages:
612
Price:
108.20
ISBN:
9780130652478
Discrete math used to be an advanced undergraduate subject, but it has migrated earlier in the curriculum and is often taught at the freshman or sophomore level today. These courses serve both math majors and computer science majors. The present text is slanted towards mathematics, although it gives heavy weight to algorithms and their analysis. At the authors' institution (University of Oregon) the corresponding course is given to math majors in their freshman year and, in addition to providing subject matter, acts as a bridge to abstract mathematics course.
The exposition is slanted heavily towards examples rather than theories or methods. A typical section would introduce a couple of concepts, talk about the kinds of problems that use these, and then launch into half a dozen or a dozen examples. In the Preface (p. xii) the authors say, "We have always believed that students at this level learn best from examples, so we have added examples to the large number already present and have revised others, all to encourage students to read the book." The examples are very well chosen and usually deal with serious mathematical problems rather than contrived ones. The exercises range from simple to moderately difficult, and tend toward numerical examples of things discussed in the body. There are answers and hints for the odd-numbered problems in the back of the book; most of these are brief.
There is not a lot of hand-holding, and it is not a cookbook where you can look up how to apply particular methods or solve particular problems — you have to study the examples.
The "bridge" part is fairly modest. Chapter 2 is an introduction to logic, with a lot of information about the structure of proofs woven in. The Preface says (p. xi), "One of our main goals is the development of mathematical maturity. Our presentation starts with an intuitive approach that becomes more and more rigorous as the students' appreciation for proofs and their skill at building them increase." There's only a modest amount of proving in this book, both in the body and in the exercises. I thought the proofs themselves did not become any more rigorous as the book progressed, but the difficulty of the proofs and the number of things that are proved do increase.
Very Good Feature: the treatment of group theory emphasizes its combinatorial uses. The book includes Burnside's Lemma (p. 477), although not labeled as such.
Very Interesting Feature: mathematical induction is explained using while loops and loop invariants rather than ladders or steps.
Although this is a fifth edition, the book has not been revised since 2003 and the publisher may be letting it approach the end of its life. The Preface (p. xiii) refers to a Companion Website, which seems not to exist. The amount of supplemental material is small by the standards of today's beginning undergraduate texts, consisting of an instructor's solutions manual (in print form). The review copy I received seems to be a black-and-white reprinting of a color book; the things that you would expect to be in color appear in a dithered gray.
The book seems to be pitched lower than most of its competition, but I think it is a good choice for a freshman or sophomore course. The examples provide an accessible look at a great deal of real mathematics. The dominant text in this field is probably Rosen's Discrete Mathematics and its Applications, but that's a much more difficult (and expensive) book. Despite the preponderance of examples in the present book, it is not very similar to Lipschutz & Lipson's Schaum's Outline of Discrete Mathematics; the present book has much better explanations and examples. | 677.169 | 1 |
Examining the pioneering ideas, works, and applications that have made math the language of science, Mathematics and the Laws of Nature looks at the many ways in which so-called ''pure'' math has been used in the applied sciences. For example, the volume explores how mathematical theories contributed to the development of Kepler's laws of planetary... more...
Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries,... | 677.169 | 1 |
Ability to
1. write working Maple code
2. write typeset text
3. work independently and collaboratively on a small mathematical project
4. present the results of a small mathematical project
5. deliver an oral presentation | 677.169 | 1 |
Lockwood, CA StatisticsIt begins with a review of advanced Algebra skills, and then advanced graphing. Understanding types of functions and how to quickly sketch them is essential to became competent in Calculus. PreCalculus also expects students to learn when and how to apply their graphing skills to practical application problems. | 677.169 | 1 |
Product Description
A welcome addition to Saxon's curriculum line, Saxon Geometry is the perfect solution for students and parents who prefer a dedicated geometry course...yet want Saxon's proven methods!
Presented in the familiar Saxon approach of incremental development and continual review, topics are continually kept fresh in students' minds. Covering triangle congruence, postulates and theorems, surface area and volume, two-column proofs, vector addition, and slopes and equations of lines, Saxon features all the topics covered in a standard high school geometry course. Two-tone illustrations help students really "see" the geometric concepts, while sidebars provide additional notes, hints, and topics to think about. Parents will be able to easily help their students with the solutions manual, which includes step-by-step solutions to each problem in the student book; and quickly assess performance with the test book (test answers included). Tests are designed to be administered after every five lessons after the first ten.
Please Note: This is the third printing and errors to date have been corrected.
The reason this book is unlike the past home school versions is because it is now Common Core alligned. And this after claiming the homeschool versions of Saxon would remain independent. Shame on you! No further explanation needed........
We've used Saxon Math. We love Saxon even though it has challenging questions. Saxon has always been very user friendly as far as explaining a concept. This book is not anything like the previous Saxon books we have used. It's difficult to understand. My son spends hours working on the practice problems and ends up with half incorrect. Don't waste your time or money on this book.
We began using this text for the first time this year at our co-op after using Saxon for Alg. I and Alg. II. Of nine students, five have dropped within the first five weeks due to frustrations with the text. This is not the Saxon I've loved and heartily endorsed. The questions are confusing and take forever to wade through (yes, we're using the corrected version). I would work through the lesson with my daughter and then she'd spend an hour doing the problems, miss 50-75% of them, and then we'd spend an hour correcting the lesson. It was with great relief we fled to a different curriculum that she is flying through. BTW, the Saxon tests are a breeze, so she obviously learned something, but we don't have 2+ hours to spend on math each day.
This was the best next step for my high-schooler. We've always used Saxon math and wanted to continue into high school. It's right on target and meets our needs perfectly. CBD was also the obvious choice of where to buy it as not only are they competitive on pricing, but the customer service is excellent. Thanks CBD for helping with all our homeschool needs.
Ask Christianbook
|
Q: What calculator is needed for the Saxon Geometry?
A:
This curriculum requires a graphing calculator.
Q: errors in Geomtery? I am hesitant to buy Saxon geometry as the Algebra half had many errors in the solution manual. Please could you tell me whether there are any errors in the geometry course as there have been complaints made on the reviews. Have the errors been corrected? Thank you.
A:
In the first print run there were some errors in this curriculum. These have been corrected and we have not heard of any problems for quite some time.
Q: geometry workbooks. Whats the difference between the student workbook and the adapted workbook, besides the number of pages?
A:
The Geometry course doesn't have either a Student Workbook or Adapted Workbook.
Q: when to study Geometry? When should a high school student study geometry? Is it after Algebra 1 or Algebra 2 Saxon math?Thank you
A:
If your student is required to complete a separate Geometry course, Saxon Geometry can be taken either between Algebra 1 and Algebra 2 or after Algebra 2. If not, the heart of the geometry course is embedded in Saxon's Algebra 2 and Advanced Math. Students who complete Algebra 2 have taken the equivalent of one semester in geometry, but they would need to complete Advanced Math in order to complete one full year of Euclidean geometry | 677.169 | 1 |
Matrices:
1 Matrix- A system or set of elements arranged in a rectangular form of array is called a matrix. 2 Order of matrix: If a matrix A has m rows & n columns then A is of order m x n .
The number of rows is written first and then number of columns . Horizontal line is row & vertical line is columns 3 Types of matrices : A matrix A = (aij)mxn
A matrix A = (aij)mxn over the field of cimplex number is said to be
4 Trace of a matrix: Sum of the elements in the principal diagonal is called the trace of a matrix.
trace (A ± B) = trace A ± trace B
trace kA = k trace A
trace A = trace AT
trace In = n when In is identity matrix.
trace AB ¹ trace A trace B. 5 Addition & subtraction of matrices : If a and B are two matrices each of order same, then A+B (or A-B) is defined and is obtained by adding (or subtracting) each element of B form corresponding element of A 6 Multiplication of a matrix by a scalar:
KA = K(aij)mxn = (Ka)mxn where K is constant.
Properties:
(i) K(A+B) = KA + KB
(ii) (K1 k2)A = K1(K2A)=K2(K1A)
(iii) (K1 + K2)A = K1A + K2A 7 Multiplication of matrices: Two matrices A & B can be multiplied only if the number of columns A is same as the number of rows in B. Properties:
(i) In general matrix multiplication is not commutative i.e. AB ¹ BA .
(ii) A(BC) = (AB)C [ Associative law]
(iii) A.(B+C) = AB + AC [ Distributive law]
(iv) If AB = AC Þ B = C
(v) If AB = 0, then it is not necessary A = 0 or B =0
(vi) AI = A = IA
(vii) ,atrix multiplication is commutative for + ve integral i.e. Am+1 = Am A = AAm 8 Transpose of a matrix:
A' or AT is obtained by interchanging rows into columns or columns into rows
Properties:
(i) (AT)T = A
(ii) (A ± B)T = AT± BT
(iii) (AB)T = BTAT
(iv) (KA)T = KAT
(v) IT = I 9 Some special cases of square matrices: A square matrix is called
(i) Orthogonal matrix : if AAT = In = ATA
(ii) Idempotent matrix: if A2 = A
(iii) Involuntary matrix : if A2 = I or A-1 = A
(iv) Nilpotent matrix : if $ p Î N such that Ap = 0
(v) Hermit an matrix : if Aq = A i.e. aij = `aji
(vi) Skew- Hermit an matrix: if A = - Aq
Determinant:
1 minor & cofactor: If A = (aij)3 x 3 then minor of a11 is
cofactor of an element aij is denoted by Cij or Fij and equal to (-1)i+j Mij
or Cij = Mij, if i = j =- Mij, if i ¹ j
Note :
|A| = a11 F11 + a12 F12 + a13 F13 and a11 F21 + a12 F22 + a13 F23 = 0 2 Determinant: if A is a square matrix then determinant of matrix is denoted by det A or |A|.
Expansion of determinant of order 3 x 3
Propertes:
(i) |AT| = |A|
(ii) By interchanging two rows (or columns), value of determinant differ by –ve sign.
(iii) If two rows (or columns) are identical then |A| = 0
(iv) |KA|=Kn det A, A is matrix of order n x n
(v) If same multiple of elements of any row (or column) of a determinant are added to the corrsponding elements of any other row (or column), then the value of the new determinant remain unchanged .
(vi) Determinant of :
(a) A nilpotent matrix is 0.
(b) An orthogonal matrix is 1 or -1
(c) A unitary matrix is of modulus unity.
(d) A Hermitian matrix is purely real.
(e) An identity matrix is one i.e. |In| = 1, where In is a unit matrix of order n.
(f) A zero matrix is zero i.e. |0n| = 0 where 0n is a zero matrix of order n
(g) A diagonal matrix = product of its diagonal elements.
(h) Skew symmetric matrix of odd order is zero. 3 Multiplication of two determinants:
Multiplication of two second order determinants is defined as follows.
If order is different then for their multiplication, express them firstly in the same order. | 677.169 | 1 |
Contact Information
Related Links
Course Delivery Options
The Inver Hills Math department offers many different options for how a math course
is taught to appeal to the many different needs of our students. Click below to find
out more about the following course delivery options:
Traditional:
These courses are taught in a typical traditional style with in-class lectures that
meet anywhere from one to five days per week depending on the course. Almost all math
courses at Inver Hills are available in a traditional format.
