Equations and Inequalities
Elementary Problems and Theorems in Algebra and Number Theory
(Sprache: Englisch)
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 divisibility and diophantine equations. In each topic,...
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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 divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.
Klappentext zu „Equations and Inequalities “
The Canadian Mathematical Society is pleased to announce the move of its well established advanced books and monographs series into a collaboration with Springer-Verlag. This new series offers authors the joint advantage of publishing with a major mathematical society and with a leading academic publishing company. The CMS Books in Mathematics series is edited by Dr. Jonathan and Dr. Peter Borwein, and the first three books are already in press. Details of these titles give a good illustration of the broad variety of publications that may be anticipated within the series.
Inhaltsverzeichnis zu „Equations and Inequalities “
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.
Bibliographische Angaben
- Autoren: Jiri Herman , Radan Kucera , Jaromir Simsa
- 2000, 344 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Herausgegeben: K. Dilcher
- Übersetzer: K. Dilcher
- Verlag: Springer, New York
- ISBN-10: 0387989420
- ISBN-13: 9780387989426
- Erscheinungsdatum: 23.03.2000
Sprache:
Englisch
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