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I would say 'plug and chug' applied problems don't work for anyone, past the first couple. At risk of anecdote: I like solving puzzles as much as anyone[1] but

I would say 'plug and chug' applied problems don't work for anyone, past the first couple. At risk of anecdote: I like solving puzzles as much as anyone[1] but the purer side wasn't a puzzle to me because there is no purpose, no picture to be pieced together[2]. [1] Back to the original topic, chemistry interestingly inverts its approach with organic chem - a class in puzzle solving that often frustrated premeds trying to memorize their way through. [2] I don't mean that the problem was open-ended, e.g. research but rather that it didn't exist. Most of my math education hasn't been trying to prove P=NP (or other easier puzzles) but demonstrating specific transformations (e.g. here are the rules for integration, after a trivial treatment of the proof). imo something like an intro to algorithms in highschool or early college would have do more for both the uninterested and the gifted than "integration, but with 1 more dimension!"

chongli 7y ago
That’s disappointing. My math education so far has included the usual calculus and the basics of analysis up to and including multi-variable calculus as well as linear algebra on abstract vector spaces, inner product spaces, and complex vector spaces. Additionally, I’ve delved into combinatorics with enumeration, combinatorial proofs, and generating functions as well as graph theory, abstract algebra including group theory and ring theory, and mathematical logic. I plan to take Euclidean geometry, real and complex analysis, fields and Galois theory, and eventually measure theory as well as differential geometry and maybe commutative algebra and representation theory. The problems I’ve studied in all of these courses have been varied, interesting, and highly challenging. Far more entertaining than any problem I encountered in high school. But not all of the material was too complex for a high school student to understand. I could definitely teach a high school class in graph theory and I bet the students would have a lot of fun with it. Despite it being a beautiful and sometimes very abstract field, it can be applied to computer science as well as games and puzzles of all sorts. Yeah, it’s not useful to any of the hard engineering disciplines but it’s far more entertaining than grinding integrals all day.
0x445442 7y ago
Gerry Sussman has a really good talk touching on [2]. It was surprising to me that his real interests are in classical mechanics but he uses computation as a tool to convey the ideas.

chongli 7y ago

That’s disappointing. My math education so far has included the usual calculus and the basics of analysis up to and including multi-variable calculus as well as linear algebra on abstract vector spaces, inner product spaces, and complex vector spaces. Additionally, I’ve delved into combinatorics with enumeration, combinatorial proofs, and generating functions as well as graph theory, abstract algebra including group theory and ring theory, and mathematical logic. I plan to take Euclidean geometry, real and complex analysis, fields and Galois theory, and eventually measure theory as well as differential geometry and maybe commutative algebra and representation theory. The problems I’ve studied in all of these courses have been varied, interesting, and highly challenging. Far more entertaining than any problem I encountered in high school. But not all of the material was too complex for a high school student to understand. I could definitely teach a high school class in graph theory and I bet the students would have a lot of fun with it. Despite it being a beautiful and sometimes very abstract field, it can be applied to computer science as well as games and puzzles of all sorts. Yeah, it’s not useful to any of the hard engineering disciplines but it’s far more entertaining than grinding integrals all day.

0x445442 7y ago

Gerry Sussman has a really good talk touching on [2]. It was surprising to me that his real interests are in classical mechanics but he uses computation as a tool to convey the ideas.