Hybrid:
These courses are web-supplemented. You will meet in-class a reduced amount of time,
and would be expected to use math software to do homework, take quizzes and/or tests
at the discretion of the instructor. Some instruction would be given via video and
software. Experience with Microsoft Windows is expected. Math courses with a section
number of 61 are available in a hybrid format.
Online:
An online course is the same as its traditional course equivalent, however it is presented
fully online, without meeting on-campus. It is recommended that students be on-time,
motivated, independent learners able to use videos, software, and online resources
for instruction, completing weekly assignments, and taking paper-pencil exams on campus
(or prearranged location). Off-campus Internet access is strongly recommended. Experience
with Microsoft Windows is expected. Refer to your instructor's website to learn more
information about what will be required of you. Math courses with a section number
of 98 or 99 are available in an online format.
Accelerated/Combined:
Math 780 is a combined course that allows students the ability to complete both Math 740
and Math 840 in one semester. Math 880 is a combined course that allows students the
ability to complete both Math 840 and Math 940 in one semester. They are both web
supplemented courses with reduced class time meant as an accelerated review for students
who are highly motivated, good independent learners, and have some basic computer
skills; and for most students it will require a minimum of 16 hours of work per week
outside of class. Students will be expected to complete assignments online and some
paper-pencil tests.
Tutors Linked to Classes (TLCs):
Math courses with Tutors Linked to Classes(TLCs) have tutors who sit in on classes
and offer weekly workshops where students receive additional instruction to help master
course content and develop learning strategies to successfully pass the course. | 677.169 | 1 |
What is taught in the Math 180 UIC class?
A:
Quick Answer
University of Illinois at Chicago's Math 180 class covers Calculus I. The course is a requirement to earn a Bachelor of Science degree in mathematics, the teaching of mathematics or mathematics and computer science. It is also required for minor degrees in mathematics or mathematics and computer science.
Keep Learning
The Math 180 Calculus I UIC course uses chapters 2 to 5 in the textbook "Calculus: Early Transcendentals" by William Briggs and Lyle Cochran. The second chapter covers the ideas, definitions and techniques for computing limits. The third chapter discusses differentiation, product and quotient rules, the chain rule, and derivatives of trigonometric functions, inverse trigonometric functions and logarithmic and exponential functions. The fourth chapter further discusses derivatives, as well as maxima and minima, graphing functions, optimization problems, linear approximation and differentials, the mean value theorem, L'Hopital's rule and anti-derivatives. The fifth chapter covers approximating areas under curves, definite integrals, the fundamental theorem of calculus, working with integrals and the substitution rule.
Students are expected to read chapters of the textbook before attending the class meetings. Both written and online homework is assigned. To access online homework, students need to create a MyMathLab account. Though basic calculators are required for some homework assignments, they are not allowed during exams. The final grade is a combination of points from homework, quizzes, hour-long exams and the final exam.
Related Questions
A nonlinear function in math creates a graph that is not a straight line, according to Columbia University. Three nonlinear functions commonly used in business applications include exponential functions, parabolic functions and demand functions. Quadratic functions are common nonlinear equations that form parabolas on a two-dimensional graph.
A math extrapolate formula is an equation used to predict the value of the dependent variable from an independent variable not found within the range of data. An example of such a formula is y=2x+5, when the range of values for x is normally between 0 and 10. If the value of x is 20, it can still be plugged into the equation to find that y=2(20)+5=45.
The most direct way to get expert-level help on math topics is to ask an expert - a professor, researcher, or strong student. Asking experts individually is not very efficient, so asking an expert-level question on a dedicated website, such as Math.StackExchange.com, usually yields quicker results. | 677.169 | 1 |
Summary
This manual provides detailed and complete solutions to the odd-numbered exercises and test questions in the text. This gives you the information you need to truly understand how these problems are solved. | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
The use of software packages to solve mathematical problems is becoming increasingly popular. This comprehensive book illustrates how Mathcad can be used to solve many mathematical tasks. It also provides the mathematical background for the Mathcad package. Practical Use of Mathcad contains many solutions to basic mathematical tasks for engineering and natural science. It can be used both as a reference and tutorial manual for lecturers and students, and as a practical manual for engineers mathematicians and computer scientists. The latest version of Mathcad V.8 Professional for Windows 95/98 is used throughout.
Synopsis:
Synopsis:
This comprehensive text illustrates how Mathcad can be used to solve many mathematical tasks. It also provides the mathematical background for the Mathcad package.
"Synopsis"
by Ingram,"Synopsis"
by Gardners,
This comprehensive text illustrates how Mathcad can be used to solve many mathematical tasks. It also provides the mathematical background for the Mathcad package | 677.169 | 1 |
This course is part one of a pre-calculus sequence that provides
an extensive study of functions and their inverses modeled algebraically,
numerically and graphically. Specific functions include exponential,
logarithmic, polynomial and power functions. Modeling real world applications
is emphasized. | 677.169 | 1 |
Summary: This is an introductory-level algorithm text. It includes worked-out examples and detailed proofs. Presents Algorithms by type rather than application.
Structures material by techniques employed, not by the application area, so students can progress from the underlying abstract concepts to the concrete application essentials.
Begins with a compact, but complete introduction to some necessary math, and also includes a long introduction to proofs by contradiction and mathematical induction. This serves to fill the gaps that many undergraduates have in their mathematical knowledge.
Gives a paced, thorough introduction to the analysis of algorithms, and uses coherent notation and unusually detailed treatment of solving recurrences.
Includes a chapter on probabilistic algorithms, and an introduction to parallel algorithms, both of which are becoming increasingly important.
Approaches the analysis and design of algorithms by type rather than by application. ...show less50 +$3.99 s/h
Good
Nettextstore Lincoln, NE
199548 +$3.99 s/h
VeryGood
Time For Books Clermont, FL
0133350681 Very Nice Copy--SPEEDY SHIPPING/100% Money BACK Guarantee!
$18.65 +$3.99 s/h
Good
Brit Books Buckingham, UNITED KINGDOM
08/10/199583 +$3.99 s/h
Good
worldofbooks Goring-By-Sea, UNITED KINGDOM
1995 Hard cover Good. The book has been read but remains in clean condition. All pages are intact and the cover is intact. Some minor wear to the spine. Trade paperback (US). Glued binding. Cloth ov...show moreer boards. 52462 | 677.169 | 1 |
04718490Discrete Mathematics With Algorithms
This first-year course in discrete mathematics requires no calculus or computer programming experience. The approach stresses finding efficient algorithms, rather than existential results. Provides an introduction to constructing proofs (especially by induction), and an introduction to algorithmic problem-solving. All algorithms are presented in English, in a format compatible with the Pascal programming language. Contains many exercises, with answers at the back of the book (detailed solutions being supplied for difficult problems | 677.169 | 1 |
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This math lesson from Illuminations helps students understand rational functions. The material uses the real-world problem. Students will write rational functions that model problem situations and use rational functions...
This geometry lesson from Illuminations uses the model of the orbits of Mars and Earth relative to the sun to illustrate parametric equations. As an interdisciplinary learning activity, the material may be used in...
This algebra lesson from Illuminations helps students develop their understanding of mathematical functions and modeling using spreadsheets, graphing calculators, and computer graphing utilities. The differences between...
This algebra lesson from Illuminations involves using linear equations and graphs in a real world context. Students will graph a line based on data points, find the equation of the line, identify y-intercept and slope,...
This word document introduces a lesson that helps students work out how much they would actually pay for a house with a 30-year fixed-rate mortgage, with interest included, after 30 years. The material involves working... | 677.169 | 1 |
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About the book:
Written for the undergraduate who has completed a year of calculus, this clear, skillfully organized text combines two important topics in modern mathematics in one comprehensive volume. As Professor Dettman (Oakland University, Rochester, Michigan) points out, "Not only is linear algebra indispensable to the mathematics major, but . . . it is that part of algebra which is most useful in the application of mathematical analysis to other areas, e.g. linear programming, systems analysis, statistics, numerical analysis, combinatorics, and mathematical physics." The book progresses from familiar ideas to more complex and difficult concepts, with applications introduced along the way, to clarify or illustrate theoretical material. Among the topics covered are complex numbers, including two-dimensional vectors and functions of a complex variable; matrices and determinants; vector spaces; symmetric and hermitian matrices; first order nonlinear equations; linear differential equations; power-series methods; Laplace transforms; Bessel functions; systems of differential equations; and boundary value problems. To reinforce and expand each chapter, numerous worked-out examples are included. A unique pedagogical feature is the starred section at the end of each chapter. Although these sections are not essential to the sequence of the book, they are related to the basic material and offer advanced topics to stimulate the more ambitious student. These topics include power series; existence and uniqueness theorems; Hilbert spaces; Jordan forms; Green's functions; Bernstein polynomials; and the Weierstrass approximation theorem. This carefully structured textbook provides an ideal, step-by-step transition from first-year calculus to multivariable calculus and, at the same time, enables the instructor to offer special challenges to students ready for more advanced materialPaperbackshop-US via United States
Softcover, ISBN 0486651916 Publisher: Dover Publications Inc., 1986 New Book. Shipped from US within 10 to 14 business days. Established seller since 2000.Used books: 1 - 25 of 78
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Softcover, ISBN 0486651916 Publisher: Dover Publications486651916 Publisher: Dover Publications6651916 Publisher: Dover Publications DOVER PUB INC, 1986 Used - Acceptable, Usually ships in 1-2 business days, No guarantee on products that contain supplements and some products may include highlighting and writing. | 677.169 | 1 |
The use of assignment matrices and linear programming has been expanded from the usual binary assignment matrix to integer and decimal matrices for solving a wide variety of Discrete Mathematics problems that are usually approached using complex scan and label and other algorithms. Among the types of problems that can be solved using assignment matrices and linear programming are knapsack, bottleneck, independent set, matching, Travelling Salesman, and max flow problems. Four different examples are given to demonstrate the methodology and ease with which these problems can be set up and solved in Excel using Excel Solvers, thus making linear programming via assignment matrices accessible to Discrete Mathematics instructors and students.
The development of this article began with one-dimensional binary assignment matrices for solving knapsack problems, expanded to twodimensional binary matrices for solving independent sets, simple bottleneck, and simple matching problems. While studying the Travelling Salesman Problem, the author realized that a one-dimensional integer matrix with alldifferent constraints was yet another form of assignment matrix. Finally, the study of transportation time and cost problems with their decimal matrices and integer allocation matrices, led to the concept of generalized assignment matrices, each type useful for solving different Discrete Mathematics problems using different linear programming constraints.
Table 1 shows the various types of problems that can be solved using linear programming and assignment matrices along with their assignment matrix type.
Assignment matrix methodology in linear programming has been used for some years [1, 2, 3, 4, 5], but the method has been severely restricted because researchers programmed each individual problem, usually in Fortran. However, if a general linear programming software could be applied to these assignment problems, the methodology could become available to the wider Discrete Mathematics community. Excel Solver and Excel Premium Solver have been found to be quite suitable for this task, providing both an easy visual platform for matrices and their constraints, along with linear programming engines that can input answers directly into assignment matrices. Using Excel Solvers in conjunction with assignment matrices gives Discrete Mathematics instructors and students a valuable tool for solving a wide variety of Discrete Mathematics problems that normally are approached via complex scan and label algorithms.
