Our lead curriculum developer wrote 100–200 pages of content, dreaming up lots of different styles and approaches we might use. (I’m guessing some of our more mathematically advanced readers have so internalized the solution process for this type of Diophantine equation that you don’t have to travel with Pythagoras to get there! Many problems (particularly geometry problems) have a lot of moving parts.Not of those pages will be in the final work, but they spurred a great many ideas for content we will use. Look back at the problem, and the discoveries you have made so far and ask yourself “What haven’t I used yet in any constructive way?
Each section features a single idea, the power and versatility of which is demonstrated in the examples and reinforc The purpose of this book is to isolate and draw attention to the most important problem-solving techniques typically encountered in undergradu ate mathematics and to illustrate their use by interesting examples and problems not easily found in other sources.
Each problem is chosen for its natural appeal and beauty, but primarily to provide the context for illustrating a given problem-solving method.
The aim throughout is to show how a basic set of simple techniques can be applied in diverse ways to solve an enormous variety of problems.
It took a few hundred hours (IIRC), but was time very well spent and was repaid later with interest.
That's not to say it's a silver bullet - working through the book requires that you be at the right current problem-solving level (neither too far ahead of the book's level, or behind). But for me it was immensely helpful.[*] TWorking through most of this book was one of the two most useful [*] things I ever did for learning to solve mathematical problems.