Winning solutions獲勝的解決方案

內(nèi)容概要

This book is intended to provide students with the appropriate mathematical tools and problem-solving experience to successfully compete in high-level problem solving competitions. In each section, the authors attempt to "fill in" the appropriate background and then provide the student with a variety of worked examples and exercises to help bridge the gap between what he or she may already know and what is required for high-level competitions. Answers or sketches of the solutions are given for all exercises. The book makes an attempt to introduce each area "gently" assuming little in the way of prior background - and teach the appropriate techniques, rather than simply providing a compilation of high-level problems.

書籍目錄

Preface1  Numbers  1.1  The Natural Numbers  1.2  Mathematical Induction  1.3  Congruence  1.4  Rational and Irrational Numbers  1.5  Complex Numbers  1.6  Progressions and Sums  1.7  Diophantine Equations  1.8  Quadratic Reciprocity2  Algebra  2.1   Basic Theorems and Techniques  2.2  Polynomial Equations  2.3  Algebraic Equations and Inequalities  2.4  The Classical Inequalities3 Combinatorics  3.1  What is Combinatofics?  3.2  Basics of Counting  3.3  Recurrence Relations  3.4  Generating Functions  3.5  The Inclusion-Exclusion Principle  3.6  The Pigeonhole Principle  3.7  Combinatorial Averaging  3.8  Some Extremal ProblemsHints and Answers for Selected ExercisesGeneral ReferencesList of SymbolsIndex

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