ASSIGNMENT MATRICES
Assignment matrices traditionally have been restricted to binary constraints in the linear programming solutions of bottleneck and assignment problems. [1, 2, 3, 4, 5] A binary assignment matrix has the following mathematical definition:
... (1)
A binary matrix consists of just 0's and l's. In the case of a simple bottleneck problem [1], where a single item is assigned to a single unit, there is only one 1 per row and column, and the rest of the binary matrix is all zeros (simple binary assignment matrix in Table 1). A simple binary matrix looks like an identity matrix, except the 1 's aren't necessarily on the main diagonal. In the case of generalized bottleneck problems, where more than one item can be assigned to each unit, the binary assignment matrix can have more than one 1 per row (complex binary matrix in Table 1).
By applying this methodology to an ever widening range of problem types, it has been discovered that the assignment matrix methodology can be extended to include non-binary matrices, including integer and decimal entries. Table 1 summarizes the problem types which can be solved using assignment matrices and linear programming, along with the type of assignment matrix, while Table 2 shows the different linear programming constraints associated with each assignment matrix type.
Based on Tables 1 and 2, we can define the generalized assignment matrix as: | 677.169 | 1 |
Beginning Algebra (8th Edition)
9780321769527
ISBN:
032176952X
Edition: 8 Pub Date: 2012 Publisher: Pearson
Summary: John Tobey Jr. is the author of Beginning Algebra (8th Edition), published 2012 under ISBN 9780321769527 and 032176952X. Four hundred eighty five Beginning Algebra (8th Edition) textbooks are available for sale on ValoreBooks.com, one hundred thirty used from the cheapest price of $38.67, or buy new starting at $63.90 shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less]
the primary subject of this book is math. The book is effective. It helped me to not only go over what I already knew and review it but also take my time to understand what I didn't know or already forgot.
The most interesting thing I learned in this book was shortcuts with fractions. I am one of many people who does not like fractions. This book has ways to simplify those fractions which makes it easier to do them.
I didn't really find anything in this book to be not helpful. I like that it has an online part to compete homework, and to help explain different parts of algebra problems so you would understand better
I think this book is closely related to other algebra books I've had to use, mostly in high school. | 677.169 | 1 |
CK-12 Middle School Math - Grade 7
Table of Contents
This chapter considers the basic principles surrounding algebra, including patterns, expressions, and equations. Additionally, students are introduced to the metric system and measurement as well as strategies for practical problem solving.
This chapter introduces students to percents, with emphasis on the relationship between percents and decimals and fractions. Other related topics covered are circle graphs, interest, and percent of change.
This chapter explores the properties of equations, inequalities, and functions, emphasizing the relationship the three concepts share. This lesson also deals with simplifying and evaluating these concepts both algebraically and with tables.
In this chapter, students will learn all about angles, triangles, polygons, similar and congruent figures, indirect measurement, transformations and symmetry, and transformations in the coordinate plane.
This chapter introduces students to concepts such as square roots and rational and irrational numbers before covering the Pythagorean Theorem and areas of parallelograms, triangles, trapezoids, and circles. | 677.169 | 1 |
Broomall GeometryMy personal notes will help the student master the basics, then expand to harder problems. It's not necessary to do all the problems, but you MUST get the easy and intermediate ones right! Most people don't write the way they speakLinda L.
...The course also introduces students to absolute value, the coordinate plane and different algebraic properties. The students will build on this basic knowledge by learning how to solve multi-step equations and inequalities and the complex algebraic functions that accompany them, such as exponent... | 677.169 | 1 |
Precalculus: Functions and Graphs with Smart CD (Windows Barnett, Ziegler, Byleen College Algebra/Precalculus series is designed to be user friendly and to maximize student comprehension. The goal of this series is to emphasize computational skills, ideas, and problem solving rather than mathematical theory. Precalculus, 5/e, introduces a unit circle approach to trigonometry and can be used in one or two semester college algebra with trigonometry or precalculus courses. The large number of pedagogical devices employed in this text will guide a student through the course. Integrated throughout the text, the students and instructors will find Explore-Discuss boxes which encourage students to think critically about mathematical concepts. In each section, the worked examples are followed by matched problems that reinforce the concept that is being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful. A Smart CD is packaged with the seventh edition of the book. The CD tutorial reinforces important concepts, and provides students with extra practice problems.
1 Equations and Inequalities
1-1 Linear Equations and Applications
1-2 Systems of Linear Equations and Applications
1-3 Linear Inequalities
1-4 Absolute Value in Equations and Inequalities
1-5 Complex Numbers
1-6 Quadratic Equations and Applications
1-7 Equations Reducible to Quadratic Form
1-8 Polynomial and Rational Inequalities
Chapter 1 Group Activity: Rates of Change
Chapter 1 Review
2 Graphs and Functions
2-1 Basic Tools: Circles
2-2 Straight Lines
2-3 Functions
2-4 Graphing Functions
2-5 Combining Functions
2-6 Inverse Functions
Chapter 2 Group Activity: Mathematical Modeling in Business
Chapter 2 Review
1&2 Cumulative Review Exercise
3 Polynomials and Rational Functions
3-1 Polynomial Functions and Graphs
3-2 Finding Rational Zeros of Polynomials
3-3 Approximating Real Zeros of Polynomials
3-4 Rational Functions
3-5 Partial Functions
Chapter 3 Group Activity: Interpolating Polynomials
Chapter 3 Review
4 Exponential and Logarithmic Functions
4-1 Exponential Functions
4-2 The Exponential Function with Base e
4-3 Logarithmic Functions
4-4 Common and Natural Logarithmic Functions
4-5 Exponential and Logarithmic Equations
Chapter 4 Group Activity: Growth of Increasing Functions
Chapter 4 Review
3&4 Cumulative Review Exercises
5 Trigonometric Functions
5-1 The Wrapping Function
5-2 Circular Functions
5-3 Angles and Their Measure
5-4 Trigonometric Functions
5-5 Solving Right Triangles
5-6 Graphing Basic Trigonometric Functions
5-7 Graphing y = k+A sin (Bx+C) and y=k+A cos (Bx+C)
5-8 Graphing More General Tangent, cotangent, Secant, and Cosec
5-9 Inverse Trigonometric Functions
Chapter 5 Group Activity: A predator - Prey Analysis - Mountain L
Chapter 5 Review
6 Trigonometric Identities and Conditional Equations
6-1 Basic Identifies and Their Use
6-2 Sum, Difference, and Cofunction Identifies
6-3 Double-Angle and Half-Angle Identifies
6-4 Product-Sum and Sum-Product Identifies
6-5 Trigonometric Equations
Chapter 6 Group Activity: From M sin Bt + N cos Bt to A sin (Bt +C)
Chapter 6 Review
7 Additional Topics in Trigonometry
7-1 Law of Sines
7-2 Law of Cosines
7-3 Geometric Vectors
7-4 Algebraic Vectors
7-5 Polar Coordinates and Graphs
7-6 Complex Numbers in Rectangular and Polar Forms
7-7 De Moivre's Theorem
Chapter 7 Group Activity: Conic Sections and Planetary Orbits
Chapter 7 Review
5,6,&7 Cumulative Review Exercise
8 Systems of Equations and Inequalities
8-1 Systems of Linear Equations and Augmented Matrices
8-2 Gauss-Jordan Elimination
8-3 Systems Involving Second-Degree Equations
8-4 Systems of Linear Inequalities in Two Variables
8-5 Linear Programming
Chapter 8 Group Activity: Modeling with Systems of Equations
Chapter 8 Review
9 Matrices and Determinants
9-1 Matrices: Basic Operations
9-2 Inverse of a Square Matrix
9-3 Matrix Equations and Systems of Linear Equations
9-4 Determinants
9-5 Properties of Determinants
9-6 Cramer's Rule
Chapter 9 Group Activity: Using Matrices to Find Cost, Revenue, and Profit | 677.169 | 1 |
Singapore Math Practice, Level 1a
Synopses & Reviews
Publisher Comments An introduction at the front of each book explains Singapore Math and its common problem types. Each unit has learning objectives, which clearly define the skills to be learned in that section, and an answer key with step-by-step worked out solutions that help students see how to work the problems. This book is perfect for students familiar with Singapore Math and for those who just need extra math practice! --Directly correlated to Singapore Math textbooks, this comprehensive practice series allows learners to practice various types of math problems while developing their thinking and analytical skills. Learning objectives and unit assessments are included to ensure that students obtain a thorough understanding of each concept. Perfect as a supplement to classroom work or as a homeschool resource, these workbooks will boost confidence in problem-solving and critical-thinking skills.
Synopsis:
Synopsis | 677.169 | 1 |
introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases. Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on "practical geometry," emphasizing topics and techniques of maximal use in all areas of mathematics. These topics include: Algebraic and Combinatoric Preliminaries Isometries and Similarities An Introduction to Crystallography Fields and Vector Spaces Affine Spaces Projective Spaces Special features include a spiral approach to symmetry; a review of the algebraic prerequisites; proofs which do not appear in other texts, such as the Polya-Burnside theorem; an extensive bibliography; and a large collection of exercises together with suggestions for term-paper topics. In addition, special emphasis is placed on the geometric significance of cosets and conjugates in a group.
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Tips and Tricks for Teaching Math Online This slide show (without sound) gives hints, tips and best practices for teaching math online from a community college professor. This is good for those teachers that may want to set up a supplementary website for their brick-and-mortar sessions. Author(s): No creator set
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Berndt Elias remembers his cousin Anne Frank Anne Frank's cousin Berndt Elias used to perform as a clown in ice shows. He talks about how Anne dreamt of performing in an ice show with him. She wrote about this in detail, and this portion of the diary is read during the video. It makes Berndt sad to know that her dream was never fulfilled. Interview with him takes place October 15, 1993, in Basel, Switzerland. English subtitles. (2:09) Author(s): No creator set
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Steven Kellogg, 2009 National Book Festival YouTube - LibraryOfCongress's Channel American children's book author and illustrator Steven Kellogg shares 25 minutes of storytelling and drawing as he talks about "the language of feeling, which is what art is." He shares the story of his family's beloved Harlequin Great Dane, Pinkerton, the picture books he created about Pinkerton, and the letters he received from people who identified with the books. He draws Second Hand Rose, the yellow cat with the small heart that his family kept and loved for 25 years. He draws and t Author(s): No creator set
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Math Equations : How to Solve Algebraic Equations Solve algebraic equations by isolating the variable that needs to be identified and keeping the equation balanced. Be sure to read the algebraic equation instructions carefully for the solution with tips from a math professor in this video math lesson.
Expert: Jimmy Chang
Bio: Jimmy Chang has been a math teacher at St. Pete College for nearly a decade. He has a master's degree in math, and his specialties include calculus, algebra, liberal arts, math and trigonometry.
