Second Step To Mathematical Olympiad Problems, A

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Contents:

• Combinatorics:

  • A Quick Reminder
  • Partial Fraction
  • Geometric Progressions
  • Extending the Binomial Theorem
  • Recurrence Relations
  • Generating Functions
  • Of Rabbits and Postmen
  • Solutions

• Geometry 3:

  • The Circumcircle
  • Incircles
  • Exercises
  • The 6-Point Circle?
  • The Euler Line and the Nine Point Circle
  • Some More Examples
  • Hints
  • Solutions
  • Glossary

• Solving Problems:

  • Introduction
  • A Problem to Solve
  • Mathematics: What is it?
  • Back to Six Circles
  • More on Research Methods
  • Georg Pólya
  • Asking Questions
  • Solutions

• Number Theory 2:

  • A Problem
  • Euler's -function
  • Back to Section 4.2
  • Wilson
  • Some More Problems
  • Solutions

• Means and Inequalities:

  • Introduction
  • Rules to Order the Reals By
  • Means Arithmetic and Geometric
  • More Means
  • More Inequalities
  • A Collection of Problems
  • Solutions

• Combinatorics 3:

  • Introduction
  • Inclusion-Exclusion
  • Derangements (Revisited)
  • Linear Diophantine Equations Again
  • Non-taking Rooks
  • The Board of Forbidden Positions
  • Stirling Numbers
  • Some Other Numbers
  • Solutions

• Creating Problems:

  • Introduction
  • Counting
  • Packing
  • Intersecting
  • Chessboards
  • Squigonometry
  • The Equations of Squares
  • Solutions

• IMO Problems 2:

  • Introduction
  • AUS 3
  • HEL 2
  • TUR 4
  • ROM 4
  • USS 1
  • Revue
  • Hints AUS 3
  • Hints HEL 2
  • Hints ROM 4
  • Hints USS 1
  • Some More Olympiad Problems
  • Solutions

Readership: School students keen to learn more of mathematics and specifically mathematics related to the IMO; coaches and instructors of mathematical competitions.
Key Features:

• An introduction to the main mathematical topics covered in the IMO
• Easily comprehensible to students
• Full solutions provided to all mathematical problems

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