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Algebra

18 customer reviews
ISBN-13: 978-0817636777
ISBN-10: 0817636773
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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

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Product Details

  • Paperback: 150 pages
  • Publisher: Birkhäuser (July 9, 2003)
  • Language: English
  • ISBN-10: 0817636773
  • ISBN-13: 978-0817636777
  • Product Dimensions: 6.1 x 0.4 x 9.2 inches
  • Shipping Weight: 10.9 ounces (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (18 customer reviews)
  • Amazon Best Sellers Rank: #119,482 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

73 of 73 people found the following review helpful By N. F. Taussig on August 22, 2004
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,
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34 of 38 people found the following review helpful By A Customer on September 10, 2003
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
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19 of 20 people found the following review helpful By Herbert Powell on January 29, 2011
Format: Paperback Verified Purchase
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. Could it be used for a main text or should it be just a supplement? I don't know, but there is much more mathematics contained in these 149 pages than in any standard 500 page high school text on the market today. That's the unsurprising result of accomplished mathematicians writing a math book. Sure, some topics are missing. You won't find 3 or 4 chapters devoted to the several "different" ways to graph a line. There aren't fifty problems in a row that start with "suppose Sam rows upstream at 5 miles per hour and it takes her seven times as long as..." Unfortunately, there isn't even a treatment of complex numbers, the only omission that seems wrong.

You will find several interesting and serious topics that would be dangerous to bright students who insist they hate math, or rather what they've been told is math. Imagine their initial embarrassment when they find out that they can enjoy the subject! Maybe more importantly, imagine their relief when they realize that there IS a reason why we "FOIL", there IS a reason why negative times negative is positive, there IS a reason why we say a^(-1)=1/a, and it's not because "the teacher said so" or "that's just the rule" (ok, it is the rule, but now you'll see why). And there's no attempt to sneak anything by the reader. The authors are quick to acknowledge any gaps in their reasoning, and to assure the reader that in the future he or she will fill them.

It's this honesty and attention to rigor without being too formal or dry that give this book some extra charm.
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12 of 12 people found the following review helpful By Shell Zipi on December 7, 2011
Format: Paperback Verified Purchase
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. I was impressed by the beauty of this book. It might be a little too slim for a textbook but every kid who wants to learn algebra should read it. More than teaching algebra it shows what math should be: simple and beautiful.

My daughter's math textbook is 5 pounds and I can't even stand looking at it. I understand that not every is enthusiastic about math and not everyone can feel the beauty of math. But you don't have to make math so ugly.

Learning math with a 5 lb textbook is simply terrifying but if your kid goes to public school you probably have no choice. Let you kid read a good book like this one, as early as possible, before he(she) grows a life time aversion to math.
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35 of 41 people found the following review helpful By A Customer on April 1, 2000
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.
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12 of 14 people found the following review helpful By B. Hoffert on November 18, 2014
Format: Paperback
As a returning college undergrad studying a math-heavy field, I picked up Gelfand's Algebra hoping to rejuvenate my very rusty algebra skills. To be honest, I didn't even learn algebra that well when I first studied it over a decade ago, but I slid by as a stereotypical "math student" in grade school. I wanted to do it right this time, and I'd heard very good things about this book.

I want to start with the positives, because there are many. If you're someone put off by the modern way of teaching math that forgoes all explanations and intuition in favor of step-by-step guides and formulas, then you'll appreciate Gelfand's approach to the field of algebra. Each subject is treated in a learn-by-doing fashion, and nothing is spoon fed. Clever intuitive explanations are provided for many topics that most books just take for granted. If you work your way through the entire book and all of its problems, you'll come away with algebraic understanding and intuition that probably exceeds that of most undergraduate math majors at the college level. As I said, I wanted to learn algebra the "right way" this time around, and I definitely achieved my goal through this book.

That said, this book has some pretty major flaws to the point that I have trouble actually recommending it. In fact, I don't think I'd even recommend it to my past self.

First, of the hundreds of exercises provided throughout the book, it feels like less than half of them have solutions provided. The author tries to explain that any problem without a solution is okay to skip if you can't solve it, but that explanation just isn't good enough.
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