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| Preface 1 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 Reciprocity 2 Algebra 2.1 Basic Theorems and Techniques 2.2 Polynomial Equations 2.3 Algebraic Equations and Inequalities 2.4 The Classical Inequalities 3 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 Problems Hints and Answers for Selected Exercises General References List of Symbols Index |
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