Mathematical Miniatures

Mathematical Miniatures / Svetoslav Savchev, Titu Andreescu.

Mathematical Miniatures is a problem collection of arresting mathematical insight and ingenuity. The authors brought together materials from mathematical competitions, books, research papers, discussions, and their own work. Such mathematical substance went far beyond the purposes of a traditional p...

Full description

Saved in:
Bibliographic Details
Other Authors: Savchev, Svetoslav, Andreescu, Titu
Format: eBook
Language:English
Published: Cambridge : Cambridge University Press, 2011.
Series:Anneli Lax new mathematical library.
Subjects:
Mathematics > Problems, exercises, etc.
Problem solving.
Mathematics
Problem solving
Problems and exercises
Online Access:Click for online access
Table of Contents:
  • Cover
  • Title page
  • Preface
  • Contents
  • Warm-up Problem Set
  • Solutions
  • 1 A Telescoping Sum
  • 2 Lagrangeâ€?s Identity
  • 3 Perfect Squares
  • 4 Least Common Multiples
  • 5 Trig Substitutions
  • Coffee Break 1
  • Solutions
  • 6 Popoviciuâ€?s Theorem
  • 7 Catalanâ€?s Identity
  • 8 Several Inequalities
  • 9 Vectors
  • 10 Mathematical Induction at Work
  • Coffee Break 2
  • Solutions
  • 11 A Highly Divisible Determinant
  • 12 Hermiteâ€?s Identity
  • 13 Complete Sequences
  • 14 Three Polynomials
  • 15 More about InductionCoffee Break 3
  • Solutions
  • 16 A Classical Identity
  • 17 Multiplicative Functions
  • 18 The “Arbitraryâ€? Proizvolov
  • 19 HÂ?olderâ€?s Inequality
  • 20 Symmetry
  • Coffee Break 4
  • Solutions
  • 21 He Knows I Know He Knows
  • 22 A Special Inequality
  • 23 Two Inductive Constructions
  • 24 Some Old-Fashioned Geometry
  • 25 Extremal Arguments
  • Coffee Break 5
  • Solutions
  • 26 The AMS Inequality
  • 27 Hellyâ€?s Theorem for One Dimension
  • 28 Two Approaches
  • 29 Radical Axis
  • 30 The Pigeonhole PrincipleCoffee Break 6
  • Solutions
  • 31 The Three Jug Problem
  • 32 Rectifying Trajectories
  • 33 Numerical Systems
  • 34 More on Polynomials
  • 35 Geometric Transformations
  • Coffee Break 7
  • Solutions
  • 36 The Game of Life Problem
  • 37 Tetrahedra with a Point in Common
  • 38 Should We Count?
  • 39 Letâ€?s Count Now!
  • 40 Some Elementary Number Theory
  • Coffee Break 8
  • Solutions
  • 41 Euclidâ€?s Game
  • 42 Perfect Powers
  • 43 The 2n â€? 1 Problem
  • 44 The 2n + 1 Problem
  • 45 The 3n Problem
  • Coffee Break 9Solutions
  • 46 Pairwise Sums
  • 47 Integer Progressions
  • 48 Incomparable Sets
  • 49 Morseâ€?s Sequence
  • 50 A Favorite of Erdos
  • Instead of an Afterword
  • Glossary
  • About the Authors

Similar Items