Functions and Graphs [Paperback]

I.M. Gelfand (Author), E.G. Glagoleva (Author), E.E. Shnol (Author)

Book Description

ISBN-10: 0817635327 | ISBN-13: 978-0817635329 | Publication Date: December 1, 1990 | Edition: 1

The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990's. As early as the 1960's, I.M. Gelfand and his colleagues in the USSR thought hard about this same question and developed a style for presenting basic mathematics in a clear and simple form that engaged the curiosity and intellectual interest of thousands of high school and college students. These same ideas, this same content, unchanged by over thirty years of experience and mathematical development, are available in the following books to any student who is willing to read, to be stimulated, and to learn. "Functions and Graphs" provides instruction in transferring formulas and data into geometrical form. Thus, drawing graphs is shown to be one way to "see" formulas and functions and to observe the ways in which they change. This skill is fundamental to the study of calculus and other mathematical topics. Teachers of mathematics will find here a fresh understanding of the subject and a valuable path to the training of students in mathematical concepts and skills.

Editorial Reviews

Review

"All through both volumes [Functions & Graphs and The Methods of Coordinates], one finds a careful description of the step-by-step thinking process that leads up to the correct definition of a concept or to an argument that clinches in the proof of a theorem. We are ... very fortunate that an account of this caliber has finally made it to printed pages... Anyone who has taken this guided tour will never be intimidated by n ever again... High school students (or teachers) reading through these two books would learn an enormous amount of good mathematics. More importantly, they would also get a glimpse of how mathematics is done." -- H. Wu, The Mathematical Intelligencer

Language Notes

Text: English (translation)

Product Details

• Paperback: 116 pages
• Publisher: Birkhäuser Boston; 1 edition (December 1, 1990)
• Language: English
• ISBN-10: 0817635327
• ISBN-13: 978-0817635329
• Product Dimensions: 9.1 x 6 x 0.3 inches
• Shipping Weight: 6.4 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #2,244,649 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

25 of 25 people found the following review helpful:

5.0 out of 5 stars An insightful introduction to analytic geometry., August 30, 2004

By 

N. F. Taussig (Bronx, NY) - See all my reviews
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This review is from: Functions and Graphs (Dover Books on Mathematics) (Paperback)

This brief text provides a clear introduction to analytic geometry. Its scope is narrow. The authors discuss the graphs and properties of linear functions, absolute value functions, quadratic functions, linear fractional functions, power functions, and rational functions (trigonometric functions are discussed in another volume of the Gelfand School Outreach Program). What distinguishes this book from other treatments of the same topics is the extent to which the authors go to explain, using both words and diagrams, why the graphs of the functions they discuss have the form they do and the many challenging exercises they include.

This book concludes with a chapter length exercise set full of challenging problems. The reader who completes these problems will gain a much fuller understanding of analytic geometry than one who reads a typical precalculus text. While calculus is not required to complete the exercises, the reader may wish to revisit these problems once she or he has had calculus in order to analyze the properties of the graphs more fully.

The text was written initially for a correspondence course in the Soviet Union. Since students could send their solutions to the authors when they were at the University of Moscow, answers or hints to only a few of the exercises are included in the back of the text.

I also highly recommend the other volumes in the Gelfand School Outreach Program. They include The Method of Coordinates, Algebra, and Trigonometry.

25 of 26 people found the following review helpful:

5.0 out of 5 stars Can You Graph?, This Book Will Bring You to Mastery, February 5, 2006

By 

J. D. Halabi "math teacher" (Bronx, NY) - See all my reviews
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Amazon Verified Purchase

This review is from: Functions and Graphs (Dover Books on Mathematics) (Paperback)

In this slim, 100 page volume, Gelfand, Glagoleva and Shnol have a wonderful review of graphing.

There is nothing here incredibly advanced; they only cover linear, quadratic, polynomial, and rational (ie, f(x) = P(x)/Q(x) ) functions. But they systematically explain how to transform, how to combine, how to shift, how to reflect... They consider asymptotes (vertical and horizontal), zeros, symmetries. They spend more time with absolute value then one might expect.

They treat these limited topics in depth. I read this book on vacation, cover to cover, completing every single exercise. It was a great refresher, and led me to think about several graphing-skill topics from new perspectives.

I am a teacher, and this book has informed my teaching. Also, I intend to use it with my math team. I do not think you could use this book to teach graphing from scratch. Rather, I see it as a source of enrichment.

The major drawback to this book is the lack of answers in the back. But if you are really stuck, the judicious use of a graphing calculator (or checking with friends or colleagues) should be good enough. At the price, there is no reason not to own "Functions and Graphs."

22 of 24 people found the following review helpful:

5.0 out of 5 stars A great book!, October 10, 2003

By 

Bruce R. Gilson (Wheaton, MD United States) - See all my reviews
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Amazon Verified Purchase

This review is from: Functions and Graphs (Dover Books on Mathematics) (Paperback)

I tend to look at elementary books like this one from the point of someone who doesn't need to learn from it but might want to use it as a text if teaching or tutoring someone. I learned almost nothing from this book, but I didn't expect to, as it's all material I learned ages ago. But for someone encountering this material for the first time, this would be an excellent book.

I see this book as used primarily in a pre-calculus math class or for tutoring someone about to take calculus. It gives a good exposition of material that will be encountered at the time a student takes calculus, but at a level that assumes the student has only the algebra that most students entering a calculus course have taken. And from that point, it explains the elements of drawing graphs of algebraic functions and the ideas of tangency that are so critical to differential calculus, and does so in a clear way, with helpful diagrams. It is a slim book, and probably by itself could not be the only text in a pre-calculus math class, but on the subjects it covers, it is the best I have seen. (And that is underrating it, because there aren't many books on the subject. So one might say that "the best there is" isn't really as high praise as it deserves.)

This book certainly deserves a 5-star rating.