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Review of Cat Muscles of the Anterior Leg Specific anterior muscles of the leg of a dissected cat are reviewed with proper pronunciation by a professor. Origin, insertion, and functions are given. This would make a great review for students preparing for a cat muscle practical. 3:51 min. Color video with soundReview of Cat Digestive System Professor review of organs of the digestive system of a dissected cat. This would make a great review for students before a lab practical. 10:00 min. Color video with sound. Run time 10:00. Author(s): No creator set
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Engineering an Empire - China, Part 5/5 WARNING: This video talks of eunuchs who have greater access to the emperors. This documentary offers information about the evolution of the empire of China and is suitable for high school students. Narrated by Peter Weller and various scholars.Is there a Crisis in World Journalism? Professor Richard Keeble Richard Keeble is a professor of journalism at Lincoln University. He is also a director of the Institute of Communication Ethics and co-edits their quarterly journal, Ethical Space. He has written a number of articles on the journalism of George Orwell and is currently co-editing for Routledge a collection of papers on literary journalists – such as Daniel Defoe, Charles Dickens, William Hazlitt, Willa Cather, Angela Carter, Truman Capote – called The Journalistic Imagination. He writes for Author(s): No creator set
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East Asian Cinema in the UK - Adam Torel, Third Window Films Adam Torel is Managing director of Third Window Films, a distribution company who bring East Asian Cinema to the UK. Here he talks about the state of Asian film distribution in the UK, Japanese pop culture and much more!
This event is organised by the Coventry University East Asian Film Society who promote, celebrate and enjoy East Asian cinema by watching a film every week, specifically those which are unreleased 8 unavailable in the UK. Author(s): No creator set
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Producing the Chelsea Flower Show - Karen Arrand The woman who was responsible for getting the Chelsea Flower Show onto the television for the BBC talks to Coventry Conversations organiser, John Mair.
The Chelsea Flower Show is a vital part of the English summer for those fortunate enough to visit the show but to those who watch it on the small screen, it has to capture the spectacle of the event live for 10 hours each year.
Karen Arrand was the BBC producer responsible for bringing the show into our living rooms in 2000 to 2003.
Karen tookCalendars Through the Ages This exhibit looks at the astronomical basis of calendars, the history of our (Gregorian) calendar, and when various countries moved from the Julian to the Gregorian calendar. Learn about Leap Year, the solar cycle, equinoxes and solstices. Author(s): No creator set
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Nicholas Stern, London School of Economics: "The Economics of ClimateNicholas Stern, London School of Economics: "The Economics of ClimateAlexander Nehamas, Professor of Philosophy and Comparative Literature: "'Because It Was He, BecauseDavid Hopkins, Princeton University: Tuning In or Tuning Out? The New World of Digital TV PDF
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David Hopkins, Princeton University: Tuning In or Tuning Out? The New World of Digital TV | 677.169 | 1 |
Popular Textbooks
Details about Precalculus Essentials:
This is the number one, best selling graphing-required version of Mike Sullivan's precalculus series because, simply, "IT WORKS." Mike Sullivan, after twenty-five years of teaching, knows exactly what readers need to do to succeed and he therefore emphasizes and organizes his text around the fundamentals; preparing, practicing, and reviewing. Readers who prepare (read the book, practice their skills learned in previous math classes), practice (work the math focusing on the fundamental and important mathematical concepts), and review (study key concepts and review for quizzes and tests) succeed. This dependable text retains its best features–accuracy, precision, depth, strong reader support, and abundant exercises, while substantially updating content and pedagogy. After completing the book, readers will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus. | 677.169 | 1 |
Calculus
Overview
Years of success with AP
Calculus students earned Paul Foerster a Presidential Award for Excellence in
Mathematics Teaching. Calculus: Concepts and Applications
is the curricula he uses to prepare students for success on the
Advanced Placement Exams. It is available in print and eBook formats for
students and teachers. Click hereto sign up for
a free digital trial.
Calculus: Concepts and Applications
closely follows the AP Calculus syllabus for both AB and BC levels and contains
numerous problems that are similar in format to the AP Exam's free-response
problems.
This textbook makes it easier to organize your
teaching and improves learning outcomes by presenting calculus as a study of
just four fundamental concepts—limits, derivatives, definite integrals, and
indefinite integrals. With just four main ideas on which to focus, your students
will find the scope of calculus more manageable, and they'll have an easier time
understanding, connecting, and remembering important concepts.
Pacing guides will help you schedule lessons so you cover all the
material needed before the AP Exams.
You will be able to easily
differentiate learning for your students because each concept is clearly
developed through graphical, algebraic, numerical, and verbal methods.
The blackline master Explorations in the Instructor's Resource Book will
enable you to familiarize your students with mathematical concepts before they
read the material in the text and deepen their understanding as you guide them
through multiple approaches to problem solving.
You will easily
integrate technology and give your students extended opportunities to explore
and understand calculus in depth with projects from the Instructor's Resource
Book that use the Texas Instruments Calculator-Based Laboratory™
(CBL™), The Geometer's Sketchpad®, and
Fathom® Dynamic Data software. | 677.169 | 1 |
Prerequisites: Appropriate placement test score, a grade of "SA" in M 061, or Math Department consent.This course is designed for those students who need to improve their pre-algebra skills in order to succeed in M 090. Topics include signed numbers, basic factoring, basic equation solving, an introduction to polynomials, square roots, basic graphing and basic exponent rules.
While an honest effort has been made to provide accurate information on these pages, Flathead Valley Community College assumes no liability for incorrect or missing data.
This information was last updated on Wednesday, May 16, 2012 at 9:40:02 AM | 677.169 | 1 |
Intermediate Algebra for College Students (6TH 13 Edition)
by Robert Blitzer Publisher Comments
ALERT: Before you purchase, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, including customized versions... (read more)
Basic Math and Pre-Algebra for Dummies
by Mark Zegarelli Publisher Comments
Understand fractions, decimals, and percentagesUnravel algebra word problemsWork with graphs and measuresGrasp prime numbers, factors, and multiples A fun and accessible guide to the fundamentals of math Somewhere along the line, you fell out of love... (read more)
Elementary and Intermediate Algebra (4TH 12 Edition)
by Mark Dugopolski Publisher Comments
The Dugopolski series in developmental mathematics has helped thousands of students succeed in their developmental math courses. Elementary & Intermediate Algebra, 4e is part of the latest offerings in the successful Dugopolski series in mathematics. In... (read more)
Intermediate Algebra: Algebra Within Reach
by Ron Larson Publisher Comments
Larson IS student success. INTERMEDIATE ALGEBRA: ALGEBRA WITHIN REACH owes its success to the hallmark features for which the Larson team is known: learning by example, a straightforward and accessible writing style, emphasis on visualization through the... (read more)
Algebra & Its Applications
by Dinh V Huynh Book News Annotation
As with preceding conferences held at the Athens campus of Ohio
University, the one held in March 2005 offered a forum for
algebraists to share their research. The 23 contributions by
international experts reflect the increasing diversification of the... (read more)
Eigenvalues, Inequalities, and Ergodic Theory
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The first and only book to make this research available in the West Concise and accessible: proofs and other technical matters are kept to a minimum to help the non-specialist Each chapter is self-contained to make the book easy-to... (read more)
A First Book in Algebra
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Intermediate Algebra: Applied Approach (9TH 14 Edition)
by Aufmann Publisher Comments
As in previous editions, the focus in INTERMEDIATE ALGEBRA remains on the Aufmann Interactive Method (AIM). Students are encouraged to be active participants in the classroom and in their own studies as they work through the How To examples and the... (read more)
Handbook of Means and Their Inequalities
by P. S. Bullen Publisher Comments
This is a revision of an earlier Means and Their Inequalities by the present author and Professors Mitrinovic and Vasic. Not only does this book bring the earlier version up to date but enlarges the scope considerably to give a full and in-depth... (read more)
Intermediate Algebra : 2010 Class Test Edition (11 Edition)
by Cynthia Anfinson About the Author
Mark Clark graduated from California State University Long Beach with a Bachelor's and Master's in Mathematics in 1995. He is a full-time Associate Professor at Palomar College and has taught there for the past 9 years. He is a member of AMATYC | 677.169 | 1 |
Search Results
The online math center at Whatcom Community College is intended for a range of audiences, particularly students looking for additional assistance on a variety of math subjects from geometry to calculus. The materials...
This website is an excellent resource for math teachers teaching any age and level of students. The National Council of Teachers of Mathematics (NCTM), "support[s] teachers to ensure equitable mathematics learning of...
Created by Lang Moore and David Smith for the Connected Curriculum Project, this is a module to review concepts of inverse functions, and to use those concepts, together with functions defined by integrals, to develop...
Graph is "an open source application used to draw mathematical graphs in a coordinate system." Anyone who wants to draw graphs of functions will find this program useful. The program makes it very easy to visualize a... | 677.169 | 1 |
This book is for a two-semester Introduction to Financial Mathematics course for undergraduates. It focuses on preparing students for the actuarial exam, motivates through a discussion of personal finances and portfolio management and goes on to cover higher level mathematics, such as stochasticThe Games People Play, Second Edition
This book demonstrates how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. With an emphasis on mathematical thinking and problem solving, the text draws on numerous examples, questions, and problems to explain the application…
Cohesively Incorporates Statistical Theory with R Implementation
Since the publication of the popular first edition of this comprehensive textbook, the contributed R packages on CRAN have increased from around 1,000 to over 6,000. Designed for an intermediate undergraduate course, Probability and……
Clear, rigorous, and intuitive, Markov Processes provides a bridge from an undergraduate probability course to a course in stochastic processes and also as a reference for those that want to see detailed proofs of the theorems of Markov processes. It contains copious computational examples that…
Mathematics for Economists with Applications provides detailed coverage of the mathematical techniques essential for undergraduate and introductory graduate work in economics, business and finance.
Beginning with linear algebra and matrix theory, the book develops the techniques of univariate and…
Explore Theory and Techniques to Solve Physical, Biological, and Financial Problems
Since the first edition was published, there has been a surge of interest in stochastic partial differential equations (PDEs) driven by the Lévy type of noise. Stochastic Partial Differential Equations, Second…
An Introduction to Probability
The Mathematics of Games: An Introduction to Probability takes an inquiry-based approach to teaching the standard material for an introductory probability course. It also discusses different games and ideas that relate to the law of large numbers, as well as some more mathematical topics not…
Hypothesis Testing and Changepoint Detection
Sequential Analysis: Hypothesis Testing and Changepoint Detection systematically develops the theory of sequential hypothesis testing and quickest changepoint detection. It also describes important applications in which theoretical results can be used efficiently.
The book reviews recent…
Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google… | 677.169 | 1 |
Matrices (the plural of matrix) are a convenient way of organizing linear functions and systems of equations. Before you can move on to the higher-math applications of matrices, you have to master the basic methods of solving matrices. Your first introduction to solving matrices will probably be using them to solve systems of equations, using basic algebraic operations.
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Steps
"Reduced row form" means that any numbers may be in the rightmost column, but the rest of the entries in any given row consist of a single "1" entry accompanied by as many zeroes as necessary to fill the rest of the spaces.
