---
product_id: 16142317
title: "Algebra"
price: "€ 69.83"
currency: EUR
in_stock: true
reviews_count: 12
url: https://www.desertcart.at/products/16142317-algebra
store_origin: AT
region: Austria
---

# Algebra

**Price:** € 69.83
**Availability:** ✅ In Stock

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- **What is this?** Algebra
- **How much does it cost?** € 69.83 with free shipping
- **Is it available?** Yes, in stock and ready to ship
- **Where can I buy it?** [www.desertcart.at](https://www.desertcart.at/products/16142317-algebra)

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## Description

This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

Review: 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. 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. It moves smoothly from basic arithmetic (which everyone should still read if only to learn a different way of explaining it to a student/younger sibling/child) all the way to proofs, both algebraic and visual when possible, of some important inequalities. Cauchy's inductive proof, first for powers of two and then filling in the gaps, of the AM-GM inequality is here, as is the standard proof of Cauchy-Schwarz by the discriminant of a polynomial. Go to your local high school and look at its algebra book. I doubt that's in there. I'll end with a few of the funny, sometimes weird, little remarks: After illustrating the associative law using the example (sugar + coffee) + milk = sugar + (coffee + milk), the next problem is: "Problem 25. Try it." "Please keep in mind that a monomial is a polynomial, so sometimes for a mathematician one is many." "Probably you are discouraged by this solution because it seems impossible to invent it. The authors share your feeling." One section begins: "62. How to confuse students on an exam: As usual, there are many evil ways to make use of knowledge."
Review: Incredibly Innovative Algebra Book - I'm writing this review from the perspective of a mathematics graduate student reading more "basic" math books in order to better tutor younger students. This book by Gelfand and Shen is amazing at provoking deep contemplation on simpler math that many take for granted. Although the problems are not too hard for me, I find myself constantly confronting new ways of thinking about basic algebra. For example, the exercises in the book outline fun periodic patterns arising from division that I've probably considered but never really thought about. The problems also encourages the reader to come up with tricks/shortcuts, essentially forcing the learner to arrive at key insights. For those looking for a step-by-step tutorial, you won't find it in this book. However, working actively through the problems will definitely deepen one's understanding of algebra beyond standard plug-and-chug textbooks. I highly recommend this book to people looking to review mathematics or motivated/talented first time students.

## Technical Specifications

| Specification | Value |
|---------------|-------|
| Best Sellers Rank | #135,862 in Books ( See Top 100 in Books ) #52 in Algebra & Trigonometry #121 in Algebra |
| Customer Reviews | 4.4 out of 5 stars 87 Reviews |

## Images

![Algebra - Image 1](https://m.media-amazon.com/images/I/51U98DglVtL.jpg)

## Customer Reviews

### ⭐⭐⭐⭐⭐ I can't think of a title. Just buy the book!
*by H***L on January 30, 2011*

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. It moves smoothly from basic arithmetic (which everyone should still read if only to learn a different way of explaining it to a student/younger sibling/child) all the way to proofs, both algebraic and visual when possible, of some important inequalities. Cauchy's inductive proof, first for powers of two and then filling in the gaps, of the AM-GM inequality is here, as is the standard proof of Cauchy-Schwarz by the discriminant of a polynomial. Go to your local high school and look at its algebra book. I doubt that's in there. I'll end with a few of the funny, sometimes weird, little remarks: After illustrating the associative law using the example (sugar + coffee) + milk = sugar + (coffee + milk), the next problem is: "Problem 25. Try it." "Please keep in mind that a monomial is a polynomial, so sometimes for a mathematician one is many." "Probably you are discouraged by this solution because it seems impossible to invent it. The authors share your feeling." One section begins: "62. How to confuse students on an exam: As usual, there are many evil ways to make use of knowledge."

### ⭐⭐⭐⭐⭐ Incredibly Innovative Algebra Book
*by N***G on November 7, 2025*

I'm writing this review from the perspective of a mathematics graduate student reading more "basic" math books in order to better tutor younger students. This book by Gelfand and Shen is amazing at provoking deep contemplation on simpler math that many take for granted. Although the problems are not too hard for me, I find myself constantly confronting new ways of thinking about basic algebra. For example, the exercises in the book outline fun periodic patterns arising from division that I've probably considered but never really thought about. The problems also encourages the reader to come up with tricks/shortcuts, essentially forcing the learner to arrive at key insights. For those looking for a step-by-step tutorial, you won't find it in this book. However, working actively through the problems will definitely deepen one's understanding of algebra beyond standard plug-and-chug textbooks. I highly recommend this book to people looking to review mathematics or motivated/talented first time students.

### ⭐⭐⭐⭐⭐ Good book
*by M***L on March 10, 2026*

Good book

## Frequently Bought Together

- Algebra
- Trigonometry
- Geometry

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---

*Product available on Desertcart Austria*
*Store origin: AT*
*Last updated: 2026-06-02*