This book is written for trainers and participants of mathematical contests of all kinds up to the highest level of international competitions, including the IMO and the Putnam Competition. It is also written for high school teachers who are conducting a mathematics club and are looking for ideas and problems for their club; for teachers who want to pose "the problem of the week", "the problem of the month", "the research problem of the year"; and for regular high school teachers who are just looking for ideas to enrich their teaching by some interesting nonroutine problems.

Autorentext

Klappentext

A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.

Inhalt

1 The Invariance Principle 2 Coloring Proofs 3 The Extremal Principle 4 The Box Principle 5 Enumerative Combinatorics 6 Number Theory 7 Inequalities 8 The Induction Principle 9 Sequences 10 Polynomials 11 Functional Equations 12 Geometry 13 Games 14 Further Strategies