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Equations and inequalities : elementary problems and theorems in algebra and number theory

Author: Jiří Herman; Radan Kučera; Jaromír Šimša
Publisher: New York : Springer, ©2000.
Series: CMS books in mathematics, 1.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

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  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Jiří Herman; Radan Kučera; Jaromír Šimša
ISBN: 0387989420 9780387989426
OCLC Number: 43616063
Description: x, 344 pages : illustrations ; 25 cm.
Contents: 1. Algebraic Identities and Equations. 1. Formulas for Powers. 2. Finite Sums. 3. Polynomials. 4. Symmetric Polynomials. 5. Systems of Equations. 6. Irrational Equations. 7. Some Applications of Complex Numbers --
2. Algebraic Inequalities. 1. Definitions and Properties. 2. Basic Methods. 3. The Use of Algebraic Formulas. 4. The Method of Squares. 5. The Discriminant and Cauchy's Inequality. 6. The Induction Principle. 7. Chebyshey's Inequality. 8. Inequalities Between Means. 9. Appendix on Irrational Numbers --
3. Number Theory. 1. Basic Concepts. 2. Prime Numbers. 3. Congruences. 4. Congruences in One Variable. 5. Diophantine Equations. 6. Solvability of Diophantine Equations. 7. Integer Part and Fractional Part. 8. Base Representations. 9. Dirichlet's Principle. 10. Polynomials --
4. Hints and Answers. 1. Hints and Answers to Chapter 1. 2. Hints and Answers to Chapter 2. 3. Hints and Answers to Chapter 3.
Series Title: CMS books in mathematics, 1.
Other Titles: Metody řešení matematických úloh I.
Responsibility: Jiří Herman, Radan Kučera, Jaromír Šimša ; translated by Karl Dilcher.
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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 Read more...

 
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