A Second Step to Mathematical Olympiad Problems
The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students.
The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions.
- An introduction to the main mathematical topics covered in the IMO
- Easily comprehensible to students
- Full solutions provided to all mathematical problems
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 ϕ-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
Number of Pages: 312
Author(s): Jiagu Xu (Former Professor of Mathematics, Fudan University, China)
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