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Self Studying the MIT Applied Math Curriculum

harshsikka.me

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Re: Self Studying the MIT Applied Math Curriculum

#11

Post by the_svd_doctor »

olooney wrote: post #5

I did Strang's linear algebra course[0] (link goes to Youtube playlist of lectures) several years after graduating and recommend it highly. I was looking for refresher but I gained a deeper understanding of several important concepts; in particular it's fair to say I barely understood, or perhaps even misunderstood, SVD until Strang. If you're not sure if you need something like that, I suggest doing something like t…

Another great "intermediate" textbook (in my opinion) is Trefethen's Numerical Linear Algebra [1]. Much more readable than Golub's I would say, which is more like a reference than a textbook.

[1]: https://www.amazon.com/Numerical-Linear-Algebra-Lloyd-Trefet...

Re: Self Studying the MIT Applied Math Curriculum

#13

Post by throwawaymath »

Speaking frankly, it's ambitious to complete even one of these courses in a single summer. Most students would be taking one or two of these in 12 - 16 weeks while doing nothing else but being a student. Accomplishing the same in about eight weeks from video lectures will be more difficult. I would strongly urge the author to slow down, choose a single course they have the background for and work from there.

I can't tell if the author has done a real analysis course before, but if they haven't that's the one they should choose next. If they already have that under their belt they should go to probability or complex variables. I don't see the utility of re-doing calculus or linear algebra if the author is already strong in both.

I appreciate the enthusiasm for math that's evident here, that's great! But if you're learning math the "right" way - by actively engaging with the material - there's only so much of it you can learn at once.

Re: Self Studying the MIT Applied Math Curriculum

#14

Post by commandlinefan »

I’ve been doing more machine learning for work, and I’ve realized a) how much calculus is involved in it and b) how much calculus I had forgotten since I took the courses as an undergraduate almost 30 years ago. I happen to still have my old calculus textbook (I couldn’t sell it back to the bookstore back then), so I dusted it off and started working through all the problems. I’m about halfway through right now, and man I get strange looks from people when I start working calculus problems. Good to know that I’m not alone, although I’m about halfway through the equivalent of 18.01 (1/10th of the poster’s coursework) after 6 months. It doesn’t look like there are that many sample exercises in the online course, though - that may make it harder to really absorb.

Re: Self Studying the MIT Applied Math Curriculum

#15

Post by hsikka »

throwawaymath wrote: post #13

Speaking frankly, it's ambitious to complete even one of these courses in a single summer. Most students would be taking one or two of these in 12 - 16 weeks while doing nothing else but being a student. Accomplishing the same in about eight weeks from video lectures will be more difficult. I would strongly urge the author to slow down, choose a single course they have the background for and work from there. I can't…

Hey, author here, I really appreciate the feedback. Are there any specific prerequisites to Real Analysis?

Re: Self Studying the MIT Applied Math Curriculum

#16

Post by hsikka »

commandlinefan wrote: post #14

I’ve been doing more machine learning for work, and I’ve realized a) how much calculus is involved in it and b) how much calculus I had forgotten since I took the courses as an undergraduate almost 30 years ago. I happen to still have my old calculus textbook (I couldn’t sell it back to the bookstore back then), so I dusted it off and started working through all the problems. I’m about halfway through right now, and…

Awesome, it's heartening to see someone else feel the same way! And great note about the problems, maybe one of the classic textbooks would be a good addition for problems

Re: Self Studying the MIT Applied Math Curriculum

#17

Post by throwawaymath »

olooney wrote: post #5

I did Strang's linear algebra course[0] (link goes to Youtube playlist of lectures) several years after graduating and recommend it highly. I was looking for refresher but I gained a deeper understanding of several important concepts; in particular it's fair to say I barely understood, or perhaps even misunderstood, SVD until Strang. If you're not sure if you need something like that, I suggest doing something like t…

Golub's Matrix Computations is definitely a gold standard, but I wouldn't characterize it as something you read so much as reference :)

Re: Self Studying the MIT Applied Math Curriculum

#20

Post by throwawaymath »

hsikka wrote: post #15
throwawaymath wrote: post #13

Speaking frankly, it's ambitious to complete even one of these courses in a single summer. Most students would be taking one or two of these in 12 - 16 weeks while doing nothing else but being a student. Accomplishing the same in about eight weeks from video lectures will be more difficult. I would strongly urge the author to slow down, choose a single course they have the background for and work from there. I can't…

Hey, author here, I really appreciate the feedback. Are there any specific prerequisites to Real Analysis?

Technically speaking, no. Real analysis is pretty self-contained. You basically start out by constructing the reals from scratch and deducing continuity as a consequence of the completeness of the real field. You use a tiny bit of set theory to establish notation and define bounds, and then from there you go into limits, derivatives, integrals and maybe the Lebesgue measure. I wouldn't expect a real analysis course targeted at applied math majors to do much other than that.

The reason real analysis is useful is because it's (loosely) a deeper calculus course with proofs. Since probability theory becomes more proof-based (and ventures into measures), real analysis is good preparation for it.

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