The most useful course that I’ve taken so far was on game theory. It explains a lot of human behavior, and is applicable to real life. It can also be a soft introduction to mathematical proofs, and helps with some Less Wrong material. (Caveat: progress was slow because it attracted many non-mathematically inclined students.)
Brief comments about math and physics courses:
Math (real analysis, linear algebra, number theory, combinatorics, abstract algebra): Learning each field of math greatly improved my abilities in other math fields and in physics, but they didn’t help much with non-academic problems. (Statistics and probability theory may be more helpful, but I’ve only studied these in high school, so I can’t comment.) However, learning real analysis was an excellent way to reveal the limits and faults of my intuition. (I was initially taught real analysis with the Moore method over two summers, which made this even more effective. Also, there are books devoted to counterexamples in real analysis.)
Physics (mechanics, quantum theory, electricity/magnetism, astronomy): Compared to math, I found the type of thinking in physics to be more practical. It may also serve as an entry point to topics in math and programming. However, be careful of these contents in physics courses—I’ve seen a lot of unjustified hand waving about math and bad programming practices.
It may be a good thing that many non-mathematically inclined students were attracted—such an audience can slow down progressing to mathematically deeper topics and make lecturer spend time on the “physics vs. mathematics division” side of things.
I consider game theory and probability theory two topics that offer a lot of possibilities for point of view change; and in game theory the most important part not to miss is thinking about real utility functions...
Current sanity waterline is low enough that writing down the incentives can explain things that (somehow) are not yet considered universally obvious.
The most useful course that I’ve taken so far was on game theory. It explains a lot of human behavior, and is applicable to real life. It can also be a soft introduction to mathematical proofs, and helps with some Less Wrong material. (Caveat: progress was slow because it attracted many non-mathematically inclined students.)
Brief comments about math and physics courses:
Math (real analysis, linear algebra, number theory, combinatorics, abstract algebra): Learning each field of math greatly improved my abilities in other math fields and in physics, but they didn’t help much with non-academic problems. (Statistics and probability theory may be more helpful, but I’ve only studied these in high school, so I can’t comment.) However, learning real analysis was an excellent way to reveal the limits and faults of my intuition. (I was initially taught real analysis with the Moore method over two summers, which made this even more effective. Also, there are books devoted to counterexamples in real analysis.)
Physics (mechanics, quantum theory, electricity/magnetism, astronomy): Compared to math, I found the type of thinking in physics to be more practical. It may also serve as an entry point to topics in math and programming. However, be careful of these contents in physics courses—I’ve seen a lot of unjustified hand waving about math and bad programming practices.
It may be a good thing that many non-mathematically inclined students were attracted—such an audience can slow down progressing to mathematically deeper topics and make lecturer spend time on the “physics vs. mathematics division” side of things.
I consider game theory and probability theory two topics that offer a lot of possibilities for point of view change; and in game theory the most important part not to miss is thinking about real utility functions...
Current sanity waterline is low enough that writing down the incentives can explain things that (somehow) are not yet considered universally obvious.