MHB Advanced Problem-Solving Strategies

AI Thread Summary
Advanced problem-solving strategies are essential for tackling complex issues, as no single method is universally applicable. The discussion highlights the importance of organizing work using structured approaches, referencing a problem-solving strategy adapted from Young and Freedman's University Physics. It emphasizes the value of George Polya's classic book "How to Solve It," which is recommended for mathematicians and engineers, along with Michalewicz and Fogel's "How to Solve It: Modern Heuristics," which builds on Polya's ideas. Additionally, the TRIZ methodology is suggested as a resource for innovative problem-solving techniques. Overall, these resources provide a foundation for enhancing problem-solving skills across various disciplines.
Ackbach
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I intend for this post to serve as one place to get ideas (the vast majority of which are quite unoriginal with me). Naturally, no one solution method can possibly work for every problem. I would argue that such a solution method does not exist. However, the ideas that so many people have culled together over time may be of use to you, and so I present a few of them here.

Firstly, the http://www.mathhelpboards.com/showthread.php?28-Problem-Solving-Strategy is a great way to organize your work. It might even work well for more advanced problems. Naturally, not every step will necessarily apply to every problem. This strategy is modified a bit from the problem-solving strategy found in Young and Freedman's University Physics with Modern Physics.

Secondly, there is the famous George Polya book How to Solve It: A New Aspect of Mathematical Method. This is a classic work that every mathematician, scientist, and engineer should read.

Thirdly, I would also highly recommend Michalewicz and Fogel's How to Solve It: Modern Heuristics. This book attempts to pick up where Polya left off; it has some delightful passages.

Finally, I would recommend looking into the http://www.triz-journal.com/archives/1997/07/b/index.html. I think there are some great ideas there. Once you've read the link in the previous sentence, you might also want to check out the TRIZ Matrix, where each principle is matched up with the contradictions it might be able to solve.

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