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140122 ||| eng |
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|a 9781461212706
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| 100 |
1 |
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|a Herman, Jiri
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| 245 |
0 |
0 |
|a Equations and Inequalities
|h Elektronische Ressource
|b Elementary Problems and Theorems in Algebra and Number Theory
|c by Jiri Herman, Radan Kucera, Jaromir Simsa
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| 250 |
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|a 1st ed. 2000
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| 260 |
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|a New York, NY
|b Springer New York
|c 2000, 2000
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| 300 |
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|a XI, 344 p
|b online resource
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| 505 |
0 |
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|a 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 Chebyshev’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 Diopha,ntine 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
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| 653 |
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|a Number theory
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| 653 |
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|a Number Theory
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| 653 |
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|a Algebra
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| 700 |
1 |
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|a Kucera, Radan
|e [author]
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| 700 |
1 |
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|a Simsa, Jaromir
|e [author]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
0 |
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|a CMS Books in Mathematics, Ouvrages de mathématiques de la SMC
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| 028 |
5 |
0 |
|a 10.1007/978-1-4612-1270-6
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| 856 |
4 |
0 |
|u https://doi.org/10.1007/978-1-4612-1270-6?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 512.7
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| 520 |
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|a This book is intended as a text for a problem-solving course at the first or second-year university level, as a text for enrichment classes for talented high-school students, or for mathematics competition training. It can also be used as a source of supplementary material for any course dealing with algebraic equations or inequalities, or to supplement a standard elementary number theory course. There are already many excellent books on the market that can be used for a problem-solving course. However, some are merely collections of prob lems from a variety of fields and lack cohesion. Others present problems according to topic, but provide little or no theoretical background. Most problem books have a limited number of rather challenging problems. While these problems tend to be quite beautiful, they can appear forbidding and discouraging to a beginning student, even with well-motivated and carefully written solutions. As a consequence, students may decide that problem solving is only for the few high performers in their class, and abandon this important part of their mathematical, and indeed overall, education
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