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Winning Solutions

by Edward Lozansky

  • ISBN: 9780387947433
  • ISBN10: 0387947434

Winning Solutions

by Edward Lozansky

  • Binding: Paperback
  • Publisher: Springer Verlag
  • Publish date: 06/01/1996
  • ISBN: 9780387947433
  • ISBN10: 0387947434
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Description: 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 Combinatorics'.- 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.
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