How to Solve Mathematical Problems

At first sight, this might seem like a book to solve math party puzzles. Indeed it can be used for that. But it also lets you understand strategies that may be applied in any context that a maths problem can arise. For instance, there is the idea of systematic trial and error. And a discussion of how to analyse what methods you have been using to tackle a problem. Very useful, because it might suggest other methods, simply by having you explicitly recap your previous methods. As the book says, think about what you did, rather than about the problem. As an inventor, this is just what I do. Plus, the book recommends "incubation", where if you are making no headway, you put aside the problem for some time. Hours or days. Then, just maybe, your subconscious might operate on it during this downtime. So that when you later explicitly return to the problem, a solution emerges. This method is sometimes commonly known as "sleep on it". Wickelgren cautions that this idea of your subconscious working on a problem might be bunk. He gives plausible alternatives. Like simply being less fatigued, physically and mentally, when you return to the problem after a hiatus.

Buy this and Paul Zeitz's "Art and Craft of Problem Solving" and you'll be on your way to being addicted to challenging Mathematical Problems. It took a few readings for me to truly appreciate this book since it is an introductory book to mathematical problems. Many of the ideas presented are second nature to an experienced solver, but the lucid, clear presentation would be an excellent learning experience for the beginner. Topics discussed include Induction, definition of problems to find and problems to prove, avoiding "running around in circles," hill climbing, and a few others. I Very much recommend this book.

Hi,This book describes mathematical techniques separate from their (often confusing) formalism. This should be on the shelf of every undergraduate in math/engineering/physics. If I'd found this book years ago, I could have saved myself a whole lot of time!