Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

Zetetic comments on The Best Textbooks on Every Subject - Less Wrong

167 Post author: lukeprog 16 January 2011 08:30AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (327)

Sort By: Popular

You are viewing a single comment's thread.

Comment author: Zetetic 15 May 2011 12:36:28AM 9 points [-]

Subject: Problem Solving

Recommendation: Street-Fighting Mathematics The Art of Educated Guessing and Opportunistic Problem Solving

Reason: So, it has come to my attention that there is a freely available .pdf for the textbook for the MIT course Street Fighting Mathematics. It can be found here. I have only been reading it for a short while, but I would classify this text as something along the lines of 'x-rationality for mathematics'. Considerations such as minimizing the number of steps to solution minimizes the chance for error are taken into account, which makes it very awesome.

in any event, I feel that this should be added to the list, maybe under problem solving? I'm not totally clear about that, it seems to be in a class of its own.

Comment author: lukeprog 17 May 2011 06:40:26PM 2 points [-]

If you come up with relevant comparison volumes, let me know!

Comment author: [deleted] 17 May 2011 07:04:31PM 5 points [-]

Seemingly relevant comparison volumes:

Numbers Rule Your World: The Hidden Influence of Probabilities and Statistics on Everything You Do

Back-of-the-Envelope Physics

How Many Licks? Or, How to Estimate Damn Near Anything

Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin

Also, the books below are listed as related resources in another class on approximation in science & engineering by the author of the Street-Fighting textbook on OCW, so they may be relevant for comparison, too, or at least interesting.

Engel, Arthur. Problem-solving Strategies. New York, NY: Springer, 1999. ISBN: 9780387982199.

Schmid-Nielsen, Knut. Scaling: Why is Animal Size So Important? New York, NY: Cambridge University Press, 1984. ISBN: 9780521319874.

Vogel, Steven. Life in Moving Fluids. 2nd rev. ed. Princeton, NJ: Princeton University Press, 1996. ISBN: 9780691026169.

Vogel, Steven. Comparative Biomechanics: Life's Physical World. Princeton, NJ: Princeton University Press, 2003. ISBN: 9780691112978.

PĆ³lya, George. Induction and Analogy in Mathematics. Vol. 1, Mathematics and Plausible Reasoning. 1954. Reprint, Princeton, NJ: Princeton University Press, 1990. ISBN: 9780691025094.

Comment author: lukeprog 17 May 2011 08:40:34PM 0 points [-]

Great list, thanks!

Comment author: Zetetic 17 May 2011 06:57:39PM *  1 point [-]

Well, they aren't necessarily comparison volumes, but the author suggested that the book should be used as a compliment to the following:

How to Solve It, Mathematics and Plausible Reasoning, Vol. II, The Art and Craft of Problem Solving

He implies that his book is more rough and ready for applications, but those books are more geared towards solving clearly stated problems in, say, a competition setting.

I would add Putnam and Beyond to the list, classifying it as advanced competition style problem solving (some of the stuff in that book is pretty tough).

Comment author: lukeprog 17 May 2011 07:02:56PM 0 points [-]

Have you read any of those? If so, what did you think of them in comparison to 'Street-Fighting Mathematics'?

Comment author: Zetetic 17 May 2011 07:37:46PM *  1 point [-]

I have only read/skimmed through/worked a few problems out of Putnam and Beyond. I can attest to its advanced level (compared to other problem solving books, I have looked at a few before and found that they were geared more towards high school level subject matter; you won't find any actually advanced [read; grad level] topics in it) and systematic presentation, but that is about it. Its problems are mainly chosen from actual math competitions, and it seems to present a useful bag of tricks via well thought out examples and explanations. I am currently working through it and have a ways to go.

I've heard How to Solve It mentioned a number of times, but I've never really looked into it. I can't really say anything about the other books beyond what the author said about them.