In reduced row form, order the rows so that the "1" entries like up in a rightward, downward diagonal line. So the first line of the matrix might be "1 0 0 24," the second line "0 1 0 46," and the third line "0 0 1 5."
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2
Switch any 2 rows in the matrix to make performing the other operations easier, or to arrange the "1" entries properly in reduced row form. This doesn't affect the overall value of the matrix.
You must swap the 2 lines completely, with no intermingling of the numbers for each row. So for example if you had a matrix with entries "3 12 2" in the first row and "4 6 3" in the second row, you could swap "4 6 3" to be the first row and "3 12 2" to be the second row. But you couldn't swap just 1 or 2 of the elements from each row.
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Method 1 of 2: Row Addition and Subtraction
1
Combine the elements of any 2 matrix rows by adding and subtracting them. This creates a third row (the result), which you then substitute for 1 of the original 2 rows.
Add and subtract each element individually, working your way across the row. So if you were to add the rows "3 12 2" and "4 6 3," the resulting new row would be "7 18 5."
The results row must replace 1 of the rows you just used to create it; you cannot arbitrarily add a new row to the matrix and keep the other rows unchanged.
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Method 2 of 2: Scalar Matrix Multiplication
1
Multiply every element of a given row by the same scalar.
As long as you multiply each element in the row by the same scalar, you don't actually change the value of the matrix. But scalar multiplication can make performing the other matrix row operations easier. For example, if you have the rows "2 5 3" and "-1 2 9," multiplying the second row by 2 is the perfect setup for then adding the resulting rows together. The scalar multiplication gives you "-2 4 18," which when added to the first row yields "0 9 21." If you then scalar multiply the resulting row by 9, you have "0 1 (21/9)", and this row is prepared for reduced row form Healthy Hair Care?
Yes
No
Healthy Hair Care
how to have healthier hair using olive oil
Can you tell us about Bicycle Brake and Chain Maintenance?
Yes
No
Bicycle Brake and Chain Maintenance
how to fix a slipped bike chain | 677.169 | 1 |
Description: WARNING!! If you were enrolled in the old PCAL 1A course, you must enroll in the old PCAL 1B course. Please contact a customer service representative to assist you.
This precalculus course is designed to incorporate the two traditional courses of trigonometry and analytic geometry. As the name suggests, the precalculus course is intended to build upon existing algebra and geometry skills while preparing a student for the concepts he or she will be learning in a calculus course. It is important that a student has taken courses in algebra II and geometry before attempting to take precalculus. Precalculus 1B will primarily cover the trigonometry and analytic geometry portion, while the first semester course, Precalculus 1A, centered more on parent functions and transformations of their graphs, sequences and series, and limits.
In this course, we use the concept of mathematical relations and functions to model, describe, and solve mathematical problems. Through the use of new functions defined in trigonometry (the study of triangles), the algebra and geometry involved in analytic geometry, and the aid of technology, you will learn how to become a more effective problem-solver | 677.169 | 1 |
This is a translation of Landau's famous Elementare Zahlentheorie with added exercises by Paul T. Bateman and Eugene E. Kohlbecker.
This three-volume classic work is reprinted here as a single volume.
Reviews
"These three excellently printed and arranged volumes form an addition of the highest importance to the literature of the theory of numbers. With them, the reader familiar with the basic elements of the theory of functions of a real and complex variable, can follow many of the astonishing recent advances in this fascinating field. His interest is enlisted at once and sustained by the accuracy, skill, and enthusiasm with which Landau marshals the analytic facts and simplifies as far as possible the inevitable mass of details ...
"The mathematical world owes a great debt of gratitude to Professor Landau for rendering accessible so many of the recent splendid achievements in the theory of numbers."
-- G. D. Birkhoff, Bulletin of the AMS
Table of Contents
Part One. Foundations of Number Theory
The greatest common divisor of two numbers
Prime numbers and factorization into prime factors
The greatest common divisor of several numbers
Number-theoretic functions
Congruences
Quadratic residues
Pell's equation
Part Two. Brun's Theorem and Dirichlet's Theorem
Introduction
Some elementary inequalities of prime number theory
Brun's theorem on prime pairs
Dirichlet's theorem on the prime numbers in an arithmetic progression; Further theorems on congruences; Characters; \(L\)-series; Dirichlet's proof
Part Three. Decomposition into Two, Three, and Four Squares
Introduction
Farey fractions
Decomposition into two squares
Decomposition into four squares; Introduction; Lagrange's theorem; Determination of the number of solutions
Decomposition into three squares; Equivalence of quadratic forms; A necessary condition for decomposability into three squares; The necessary condition is sufficient | 677.169 | 1 |
CliffsQuickReview course guides cover the essentials of your toughest classes. You're sure to get a firm grip on core concepts and key material and be ready for the test with this guide at your side.
Whether you're new to functions, analytic geometry, and matrices or just brushing up on those topics, CliffsQuickReview Precalculus can help. This guide introduces each topic, defines key terms, and walks you through each sample problem step-by-step. In no time, you'll be ready to tackle other concepts in this book such as
Arithmetic and algebraic skills
Functions and their graphs
Polynomials, including binomial expansion
Right and oblique angle trigonometry
Equations and graphs of conic sections
Matrices and their application to systems of equations
Stumped trying to make sense of physics? Here's your solution. "Physics Demystified," Second Edition helps you grasp the essential concepts with ease.
Written in a step-by-step format, this practical guide begins by covering classical physics, including mass, force, motion, momentum, work, energy, and power, as well as the temperature and states of matter. Electricity, magnetism, and electronics are discussed as are waves, particles, space, and time. Detailed examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.
"Simple enough for a beginner, but detailed enough for an advanced student, Physics Demystified, Second Edition helps you master this challenging and diverse subject. It's also the perfect resource to prepare you for higher-level physics classes and college placement tests. | 677.169 | 1 |
Mathematics Teacher (1977) Vol. 70, No. 2
klax and Enjoy it I "'--~ Here's an algebra/geometry program that makes teaching more enjoyable because it makes learning easier. It's Algebra Books One and Two, Modern Edition, and Plane Geometry with Space Concepts by Welchons, Krickenberger, and Pearson. These are books your students can read and understand. Which m
This is available to members of NCTM. Please log in now to view this article. If you are interested in a NCTM membership join now. | 677.169 | 1 |
Against all odds inside statistics(
Visual
) 29
editions published
between
1988
and
2015
in
English
and held by
772 WorldCat member
libraries
worldwide
Presents the why as well as the how of statistics using computer animation, colorful on-screen computations, and documentary
segments
The UMAP journal by Education Development Center. Undergraduate Mathematics Applications Project(
)
in
English
and held by
749 WorldCat member
libraries
worldwide
Consortium(
)
in
English
and held by
237 WorldCat member
libraries
worldwide
Statistics decisions through data by David S Moore(
Visual
) 9
editions published
between
1990
and
1997
in
English
and held by
203 WorldCat member
libraries
worldwide
An introductory statistics course composed of five hour-long instructional videos that contain a total of twenty-one individual
segments, and a 200-page text, which includes exercises, group activities, and quizzes
College algebra in simplest terms(
Visual
) 5
editions published
in
1991
in
English
and held by
179 WorldCat member
libraries
worldwide
Presents the role of algebra in daily life and demonstrates practical applications in the workplace. Uses symbols, charts,
pictures, and state-of-the-art computer graphics to illustrate basic algebraic techniques. Reviews problems step-by step,
focusing on the methods students find most difficult to grasp
For all practical purposes(
Visual
) 16
editions published
between
1986
and
1997
in
English
and held by
155 WorldCat member
libraries
worldwide
A series which stresses the connections between contemporary mathematics and modern society. Presents a great variety of problems
that can be modeled and solved by quantitative means
Algebra in simplest terms(
Visual
) 14
editions published
between
1990
and
2000
in
English
and held by
152 WorldCat member
libraries
worldwide
Solving equations is a basic operation of all higher math. This set shows algebra's usefulness to retailers, biologists, and
even anyone who drives a car. Host Sol Garfunkel walks viewers through realistic problems, highlighting the common trouble
spots
Statistics : the shape of the data by Susan Jo Russell(
Book
) 2
editions published
between
1989
and
1997
in
English
and held by
115 WorldCat member
libraries
worldwide
For teaching elementary and middle school students how to collect and analyze real world data
For all practical purposes introduction to contemporary mathematics(
Visual
) 3
editions published
in
1987
in
English
and held by
109 WorldCat member
libraries
worldwide
This series provides an understanding of math in both personal matters and the world around us. Relevant applications of mathematics
are presented, focusing on contemporary math as a problem solving tool
Measuring : from paces to feet by Rebecca B Corwin(
Book
) 1
edition published
in
1990
in
English
and held by
102 WorldCat member
libraries
worldwide
Teaches elementary and middle school students how to collect and analyze real world data
Mathematics : modeling our world(
Book
) 13
editions published
between
1998
and
2010
in
English
and held by
99 WorldCat member
libraries
worldwide
The authors of this text demonstrate using mathematical concepts to solve truly interesting problems about how our world works.
Mathematical modeling is the process of looking at a problem, finding a mathematical core, working within that core, and coming
back to see what mathematics tells you about the problem. Real problems ask such questions as: How do we create computer animations?
Where should we locate a fire station? How do we effectively control an animal population? This approach integrates a mix
of ideas in geometry, algebra, and data analysis with technologies of computers and graphing calculators | 677.169 | 1 |
Fibonacci sequence is one of the most rapidly growing area of mathematics which has a wide variety of applications in science and mathematics. The manuscript of proposed book is centered on... More > generalization of Fibonacci pol-ynomials. The book will consists of three chapters. Each chapter will be di-vided into several sections.
In Mathematics, the Polynomials are an important class of simple and smooth functions. Here, simple means they are constructed using only multiplication and addition and smooth means they are infinitely differentiable, i.e., we can say that they have derivatives of all finite orders. Because of their simple structure, the polynomials are very easy to evaluate, and are used extensively in numerical analysis for polynomial interpolation or to numerically integrate more complex functions. In linear algebra, characteristic polynomial of a square matrix encodes several important properties of the matrix | 677.169 | 1 |
97898102324Matrix Calculus and Kronecker Product With Applications and C++ Programs
The Kronecker product of matrices plays a central role in mathematics and in applications found in engineering and theoretical physics. These applications are signal processing, statistical physics, quantum groups and quantum computers. This text provides a comprehensive introduction to the Kronecker product of matrices together with its software implementation in C++ using an object-orientated design. | 677.169 | 1 |
Course Description. Math Analysis is a pre-calculus course that includes an in-depth conceptual analysis of algebraic, polynomial, rational, logarithmic, exponential, and trigonometric functions. Topics include graphical behavior, domains and ranges, roots (real & complex), turning points using the first derivative, graphing (using transformations with and without a graphing calculator), application problem solving and data analysis (using introductory statistics, given data, and data gathered in laboratory activities), and an introduction to integration. Parametric equations are presented with a focus on applications and conceptual analysis. Analysis includes required algebraic proofs and/or conceptual explanations in all written and oral presentations. Graphing calculators, spreadsheets, and a computer algebra system are used extensively. The study of matrices is included and optional topics include an introduction to sequences and series.
