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Cover: 9781461270713 | Equations and Inequalities | Jiri Herman (u. a.) | Taschenbuch | xi
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Equations and Inequalities
Elementary Problems and Theorems in Algebra and Number Theory
Taschenbuch von Jiri Herman (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung
This is a translation of a successfeul Czech book with more than 1000 problems. The problems can be used to prepare for the International Mathematical Olympiads or the Putnam exam (a prestigious math competition). Each topic contains brief theoretical discussions that are immediately followed by carefully worked out examples of increasing degrees of difficulty, and by exercises which range from routine to rather challenging problems.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2012
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: CMS Books in Mathematics
Inhalt: xi
344 S.
ISBN-13: 9781461270713
ISBN-10: 1461270715
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Herman, Jiri
Simsa, Jaromir
Kucera, Radan
Übersetzung: Dilcher, K.
Auflage: Softcover reprint of the original 1st ed. 2000
Hersteller: Springer New York
Springer US, New York, N.Y.
CMS Books in Mathematics
Maße: 235 x 155 x 20 mm
Von/Mit: Jiri Herman (u. a.)
Erscheinungsdatum: 05.10.2012
Gewicht: 0,546 kg
Artikel-ID: 105721238
Zusammenfassung
This is a translation of a successfeul Czech book with more than 1000 problems. The problems can be used to prepare for the International Mathematical Olympiads or the Putnam exam (a prestigious math competition). Each topic contains brief theoretical discussions that are immediately followed by carefully worked out examples of increasing degrees of difficulty, and by exercises which range from routine to rather challenging problems.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2012
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: CMS Books in Mathematics
Inhalt: xi
344 S.
ISBN-13: 9781461270713
ISBN-10: 1461270715
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Herman, Jiri
Simsa, Jaromir
Kucera, Radan
Übersetzung: Dilcher, K.
Auflage: Softcover reprint of the original 1st ed. 2000
Hersteller: Springer New York
Springer US, New York, N.Y.
CMS Books in Mathematics
Maße: 235 x 155 x 20 mm
Von/Mit: Jiri Herman (u. a.)
Erscheinungsdatum: 05.10.2012
Gewicht: 0,546 kg
Artikel-ID: 105721238
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