Equations and Inequalities [Hardcover]

Jiri Herman (Author), Radan Kucera (Author), Jaromir Simsa (Author), K. Dilcher (Translator)

Book Description

ISBN-10: 0387989420 | ISBN-13: 978-0387989426 | Publication Date: March 23, 2000 | Edition: 1

A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.

Editorial Reviews

Review

From the reviews:

MATHEMATICAL INTELLIGENCER

"I have nothing but praise for this book, and I can't imagine a mathamtician who wouldn't want to own it."

MAA ONLINE

"This book contains over 300 examples and then over 700 exercises for the reader. The authors have even included a fourth chapter with hints and answers to the exercises. So, even if the solution isn't given in the back, at least the reader will have some hint about which direction to start looking. The book provides a nice introduction into many of the problems-solvers' 'tricks of the trade.' There is a lot presented here, so the reader (especially an undergraduate) may want to take the following approach: read just a few pages at a time, work out some of the exercises, then take some time to digest the material before going on."

 

Product Details

• Hardcover: 360 pages
• Publisher: Springer; 1 edition (March 23, 2000)
• Language: English
• ISBN-10: 0387989420
• ISBN-13: 978-0387989426
• Product Dimensions: 9.4 x 6.3 x 0.9 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,451,145 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

10 of 10 people found the following review helpful:

5.0 out of 5 stars Unusual math here, October 27, 2004

By 

Carl F. Mclaren Jr. (Haines City, Florida USA) - See all my reviews
(REAL NAME)   

This review is from: Equations and Inequalities (Hardcover)

This book contains just 4 chapters:
(1) Algebraic Identities and Equations
(2) Algebraic Inequalities
(3) Number Theory
(4) Hints and Answers
The material is not readily available in any book I have seen. The 1st chapter covers finite sums, polynomials, and irrational equations. The 2nd chapter covers how to prove many inequalities and the 3rd chapter uses congruences and other principles to derive many interesting number theory results.
For example in chapter 3 I encountered the following "Show that among 50 arbitrarily chosen distinct prime numbers one can always find 13 primes such that the difference between any two of them is divisible by 5". Sounds difficult but is really trivial using methods in the book. There are lots of worked examples and exercises after each topic. The methods are understandable but not trivial ! Chapter 4 is the jewel as it gives the solutions to the exercises, I hate it when I don't know how to do a problem and have no way to find out. Also, sometimes one solves a problem incorrectly or there is a better way. Most math students today do not do anywhere near enough calculations and so are weak in standard manipulation and this will correct that if the exercises are attempted. I really like this book and so will you !

6 of 6 people found the following review helpful:

5.0 out of 5 stars Great First course in Problem Solving, August 3, 2001

By A Customer

This review is from: Equations and Inequalities (Hardcover)

This is a great book for high school students and undergrads who don't have much experience with solving problems. Sums, inequalities, systems of equations, and number theory are the core of the book. The author provides worked examples and then a set of exercises and some challenging problems are included at the end of each chapter(almost all of the solutions are given). Very readable and a great addition to any mathematics library. Highly recommend.