Course Focus. The course is designed to better integrate mathematics and the world around you. Mathematics units will sometimes be chosen to complement particular physics units. For one example, mathematics and physics will coordinate the study of the derivative. This organization is an attempt to make the topics more meaningful and to save your time by "sharing" concepts. Throughout the course, emphasis is on active participation, investigation of the problems, interpretations of solutions, understanding of techniques, and communication of results.
Class Methodology (and Expectations): Class activities include lecture (including discussion and question answering), group activities and projects, group work on homework, individual work, and individual consultation with the instructor. Some specific expectations follow.
I expect you to learn the material thoroughly. Through the lectures, activities, and individual meetings, I will try to facilitate your learning, but ultimately, you must actively take responsibility for your learning. I encourage you to work with the other members of the class to learn the material.
I expect you to participate in each class meeting. During the lecture portion, be attentive, ask questions, and provide answers to questions posed by your classmates and myself. Work cooperatively with your classmates during the independent portion.
I expect you to work diligently on each homework assignment and each project. Working on these problems is the most important part of the course.
I expect you to carefully read the textbook. During lecture, I will address major ideas and some examples, but there will be topics and examples you should learn from the textbook. You will often have to creatively solve problems based on your knowledge of the concepts.
I expect you to take the tests as scheduled. If you need to miss an test, you must make arrangements in advance. For policies concerning the exams, please refer to the CVGS Student Handbook. Many test and exam questions will be quite similar to homework questions and/or examples from class; however, you will also be asked a few questions based on your understanding of the concepts.
Absences/Tardiness/Behavior. If a student is absent (excused) for only one class meeting, then upon return, the student is expected to submit any work that was due during the absence. If a test was missed, the student is expected to take the test on the day of return. If a student misses two or more consecutive class meetings, then the student should talk to the instructor on the day of return to devise a plan to catch up. For planned absences (e.g., college visits, conference attendance, etc.), the student should discuss the plan with the instructor in advance. Failure to do so will result in an unexcused absence. For any unexcused absence, homework will not be accepted late and test grades will be lowered by 10 points per day (counted from the scheduled test date until the day the test is taken).
You are expected to be in class on time. During each semester, your first two tardies will be excused; for each additional tardy, ½ point will be deducted from your overall semester average.
You are expected to work diligently during class time, both during class discussions/lectures and during independent work time. During independent work time you are expected to work on mathematics unless you have completed the current assignment; in that case, you may do any academic work. Any disruptive behavior during class will result in point deductions from your overall semester average; there will be no warnings, just the penalty. Also, you can receive more than one penalty in a day. You can also receive a penalty for goofing off, even though you are not disruptive.
Honor Code: Students are required to pledge all work that they turn in for a grade. Please refer to the CVGS Student Handbook for complete requirements.
Typical Hours for Students Session I (7:30-10:10)Session II (8:25-11:05)
Period 1: 7:30-8:20 Period 2: 8:25-9:15
Period 2: 8:25-9:15 Period 3: 9:20-10:10
Period 3: 9:20-10:10 Period 4: 10:15-11:05 | 677.169 | 1 |
Publisher's Description
REA's Crash Course for the AP® Calculus AB & BC Exams Calculus AB & BC exams yet? How will you memorize everything you need to know before the tests? Do you wish there was a fast and easy way to study for the exams AND boost your score?
If this sounds like you, don't panic. REA's Crash Course for AP® Calculus AB & BC is just what you need. Our Crash Course gives you:
Targeted, Focused Review - Study Only What You Need to Know The Crash Course is based on an in-depth analysis of the AP® Calculus AB & BC course description outline and actual AP® test questions. It covers only the information tested on the exams, so you can make the most of your valuable study time. Written by experienced math teachers, our easy-to-read format gives you a crash course in functions, graphs, units, derivatives, integrals, and polynomial approximations and series.
Expert Test-taking Strategies Our authors share detailed question-level strategies and explain the best way to answer AP® questions you'll find on the exams. By following their expert tips and advice, you can boost your overall point score!
Take REA's Calculus AB & BC student must have.
When it's crucial crunch time and your Advanced Placement® exam is just around the corner, you need REA's Crash Course for AP® Calculus AB & BC!
Author Bio
Flavia Banu graduated from Queens College of the City University of New York with a B.A. in Pure Mathematics and an M.A.in Pure Mathematics in 1997. Ms. Banu was an adjunct professor at Queens College where she taught Algebra and Calculus II. Currently, she teaches mathematics at Bayside High School in Bayside, New York, and coaches the math team for the school. Her favorite course to teach is AP® Calculus because it requires "the most discipline, rigor and creativity."
Joan Marie Rosebush is teaching calculus courses at the University of Vermont. Ms. Rosebush has taught mathematics to elementary, middle school, high school, and college students. She taught AP® Calculus via satellite television to high school students scattered throughout Vermont. Ms. Rosebush earned her Bachelor of Arts degree in elementary education, with a concentration in mathematics, at the University of New York in Cortland, N.Y. She received her Master's Degree in education from Saint Michael's College, Colchester, Vermont | 677.169 | 1 |
Learning Math: Patterns, Functions & Algebra"Algebraic Thinking"
Begin to explore what it means to think algebraically and learn to use algebraic thinking skills to make sense of different situations. This session covers describing situations through pictures, charts, graphs, and words; interpreting and drawing conclusions from graphs; and creating graphs to match written descriptions of real-life situations.G
11:30 pm
Learning Math: Patterns, Functions & Algebra"Patterns In Context"
Explore the processes of finding, describing, explaining, and predicting using patterns. Topics covered include how to determine if patterns in tables are uniquely described and how to distinguish between closed and recursive descriptions. This session also introduces the idea that there are many different conceptions of what algebra is.G | 677.169 | 1 |
Rafique,
Almost any good math history book would be a good beginning, but some are
more fruitful than others. Eric Bell's, "Men of Mathematics" is a classic
and is relatively inexpensive. Carl Boyer is an excellent source also. Try
looking through the NCTM materials, I believe they offer a book that Victor
Katz edited directed at high school and early college.
You don't specify a grade level, so I might include Lancelot Hogben's
"Mathematics for the Million", another classic that is rich in historical
ideas. Try one of the online book companies and pick books about topics
you teach that are written for popular consumption or stroll the shelves of
your local book store in the math section. Paul Nahin's "Imaginary Tale"
about the history of the imaginary constant is one that comes to mind,
Maor's, "e, the story of a number" is another.
I guess the classic translation of Euclid by Sir Thomas Heath would fit nicely
hear too, since it goes into such detail about the related mathematicians and
ideas.
Good luck. Hope this is of some help to you.
-Pat Ballew, for the T2T service | 677.169 | 1 |
16Mymathlab Mystatlab Student Access Kit For Ad Hoc Valuepacks
Prealgebra An Integrated Approach
Student Solutions Manual for Prealgebra An Integrated Approach
Prealgebra: An Integrated Approach
Summary
This book helps to better prepare students for higher-level math courses by integrating basic algebraic concepts early and continuing to revisit those concepts throughout. The friendly composition and the many pedagogical features are designed to help with student comprehension. The modern, relevant applications increase student motivation by immersing them in truly genuine and realistic mathematical situations. | 677.169 | 1 |
Intermediate Algebra (with CD-ROM and iLrn™ TutorialLearn math the easy way with Tussy and Gustafson's INTERMEDIATE ALGEBRA! Study sets at the end of every chapter will improve your ability to read, write, and communicate mathematical ideas. Difficult concepts are made clear with a five-step approach to problem-solving: analyze the problem, form an equation, solve the equation, state the result, and check the solution. Prepare for exams with numerous resources located online and throughout the text such as live online tutoring, tutorials, a book companion website, chapter summaries, self-checks, practice sections, and reviews. Take advantage of the accompanying Video Skillbuilder CD-ROM that will save you class preparation time through video lessons, web quizzes, and chapter tests. | 677.169 | 1 |
Intermediate Algebra
Major topics include linear equations, linear inequalities, systems of linear equations, inequalities in two variables and their graphs, introduction to relations and functions, rational exponents, operations with rational expressions, complex fractions and rational equations, operations with radical expressions complex fractions and rational equations, operations with radical expressions and radical equations, and quadratic equations. Each section of this class will contain a computer component.
Trained tutors and a variety of resources are available in the Learning Commons to assist with these topics. Student should bring their notes, course handouts and assignments with them. Online homework can also be accessed in the LC.
Textbook Information
Hardcopies of this textbook are available for use at the Intermediate Algebra table in the Learning Commons.
MAT 1033
Intermediate Algebra with Applications and Visualization, 3e, Rockswold and Krieger
Handouts
The Learning Commons offers handouts to help students understand important concepts
in intermediate algebra | 677.169 | 1 |
This course provides teachers of grades 3 through 5 with an opportunity to explore how activities that foster algebraic thinking can be integrated into the elementary classroom. Algebraic thinking consists of more than just learning how to solve for the variables x and y; it helps students think about mathematics at an abstract level, and provides them with a way to reason about real-life problems. In this course, participants will explore three components of algebraic thinking: making generalizations, thinking about the equals sign, and being able to reason about unknown quantities. As participants stretch their own algebraic reasoning skills, they will also spend considerable time thinking about how to integrate algebraic tasks into their own classroom instruction. This course uses readings, video, online discussion boards, a final project, and engaging mathematics problems to promote the idea that the incorporation of algebraic thinking tasks in elementary school mathematics is critical to students' future success.
*This course is open to all certified WV educators for multi-subjects grades K-8.
**If you are taking this course to apply toward paraprofessional certification, then you must be working with a grades 3-5 certified elementary school teacher or a middle school/high school certified mathematics teacher for the duration of the course. You must submit a letter from your school principal indicating that you will be taking the course under the direction of the classroom teacher, a grades 3-5 certified elementary school teacher or a middle school/high school certified mathematics teacher, for the duration of the course. Course dates must be included in this letter. This letter must be received prior to the beginning date of the course. Course assignments will require that you and the classroom teacher complete assignments with students.
Course Syllabus
Algebraic Thinking in the Elementary School
Catalog Description:
This course provides elementary teachers with resources and opportunities to work with activities that promote algebraic thinking in the elementary math classes. Participants will learn how to integrate strategies and instructional procedures to help students think about mathematics at an abstract level, reason about real-life problem scenarios and make sense of their thinking. Participants will explore three components of algebraic thinking: making generalizations, thinking about "equals" and being able to reason about unknown quantities.
Participants will consider how to integrate algebraic tasks into their classroom instruction, how to utilize various media resources and how to engage in mathematical problem solving to promote algebraic thinking of elementary school students laying the foundation of future success of students.
Prerequisites:
This is an introductory course for teachers, particularly elementary teachers of mathematics, technology specialists, curriculum specialists, professional development specialists and administrators. Participants are expected to have regular access to computers. Although not a requirement, high speed Internet access definitely enhances the online experience. Participants should be proficient with using email, browsing the Internet, and navigating through computer files. Access to Microsoft Office is recommended. Participants who do not have access to Microsoft Office should download Open Office documents (a free download from Microsoft) to enable them to read and send word documents throughout this course.
