Equations and inequalities : elementary problems and theorems in algebra and number theory / Jiří Herman, Radan Kučera, Jaromír Šimša ; translated by Karl Dilcher.

Format:

Book

Author/Creator:

Herman, Jiří.

Contributor:

Kučera, Radan.

Šimša, Jaromír.

Series:

CMS books in mathematics

Standardized Title:

Metody řešení matematických úloh I. English

Language:

Czech

English

Subjects (All):

Equations--Numerical solutions.

Inequalities (Mathematics).

Problem solving.

Physical Description:

x, 344 pages : illustrations ; 25 cm.

Place of Publication:

New York : Springer, [2000]

Summary:

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.

Contents:

1 Algebraic Identities and Equations 1

1 Formulas for Powers 1

2 Finite Sums 5

3 Polynomials 23

4 Symmetric Polynomials 38

5 Systems of Equations 46

6 Irrational Equations 60

7 Some Applications of Complex Numbers 75

2 Algebraic Inequalities 89

1 Definitions and Properties 90

2 Basic Methods 94

3 The Use of Algebraic Formulas 106

4 The Method of Squares 113

5 The Discriminant and Cauchy's Inequality 124

6 The Induction Principle 135

7 Chebyshev's Inequality 145

8 Inequalities Between Means 150

9 Appendix on Irrational Numbers 169

3 Number Theory 173

2 Prime Numbers 183

3 Congruences 189

4 Congruences in One Variable 201

5 Diophantine Equations 217

6 Solvability of Diophantine Equations 238

7 Integer Part and Fractional Part 251

8 Base Representations 258

9 Dirichlet's Principle 268

10 Polynomials 274.

Notes:

Includes bibliographical references and index.

ISBN:

0387989420

OCLC:

43616063