Algebra [Paperback]

Israel M. Gelfand (Author), Alexander Shen (Author)

Book Description

ISBN-10: 0817636773 | ISBN-13: 978-0817636777 | Publication Date: December 1, 1993

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

Editorial Reviews

Review

“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

Product Details

• Paperback: 150 pages
• Publisher: Birkhäuser Boston (December 1, 1993)
• Language: English
• ISBN-10: 0817636773
• ISBN-13: 978-0817636777
• Product Dimensions: 8.9 x 6 x 0.4 inches
• Shipping Weight: 9.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.8 out of 5 stars  See all reviews (9 customer reviews)
• Amazon Best Sellers Rank: #135,890 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

54 of 54 people found the following review helpful:

5.0 out of 5 stars Splendid and illuminating algebra text., August 22, 2004

By 

N. F. Taussig (Bronx, NY) - See all my reviews
(REAL NAME)   

This review is from: Algebra (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.

23 of 25 people found the following review helpful:

5.0 out of 5 stars Makes you a master of high school algebra and..., September 10, 2003

By A Customer

This review is from: Algebra (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

28 of 32 people found the following review helpful:

5.0 out of 5 stars Great little book, April 1, 2000

By A Customer

This review is from: Algebra (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.