Goals
This course will enable participants to:
learn how children in grades 3-5 can think about basic algebraic concepts,
appreciate the importance of algebraic thinking in the upper elementary curriculum,
read and discuss relevant research on the importance of algebraic thinking in elementary school instruction,
explore a variety of problems that can be used with students to develop their algebraic thinking,
understand student misconceptions about the sign "=" and why this is such a pivotal concept in elementary mathematics,
identify generalization as a strategy for solving some, but not all, algebraic problems,
appreciate the role of "unknown quantity" problems in the development of algebraic reasoning,
learn how to design and "algebrafy"** activities that encourage algebraic thinking,
create a collection of activities which promote algebraic thinking that can be integrated into classroom practice and
promote a "learning-by-doing" methodology, which is applicable to students at all ages.
Assessment and Course Requirements
Each session includes readings, activities and a discussion assignment, which participants are required to complete. High-quality, active participation in the online discussions is vital to the understanding and completion of the course. Additionally, participants will develop portions of a final project during each week's session. Weekly assignments address sections of this project and a midterm check will occur during Session Three.
Course Products
The project for this course is a collection of classroom activities that promote algebraic thinking which include activities, follow-up questions, and a brief reflection piece where the teacher describes his/ her expectations in terms of what students will know and be able to do upon completion of each activity.
Discussion Participation
Participants will be evaluated weekly on the frequency and quality of their participation in the discussion forum. Participants are required to post a minimum of three substantial postings each session, including one that begins a new thread and two that respond to existing threads. Postings that begin new threads will be reviewed based on their relevance, demonstrated understanding of course concepts, examples cited, and overall quality. Postings that respond to other participants will be evaluated on relevance and the degree to which they extend the discussion. Participants are to read all original messages by course colleagues and enough additional responses to make a total of 50% of the messages posted for that session.
Sessions Overview:
Session One: What is Algebraic Reasoning?
During this session, participants will learn why algebraic reasoning is important in elementary math instruction and what exactly "algebraic reasoning" means. Participants will utilize knowledge of the NCTM Algebra strand goals and will investigate activities such as identifying patterns, analyzing change, representing situations and using math models to understand relationships such as algebraic thinking.
Session Two: Understanding Algebraic Representations and Patterns
In this session, participants explore two algebraic problems and compare their methods for solving them. Participants learn that different methods of solving problems contribute much to the understanding of the problem and that there is no "one right" way to solve these problems. This session focuses on "doing the math".
Session Three: The Meaning of Equality
In this session, participants focus on "equality/ equals/=" and consider why youngsters have a difficult time solving algebraic problems of the sort "3=5=__+4" and "__ =2=3+6. The idea that the equals sign should be introduced as a balance and not as an operator, will be investigated. During this session, participants will interview a student about his/ her thinking about this topic.
Session Four: Using Algebra to Think About Unknown Quantities
During this session, participants will consider ways to solve algebraic problems when multiple possibilities exist for a number n. Participants will explore problems that compare two quantities in order to think about students' understanding of algebraic tasks. This session is designed to illustrate that algebraic thinking does not always involve finding a missing quantity; sometimes it's more about relating two quantities that happen to have an element in common.
Session Five: "Algebrafying" Elementary Math Instruction
In this session, participants will learn how to "algebrafy" their math instruction by applying new questioning techniques to delve into student thinking. They will also think about what types of problems they can algebrafy and which types of questions are not appropriate for that. Attention will be given to identifying math problems which are algebraic in nature and how to bring out algebraic ideas in these problems. Participants will also consider how to ask questions that promote algebraic thinking.
Session Six: What is the Value of Algebra in Elementary School?
In this session, participants will continue to work with algebrafying their instruction and will consider the deeper importance of incorporating algebra into their instruction. Participants will also continue working on problems that were introduced in Session 5, and will complete work on their Final Project. | 677.169 | 1 |
Description
This app introduces concepts and develops techniques to enable the user to correctly perform and interpret calculations with data. This content is found in GCSE Mathematics courses, GCSE Statistics courses and in some first applied modules of A-Level Mathematics.
With an inexpensive in-app purchase, the full nine sections of teaching, questions and worked solutions become available. Four useful introductory sections are immediately accessible from the initial download. This app makes an ideal companion for learning, revision, examination practice, and checking knowledge.
* Suitable for students, parents, tutors and teachers.
* Visit to sign up for 1600 questions and solutions from 188 A-Level papers, spanning over 2000 pages and including video demonstrations for over 60 of the subsections. There are 1000+ pages of maths e-text covering Statistics and Pure Mathematics | 677.169 | 1 |
97802011537mediate algebra
The goal of Intermediate Algebra: Concepts and Applications, 7e is to help today s students learn and retain mathematical concepts by preparing them for the transition from skills-oriented intermediate algebra courses to more concept-oriented college-level mathematics courses, as well as to make the transition from skill to application. This edition continues to bring your students a best-selling text that incorporates the five-step problem-solving process, real-world applications, proven pedagogy, and an accessible writing style. The Bittinger/Ellenbogen series has consistently provided teachers and students with the tools needed to succeed in developmental mathematics. This edition has an even stronger focus on vocabulary and conceptual understanding as well as making the mathematics more accessible to students. Among the features added are new Concept Reinforcement exercises, Student Notes that help students avoid common mistakes, and Study Summaries that highlight the most important concepts and terminology from each chapter | 677.169 | 1 |
1/7Mathematical Ideas
Mathematical Ideas plus MyMathLab -- Access Card Package
Mathematical Ideas
Vid Lect On CD W Op Mathematical Ideas
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Customer Reviews
Good book!September 27, 2011 by Jacob Miller from Richmond, KY
I'm really not a math-minded person, but this book makes it easy to understand. It's also important to distinguish this book from other math texts because it's more than just numbers and symbols. Mathematical Ideas has more in depth explanations than any other math text I've used. 4 Stars.
Summary
What does your math course have to do with the latest TV shows or Hollywood movies? Plenty#x13;if you#x19;re using the right text. Mathematical Ideas, Twelfth Editionbrings the best of Hollywood into the classroom through descriptions of video clips from popular cinema and television. Well-known author John Hornsby#x19;s innovative approach is enhanced with great care in this revision, and refined to serve the needs of you and your instructor. Streamlined and updated, it offers a modernized design, new bubble pointers for Example annotations, and much more. It retains the consistent features, friendly writing style, clear examples, and exercise sets for which this text is known.
Author Biography
Charles Miller has taught at America River College for many years.
Vern Heeren received his bachelor's degree from Occidental College and his master's degree from the University of California, Davis, both in mathematics. He is a retired professor of mathematics from American River College where he was active in all aspects of mathematics education and curriculum development for thirty-eight years. Teaming with Charles D. Miller in 1969 to write Mathematical Ideas, the pair later collaborated on Mathematics: An Everyday Experience; John Hornsby joined as co-author of Mathematical Ideas on the later six editions. Vern enjoys the support of his wife, three sons, three daughters in-law, and eight grandchildren.
John Hornsby: When a young John Hornsby enrolled in Lousiana State University, he was uncertain whether he wanted to study mathematics education or journalism. Ultimately, he decided to become a teacher. After twenty five years in high school and university classrooms, each of his goals has been realized. His passion for teaching and mathematics manifests itself in his dedicated work with students and teachers, while his penchant for writing has, for twenty five years, been exercised in the writing of mathematics textbooks. Devotion to his family (wife Gwen and sons Chris, Jack, and Josh), numismatics (the study of coins) and record collecting keep him busy when he is not involved in teaching or writing. He is also an avid fan of baseball and music of the 1960's. Instructors, students, and the 'general public' are raving about his recent Math Goes to Hollywood presentations across the country. | 677.169 | 1 |
McGraw-Hill's GED Mathematics
(McGraw-Hill's GEDBloomingdale
ILWatauga
TXParadise-Valley
AZ, USA
$11.29
FREE
About the Book
Create your own path to GED success with help from McGraw-Hill's GED test series
The newly revised McGraw-Hill's GED test series helps you develop the skills you need to pass all five areas of the GED test.
Presented in a clear, appealing format, these books offer many opportunities for test practice and explain the essential concepts of each subject so you can succeed on every portion of the GED exam. The series covers: Language Arts, Reading * Language Arts, Writing * Mathematics * Science * Social Studies
"McGraw-Hill's GED Mathematics" guides you through the GED preparation process step-by-step. A Pretest helps you find out your strengths and weaknesses so you can create a study plan to fit your needs. The following chapters introduce you to math concepts on which hundreds of GED questions are based. Then check your understanding of these ideas with the Posttest, presented in the GED format. You can then see how ready you are for the big exam by taking the full-length Practice Test.
"McGraw-Hill's GED Mathematics" includes: Clear instructions to show you how to use number grids and coordinate plane grids Instruction and frequent practice with the "Casio fx-260" calculator Problem-solving strategies to help you understand word problems Easy-to-follow lessons to develop essential math skills in whole numbers, decimals, fractions, percents, ratios, data analysis, geometry, and algebra
With "McGraw-Hill's GED Mathematics," you will sharpen your study skills for test success! | 677.169 | 1 |
Combinatorial Problems and Exercises
9780821842621
ISBN:
0821842625
Pub Date: 2007 Publisher: American Mathematical Society
Summary: The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems.
Lovász, László is the author of Combinatorial Problems and Exercises, published 2007 under ISBN 9780821842621 and 0821842625. Fifty six Combi...natorial Problems and Exercises textbooks are available for sale on ValoreBooks.com, one used from the cheapest price of $145.61, or buy new starting at $85.94.[read more] | 677.169 | 1 |
FOR STUDENTS REQUIRING ADDITIONAL ASSISTANCE WITH THEIR STUDY FOR THE FINAL EXAM. THIS SEGMENT WILL INCLUDE SOLVING SYSTEMS OF EQUATIONS, GRAPHING, RECOGNIZING THE EQUATION OF A GRAPH, SOLVING EQUATIONS, LINEAR AND QUADRATIC, LONG AND SYNTHETIC DIVISION, FACTORING TO SOLVE, COMPLETING THE SQUARE TO SOLVE EQUATIONS, FINDING THE VERTEX USING COMPLETING THE SQUARE AND A SIMPLER METHOD, USING THE SQUARE ROOT PROPERTY, PROPERTIES OF EXPONENTS AND RADICALS, SOLVING COMPLEX FRACTIONS, SOLVING RATIONAL EQUATIONS, SIMPLIFYING RATIONAL EXPRESSIONS, ADDING AND SUBTRACTING RATIONAL EXPRESSIONS. FOILing, FINDING THE X- AND Y-INTERCEPT, DIFFERENCE OF 2 SQUARES, SUM OR DIFFERENCE OF 2 CUBES, BASIC GEOMETRY, AND MUCH, MORE BASED ON STUDENTS CALLING IN . | 677.169 | 1 |
Introduction to MATLAB 2nd edition
0136081231
9780136081234
Details about Introduction to MATLAB:
Introduction to MATLAB, 2/e is appropriate for Introductory Engineering courses.
