Advanced book on Mathematics Olympiad

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Putnam and Beyond ...

Razvan Gelca ̆ Titu Andreescu Putnam and Beyond ...

R ̆azvan Gelca Texas Tech University Department of Mathematics and Statistics MA 229 Lubbock, TX 79409 USA [email protected] Titu ...

Life is good for only two things, discovering mathematics and teaching mathematics. Siméon Poisson ...

Contents Preface............................................................ xi ...

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1 Methods of Proof................................................ A Study Guide............................................... ...

Preface A problem book at the college level. A study guide for the Putnam competition. A bridge between high school problem solv ...

xii Preface mathematics. It is assumed that the reader possesses a moderate background, familiarity with the subject, and a cert ...

Preface xiii for the reader to solve. And since our problems are true brainteasers, complete solutions are given in the second p ...

A Study Guide The book has six chapters: Methods of Proof, Algebra, Real Analysis, Geometry and Trigonometry, Number Theory, Com ...

xvi A Study Guide and Beyondcan be used as a textbook for problem-solving courses, in which case we recommend beginning with the ...

1 Methods of Proof In this introductory chapter we explain some methods of mathematical proof. They are argument by contradictio ...

2 1 Methods of Proof We continue our illustration of the method of argument by contradiction with an example of Euler. Example.P ...

1.2 Mathematical Induction 3 4.Every point of three-dimensional space is colored red, green, or blue. Prove that one of the colo ...

4 1 Methods of Proof Solution.We prove this by induction on the numbernof lines. The base casen=1is straightforward, color one h ...

1.2 Mathematical Induction 5 The third example is a problem from the 5th W.L. Putnam Mathematical Competition, and it was select ...

6 1 Methods of Proof g 0 (n)g 1 (n)···gk+ 1 (n)=g 0 (n)g 0 (n!)···gk(n!)<g 0 (n)(n!)g^0 (n!)g^1 (n!)···gk−^1 (n!) < n(n!)g ...