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Problem-Solving Through Problems
This is a practical anthology of some of the best elementary problems in different branches of mathematics. They are selected for their aesthetic appeal as well as their instructional value, and are organized to highlight the most common problem-solving techniques encountered in undergraduate mathematics. Readers learn important principles and broad strategies for coping with the experience of solving problems, while tackling specific cases on their own. The material is classroom tested and has been found particularly helpful for students preparing for the Putnam exam. For easy reference, the problems are arranged by subject.
332 pages, Hardcover
First published November 30, 1982
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November 26, 2023
Working through most of this book was one of the two most useful [*] things I ever did for learning to solve mathematical 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). It's only part of a much longer process. But for me it was immensely helpful.
[*] The other was starting to treat the theorems in mathematical books as a series of problems, where the goal was to prove the theorem without reading the proof. This is an extremely slow way of reading - a page an hour was often optimistic - but it does improve your problem solving. I recommend extensively trying it; among other things, getting good at being stuck is an immensely valuable part of learning to problem solve.
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). It's only part of a much longer process. But for me it was immensely helpful.
[*] The other was starting to treat the theorems in mathematical books as a series of problems, where the goal was to prove the theorem without reading the proof. This is an extremely slow way of reading - a page an hour was often optimistic - but it does improve your problem solving. I recommend extensively trying it; among other things, getting good at being stuck is an immensely valuable part of learning to problem solve.
Displaying 1 of 1 review