Best-selling author Delores Etter provides an up-to-date introduction to MATLAB. Using a consistent five-step problem-solving methodology, Etter describes the computational and visualization capabilities of MATLAB and illustrates the problem solving process through a variety of engineering examples and applications.
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Rent Introduction to MATLAB 2nd edition today, or search our site for Delores M. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Prentice Hall. | 677.169 | 1 |
Big Sur PrecalMatthew H. success in the math portions of the SAT and GMATRachel B.
...Excel is a very useful program for a variety of reasons. A few examples are making graphs, performing multiple math computations at once, and manipulating data. Don't go to college without a basic understanding of this program.
Neal B.
...In fact, they require many hours of practice and thought even for the people that are 'good' at them. And you may very well feel like it doesn't come naturally to you. Often the material in one chapter is built upon a foundation of many ideas. | 677.169 | 1 |
Product description
Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.
In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.
Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.
Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..
Author information
The Holy Grail of Number Theory
George E. Andrews, Evan Pugh Professor of Mathematics at Pennsylvania State University, author of the well-established text "Number Theory" (first published by Saunders in 1971 and reprinted by Dover in 1994), has led an active career discovering fascinating phenomena in his chosen field number theory. Perhaps his greatest discovery, however, was not solely one in the intellectual realm but in the physical world as well. In 1975, on a visit to Trinity College in Cambridge to study the papers of the late mathematician George N. Watson, Andrews found what turned out to be one of the actual Holy Grails of number theory, the document that became known as the "Lost Notebook" of the great Indian mathematician Srinivasa Ramanujan. It happened that the previously unknown notebook thus discovered included an immense amount of Ramanujan's original work bearing on one of Andrews' main mathematical preoccupations mock theta functions. Collaborating with colleague Bruce C. Berndt of the University of Illinois at Urbana-Champaign, Andrews has since published the first two of a planned three-volume sequence based on Ramanujan's Lost Notebook, and will see the project completed with the appearance of the third volume in the next few years. In the Author's Own Words:
"It seems to me that there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally surprise me. I do not think of mathematics as invented but rather discovered." George E. Andrews" | 677.169 | 1 |
In addition to the Introduction to Analysis chapters contained in previous editions, this edition presents two new chapters that give an introduction to Abstract Algebra via group theory. While this is a standard topic and there are many texts on group theory, this is a "taster" as an introduction…
The authors of this classroom-tested, student-friendly text illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems such as congruences in the ISBN systemThis book provides a comprehensive introduction to the use of graph analysis in the study of social media and digital media. It covers the following topics: graphs in social media, graph theory, algebraic analysis of graphs, graph clustering, diffusion in social media, label propagation in graphs,…
First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a fourth edition. It reflects the exciting developments in number theory during the past decades that culminated in the proof of Fermat's Last Theorem. AnBased on the research experience of the authors, this book provides a theoretical structure of fundamental number theory algebra knowledge supporting public-key cryptography. The authors integrate the results and thinking from more than 20 years of research and teaching, bridging the gap betweenVolume l, Kemer's Theorems, 2nd Edition
This book contains a complete proof of Kemer's Theorem. In addition, it includes a new and much faster proof of Beidar's representability theorem for Noetherian rings and a thorough treatment of Zubilin's method.…
Analyze Global Nonlinear Problems Using Metasolutions
Metasolutions of Parabolic Equations in Population Dynamics explores the dynamics of a generalized prototype of semilinear parabolic logistic problem. Highlighting the author's advanced work in the field, it covers the latest developments in the…
Divided into three parts, this book fills in the gap between introductory texts in discrete mathematics and advanced graduate textbooks in enumerative combinatorics. Part I deals with basic counting principles, compositions and partitions, and generating functions. Part II focuses on the structure | 677.169 | 1 |
There's no such thing as too much practice. This reproducible program builds skills incrementally. By inviting students to "show what they know" in a variety of new formats, these stimulating lessons will enable struggling students to actually enjoy the learing process. As in all of the binder programs, the dual emphasis is on (1) mastery of the basics... more...
version of its predecessor. With an emphasis on clarity and brevity, each new title features a streamlined... more...
This third edition of the perennial bestseller defines the recent changes in how the discipline is taught and introduces a new perspective on the discipline. New material in this third edition includes:
A modernized section on trigonometry
An introduction to mathematical modeling
Instruction in use of the graphing calculator
2,000 solved... more...
§22. K-theory 230 A. Topological X-theory 230 Vector bundles and the functor Vec(X). Periodicity and the functors KJX). K(X) and t the infinite-dimensional linear group. The symbol of an elliptic differential operator. The index theorem. B. Algebraic K-theory 234 The group of classes of projective modules. K , K and K of a ring. K of a field and o... more...
This book contains nine refereed research papers in various areas, from combinatorics to dynamical systems, with computer algebra as an underlying and unifying theme. Topics covered are irregular connections, summability of solutions and rank reduction of differential systems, asymptotic behaviour of divergent series, integrability... more...
Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter... more...
This insightful book combines the history, pedagogy, and popularization of algebra to present a unified discussion of the subject. Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical... more... | 677.169 | 1 |
This site's author created this unique wavelet tutorial to help people with no prior knowledge of wavelet theory. In contrast with many other resources on the topic, which are more advanced in nature, this site starts...
This excellent metasite for prime numbers is mind-boggling, not only in terms of the quality of information provided, but also in the breadth and variety of the hyperlinks, from discourse on the Riemann hypothesis to...
Does knowing about Descartes help students understand the Cartesian coordinate system? Will teaching students the origin of the term parabola help them understand the mathematical importance of parabolas and other...
From polynomials to rational expressions, the world of algebra can be a befuddling place. Of course, trigonometry presents certain challenges as well, what with its sine graphs and inverse functions. Students and... | 677.169 | 1 |
Elements of the Theory of Numbers
By
Thomas Dence, Ashland University, Ohio, U.S.A.
Joseph Dence, University of Missouri, Columbia, U.S.A.
Elements of the Theory of Numbers teaches students how to develop, implement, and test numerical methods for standard mathematical problems. The authors have created a two-pronged pedagogical approach that integrates analysis and algebra with classical number theory. Making greater use of the language and concepts in algebra and analysis than is traditionally encountered in introductory courses, this pedagogical approach helps to instill in the minds of the students the idea of the unity of mathematics. Elements of the Theory of Numbers is a superb summary of classical material as well as allowing the reader to take a look at the exciting role of analysis and algebra in number theory.
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Book information
Reviews
"I definitely appreciate the unified approach. I think it is important that the students realize that mathematics does not consist of separate entities." --Maureen Fenrick, Mankato State University
"The authors communicate successfully the joy they find in number theory. Students will be excited by learning from this (text)." --Frank DeMeyer, Colorado State University"The book's biggest advantage is its thorough integration of the relevant algebra into the development. It's about time!" --Thomas McLaughlin, Texas Tech University
Table of Contents
Part I The FundamentalsIntroduction: The PrimesThe Fundamental Theorem of Arithmetic and Its ConsequencesAn Introduction to CongruencesPolynomial CongruencesPrimitive RootsResiduesMultiplicative Functions Part II Special TopicsRepresentation ProblemsAn Introduction to Number FieldsPartitionsRecurrence Relations Appendix I: NotationAppendix II: Mathematical TablesAppendix III: Sample Final ExaminationsAppendix IV: Hints and Answers to selected problems | 677.169 | 1 |
Well known for accuracy, Soo Tans APPLIED CALCULUS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Eighth Edition balances applications, pedagogy, and technology to provide students the context they need to stay motivated in the course and interested in the material. Accessible for majors and nonmajors alike, the text uses an intuitive approach that introduces abstract concepts through examples drawn from common, reallife experiences to which students can relate. | 677.169 | 1 |
Developmental Arithmetic (3-0-3). Credit not applicable toward degrees. Required of students whose ACT Mathematics Main score is less than 15 or COMPASS Math score of 30 or less. Fundamental topics in arithmetic, geometry, and pre-algebra.
099 Developmental Algebra (3-0-3). Credit not applicable toward degrees. Required of students whose ACT Mathematics Main score is at least 15 but less than 19 or COMPASS Math score of 31 to 58. Fundamental topics in algebra for students with insufficient knowledge of high school level mathematics. PR: ACT Mathematics Main score of 15 or grade of "S" in MATH 098.
109 Algebra (3-0-3). Real numbers, exponents, roots and radicals; polynomials, first and second degree equations and inequalities; functions and graphs. PR: ACT Mathematics main score of 19 or grade of "S" in MATH 099.
211 Informal Geometry (3-0-3). Theorems are motivated by using experiences with physical objects or pictures and most of them are stated without proof. Point approach is used with space as the set of all points; review elementary geometry, measurement, observation, intuition and inductive reasoning, distance, coordinate systems, convexitivity, separation, angles, and polygons. No field credit for math majors/minors. PR: MATH 101 or higher.
220 Calculus I (4-0-4). A study of elements of plane analytical geometry, including polar coordinates, the derivative of a function with applications, integrals and applications, differentiation of transcendental functions, and methods of integration. PR: MATH 109 and MATH 110, or GNET 116, or ACT Mathematics main score of 26 or COMPASS Trigonometry score of 46 or above.
250 Discrete Mathematics (3-0-3). Treats a variety of themes in discrete mathematics: logic and proof, to develop students' ability to think abstractly; induction and recursion, the use of smaller cases to solve larger cases of problems; combinatorics, mathematics of counting and arranging objects; algorithms and their analysis, the sequence of instructions; discrete structures, e.g., graphs, trees, sets; and mathematical models, applying one theory to many different problems. PR: MATH 109 and MATH 110 or GNET 116.
290 Topics in Mathematics (1-4 hours credit). Formal course in diverse areas of mathematics. Course may be repeated for different topics. Specific topics will be announced and indicated by subtitle on the student transcript. PR: Consent of instructor.
400 Introduction to Topology (3-0-3). A study of set theory; topological spaces, cartesian products, connectedness; separation axioms; convergences; compactness. Special attention will be given to the interpretation of the above ideas in terms of the real line and other metric spaces. PR: MATH 240.
490 Topics in Mathematics (1-4 hours credit per semester). Advanced formal courses in diverse areas of mathematics. Courses may be repeated for different topics. Specific topics will be announced and indicated by subtitle on transcript. PR: Consent of instructor. | 677.169 | 1 |
Description
Math Formulary Pro covers all mathematical formulas that are usually used in the school and the university. Where necessary graphics are included to depict and explain the topic better. This Pro Version contains no ads and don't require any permissions.
SD-Card Installation is supported. Bug reports related to the content and the app itself are more than welcome. Proposals for new features would be great | 677.169 | 1 |
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includes many high-quality open source math packages.
Use Most Mathematics Software from Within SAGE. SAGE makes it easy for you to use most mathematics software together. SAGE includes interfaces to Magma, Maple, Mathematica, MATLAB, and MuPAD, and the free programs Axiom, GAP, GP/PARI, Macaulay2, Maxima, Octave, and Singular.
Use a Standard Programming Language. You work with SAGE using the highly regarded scripting language Python instead of an obscure language designed for a particular mathematics program. You can write programs that combine serious mathematics with anything else. | 677.169 | 1 |
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