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Equations and Inequalities : CMS Books in Mathematics - Jiri Herman

Equations and Inequalities

CMS Books in Mathematics

Hardcover Published: March 2000
ISBN: 9780387989426
Number Of Pages: 344

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This book presents methods of 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 immediately followed by carefully worked out examples of increasing degrees of difficulty, and by exercises which range from routine to rather challenging problems. While this book emphasizes some methods that are not usually covered in beginning university courses, it nevertheless teaches techniques and skills which are useful not only in the specific topics covered here. There are approximately 330 examples and 760 exercises.

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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."

Prefacep. v
Symbolsp. xi
Algebraic Identities and Equationsp. 1
Formulas for Powersp. 1
Finite Sumsp. 5
Polynomialsp. 23
Symmetric Polynomialsp. 38
Systems of Equationsp. 46
Irrational Equationsp. 60
Some Applications of Complex Numbersp. 75
Algebraic Inequalitiesp. 89
Definitions and Propertiesp. 90
Basic Methodsp. 94
The Use of Algebraic Formulasp. 106
The Method of Squaresp. 113
The Discriminant and Cauchy's Inequalityp. 124
The Induction Principlep. 135
Chebyshev's Inequalityp. 145
Inequalities Between Meansp. 150
Appendix on Irrational Numbersp. 169
Number Theoryp. 173
Basic Conceptsp. 174
Prime Numbersp. 183
Congruencesp. 189
Congruences in One Variablep. 201
Diophantine Equationsp. 217
Solvability of Diophantine Equationsp. 238
Integer Part and Fractional Partp. 251
Base Representationsp. 258
Dirichlet's Principlep. 268
Polynomialsp. 274
Hints and Answersp. 283
Hints and Answers to Chapter 1p. 283
Hints and Answers to Chapter 2p. 294
Hints and Answers to Chapter 3p. 312
Bibliographyp. 337
Indexp. 341
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780387989426
ISBN-10: 0387989420
Series: CMS Books in Mathematics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 344
Published: March 2000
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 0.69

Earn 371 Qantas Points
on this Book