Customer Reviews

Problem-Solving Strategies (Problem Books in Mathematics)

5 star:		(11)
4 star:		(4)
3 star:		(2)
2 star:		(1)
1 star:		(0)

 

 

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!

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.

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

Problem-Solving Strategies is a great book for anyone interested in Mathematical Contests. It is not however a book for starters but rather a book for university students and high-school contest participants.

I have just started working on this book recently. I've been reading through and working on the problems in the number theory section which are excellent so far. There is a good balance between warm-up/basic training problems and hard contest problems so you won't be discouraged too easily. I have browsed through the other sections and they seem very good. Must have if you are preparing for math contests!

I disagree with another reviewer(Math Messiah) who thinks this is a book only for intelligent people like himslf. The problems are wide ranging and numerous and even dumb people (me, for instance) can find fun and excitement in many of them. I also have an advice for the Math Messiah who is on brink of some major discoveries: hold on to that brink, and don't drop.

I am a student at a college in New England and I bought this book in high school. The book claims no knowledge of higher mathematics is necessary to complete the problems but that claim is simply untrue. You need higher mathematics to solve some of these problems. The author says anyone with a standard high school mathematics education can solve these problems. I strongly disagree. They are similar to high school problems but they are in much much greater depth.

Wow! The problems in the book are extremely difficult but not impossible. I would recommend only buying this book if you have access to mathematics professor(s) who can help you understand these problems for the Putnam Competition or you have a committed group of friends who like math. It takes me hours to solves these problems but I love it!

This is a rather complete book for students and coaches who are preparing for mathematics competitions such as the IMO. It is loaded with problem-solving strategies for a large variety of mathematics problems ranging from combinatorics, number theory, sequences, polynomials and geometry to game theory, a topic which is not normally included in mathematics competitions. There are tons of problems (around 1300) to hone your mathematical skills. Another very good book in a similar category is the IMO Compendium. The books by Titu Andreescu are also excellent for mathematics competitions.

My own field is computer science but love reading mathematics for its purity and occasional aha moments. This one I bought for my son at his request and I must admit that I was the first one to peruse through it. In my cursory reading I did enjoy going through each of the chapters. The author has a good command over his teaching style and he peppers it with thrilling anecdotes. It should definitely be seen on the desk of any serious mathematics student (at least at high school level). But I did also find some errors randomly and I wanted to exchange notes with others but sadly I could not find any site. Even springer does not have any errata listed for this book. Now that the book is out of the press, the publishers need to show some compassion for the buyers and issue an errata soon.

This is one book that I would like to keep with me all the time even after all my interest in Maths. is gone. For, it gives me food for thought and does not allow my mind to be dried of thoughts. This is a most fascinating book since the author, even when he gives hints at the solution, he does it in such an effective manner, that you have to really pursue a very thrilling chase of the solution. The challenge and thrill make it a pleasurable experience. I am sure this will be so for both the learner and the learned. Every mathematician should possess this book.

V. Krishnamurthy