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 development, are available in the following books to any student who is willing to read, to be stimulated, and to learn. "Algebra" is an elementary algebra text from one of the leading mathematicians of the world -- a major contribution to the teaching of the very first high school level course in a centuries old topic -- refreshed by the author's inimitable pedagogical style and deep understanding of mathematics and how it is taught and learned. This text has been adopted at: Holyoke Community College, Holyoke, MA * University of Illinois in Chicago, Chicago, IL * University of Chicago, Chicago, IL * California State University, Hayward, CA * Georgia Southwestern College, Americus, GA * Carey College, Hattiesburg, MS
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“The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy lies behind the current text by Gelfand and Shen. There are specific ‘practical’ problems but there is much more development of the ideas … [The authors] have shown how to write a serious yet lively look at algebra.” —The American Mathematics Monthly “Were ‘Algebra’ to be used solely for supplementary reading, it could be wholeheartedly recommended to any high school student of any teacher … In fact, given the long tradition of mistreating algebra as a disjointed collection of techniques in the schools, there should be some urgency in making this book compulsory reading for anyone interested in learning mathematics.” —The Mathematical Intelligencer
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Most Helpful Customer Reviews
62 of 62 people found the following review helpful
Format:Paperback
This text, which is intended to supplement a high school algebra course, is a concise and remarkably clear treatment of algebra that delves into topics not covered in the standard high school curriculum. The numerous exercises are well-chosen and often quite challenging.
The text begins with the laws of arithmetic and algebra. The authors then cover polynomials, the binomial expansion, rational expressions, arithmetic and geometric progressions, sums of terms in arithmetic and geometric progressions, polynomial equations and inequalities, roots and rational exponents, and inequalities relating the arithmetic, geometric, harmonic, and quadratic (root-mean-square) means. The book closes with an elegant proof of the Cauchy-Schwarz inequality.
Topics are chosen with higher mathematics in mind. In addition to gaining facility with algebraic manipulation, the reader will also gain insights that will help her or him in more advanced courses.
The exercises, which are numerous, often involve searching for patterns that will enable the reader to tackle the problem at hand. Many of the exercises are quite challenging because they require some ingenuity. Some of the exercises are followed by complete solutions. These are instructive to read because the authors present alternate solutions that offer additional insights into the problem.
I also highly recommend the other texts in the Gelfand School Outreach Program. They include The Method of Coordinates, Functions and Graphs (Dover Books on Mathematics), and Trigonometry. Also, to gain additional insights into the inequalities at the end of this text, the reader may wish to consult an Introduction to Inequalities (New Mathematical Library) by Edwin Beckenbach and Richard Bellman.
The text begins with the laws of arithmetic and algebra. The authors then cover polynomials, the binomial expansion, rational expressions, arithmetic and geometric progressions, sums of terms in arithmetic and geometric progressions, polynomial equations and inequalities, roots and rational exponents, and inequalities relating the arithmetic, geometric, harmonic, and quadratic (root-mean-square) means. The book closes with an elegant proof of the Cauchy-Schwarz inequality.
Topics are chosen with higher mathematics in mind. In addition to gaining facility with algebraic manipulation, the reader will also gain insights that will help her or him in more advanced courses.
The exercises, which are numerous, often involve searching for patterns that will enable the reader to tackle the problem at hand. Many of the exercises are quite challenging because they require some ingenuity. Some of the exercises are followed by complete solutions. These are instructive to read because the authors present alternate solutions that offer additional insights into the problem.
I also highly recommend the other texts in the Gelfand School Outreach Program. They include The Method of Coordinates, Functions and Graphs (Dover Books on Mathematics), and Trigonometry. Also, to gain additional insights into the inequalities at the end of this text, the reader may wish to consult an Introduction to Inequalities (New Mathematical Library) by Edwin Beckenbach and Richard Bellman.
34 of 38 people found the following review helpful
By A Customer
Format:Paperback
This is a great book for people who are trying to learn or re-learn algebra. Explanations are very clear and there are many examples to work through.
29 of 32 people found the following review helpful
By A Customer
Format:Paperback
This book inspires even those with minimal interest in mathematics. If you are passionate about math, this is a must for you. The book is simply a refresher for high school algebra. It contains numerous gems that you could hardly find in a standard algebra text. If you are a teacher, you would have learned much to improve your teaching style and knows how to make your math classes more interesting...overall, a key source to keep on your bookshelf
Most Recent Customer Reviews
3.0 out of 5 stars
Not for algebra students
This might be a fine book for a mathematician who likes algebra textbooks, but it will be daunting for students. Read more
Published 1 month ago by Tumblemark
5.0 out of 5 stars
High School Algebra
Here is a down-to-earth book on the essentials of what a student should know by they time they leave high school.
Published 3 months ago by MZ
5.0 out of 5 stars
good text
excellent source for k-12 teachers of mathematics
skips all the useless stuff from those books that keep being published again each year
arrived on time, tho a bit pricey
skips all the useless stuff from those books that keep being published again each year
arrived on time, tho a bit pricey
Published 6 months ago by cmmm
5.0 out of 5 stars
Good introduction for the general reader
This book is for the intelligent general reader with nothing more than everyday, elementary-school training in mathematics. It is an excellent book for such a reader.
Published 14 months ago by Reader
5.0 out of 5 stars
Beautifully written!
I bought this book for my daughter (10 years old) and we read it together. We went very slow and I supplement it with a work book. She likes it. Read more
Published 17 months ago by Shell Zipi
5.0 out of 5 stars
I can't think of a title. Just buy the book!
Well, H. Wu on his page and N.F Taussig here have written quite good reviews, so I guess I can't really add anything new. Still, I feel the need to praise this book some more. Read more
Published on January 29, 2011 by Herbert Powell
4.0 out of 5 stars
Great book, not hard enough
Its a great book! You can't deny it! But, if you have more than some experience in algebra, you may want to consider something else. Read more
Published on December 17, 2009 by N. Pandya
4.0 out of 5 stars
A few novelties
This is a good, intelligent introduction. I assume most readers will know their algebra already and look for novelties departing from the norm in this book. Read more
Published on July 6, 2009 by Viktor Blasjo
5.0 out of 5 stars
good introductory text on algebra
I use this text to teach my 9-year old son algebra. The book is good, but beware that the scope is quite limited. I consider it a good text for elementary algebra. Read more
Published on March 8, 2008 by T. Liu
5.0 out of 5 stars
School level text
An excellent source of exercises and examples to work out Algebra, at a school level. Gives just what school lessons usually lack of. Enjoyable.
Published on November 2, 2007 by Francesco Erriques
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