Problem-Solving Strategies (Problem Books in Mathematics) (Paperback)

by Arthur Engel (Author) "We present our first Higher Problem-Solving Strategy..." (more)
Key Phrases: use infinite descent, find all integral solutions, extremal principle, Classical Euclidean Geometry, Coloring Proofs, Further Strategies (more...)

Editorial Reviews

Product Description
PROBLEM SOLVING STRATEGIES is a unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. The discussion of problem solving strategies is extensive. It is written for trainers and participants of contests of all levels up to the highest level: IMO, Tournament of the Towns, and the noncalculus parts of the Putnam Competition. It 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", "problem of the month", and "research problem of the year" to their students, thus bringing a creative atmosphere into their classrooms with continuous discussions of mathematical problems. This volume is a must-have for instructors wishing to enrich their teaching with some interesting non-routine problems and for individuals who are just 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. Very few problems have no solutions. Readers interested in increasing the effectiveness of the book can do so by working on the examples in addition to the problems thereby increasing the number of problems to over 1300. In addition to being a valuable resource of mathematical problems and solution strategies, this volume is the most complete training book on the market.

Product Details

• Paperback: 403 pages
• Publisher: Springer; Corrected edition (May 23, 2008)
• Language: English
• ISBN-10: 0387982191
• ISBN-13: 978-0387982199
• Product Dimensions: 9.1 x 6.1 x 1 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)
• Average Customer Review: 4.8 out of 5 stars See all reviews (13 customer reviews)
• Amazon.com Sales Rank: #206,636 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

41 of 42 people found the following review helpful:

5.0 out of 5 stars One of hte Best or maybe the best in it's class, February 28, 2000

By	Julio Cesar De Yncera (Germantown, MD USA) - See all my reviews (REAL NAME)

Are you training for Math competitions anywhere? , for National Math Olympiad in any country or IMO (International Mathematical Olympiad) This is probably one of the most complete books in the market. Arthur Engel (coach for the German IMO team)has done a wonderful job in this Gem

I will list the chapters title and that should give good Idea about this excellent book.

The Invariance Principle;
Coloring Proofs;
The extremal Principle;
The Box Principle;

Enumerative Combinatorics;
Number Theory;
Inequalities;
The Induction Principle;
Sequences;
Polynomials;
Functional Equations;
Geometry;
Games;
Further Strategies

Each chapter is full of sample exercises and end by around a 100 problems to solve making the total number of problems in the book to 1300. The problems are selected to illustrate techniques in difficult and non-routine problem solving using problems from past IMO, Tournament of the Towns non Calculus Putnam problems and National competitions from many countries.

Happy Problem Solving!

28 of 29 people found the following review helpful:

5.0 out of 5 stars Excellent!, August 26, 2000

By	Jose Nieto S. (Maracaibo, Zulia Venezuela) - See all my reviews

A must for participants in math contests and their trainers, and a real treasure for all math lovers and problem-solving fans. The author focuses on the main ideas, techniques and strategies needed to solve the kind of problems found at "elementary" math competitions, up to the IMO level. With more than 1300 problems and examples, it is also an excellent source for teachers in search of interesting, non-routine problems to challenge their students, stimulate their creativity or even to motivate the study of some subjects. My only concern is that, at the sight of such abundance of material, some students might be overwhelmed or discouraged. Ideally, a qualified teacher should select the problems and assign them in adequate doses to the math strength of their students.

16 of 16 people found the following review helpful:

5.0 out of 5 stars WOW!!!! A GEM!!, June 23, 2001

By A Customer

Firstly, this book is probably not well suited for the beginner. It is definitely a comprehensive presentation of elementary and ingenious problem solving methods. Techniques such as Pigeonhole(box principle), invariants, Plane and transformational geometries, coloring proof, number theory, enumarative combinatorics, and quite a few more are presented with many(MANY!) examples and problems. This is definitely the most complete book on mathematical technique that I have seen to date. This book is magnificent. Highly Recommend