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The minimal classical way to bootstrap your math knowledge is algebra (mostly linear) + analysis. This is the approach used by e.g. Harvard Math 55, which is a
by nextos 8y ago
The minimal classical way to bootstrap your math knowledge is algebra (mostly linear) + analysis. This is the approach used by e.g. Harvard Math 55, which is a really famous course.
Harvard Math 55 employed Halmos + baby Rudin as main textbooks. Halmos has now been replaced by Axler, which is an excellent textbook (but the typographic changes in the last edition are very distracting).
Rudin is probably too synthetic and dry for a beginner. You could easily replace it by Hubbard & Hubbard (which was the sole main textbook in one Harvard Math 55 edition), or use an aid text like Gelbaum & Olmsted. You can also skip Axler if you go the Hubbard way.
A favorite open question of mine is what would a math bootcamp look like if you went up one level of abstraction and focus more on logic and abstract algebra.
- dorchadas 8y agoI would love a bootcamp like that. Or even one that helped you with proofs. I've found that's my biggest issue trying to teach myself pure mathematics. I just can't start the damn proof. Once I get the start, I can usually finish it, but starting the proof I just feel so clueless how to do it.
- nextos 8y agoYou can learn to do basic proofs the way old school Tsarist and Soviet Russia students did, by studying geometry from Kiselev. It should be pretty straightforward for any adult, and a nice stepping stone to build your knowledge on. A more advanced approach would be to go through a logic book like Velleman that teaches proofs as structured programming.