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Self Studying the MIT Applied Math Curriculum

harshsikka.me

51–60 of 102 posts

Re: Self Studying the MIT Applied Math Curriculum

#51
post #3

Earlier quoted context omitted.

Yeah, it is, its more of a loose goal, I'm doing research and working on finishing 2 Master's alongside it, so we'll see what happens! I really just want to learn and grow, so if it takes months or if it takes years, I'm in!

What are you Mastering in? What’s your research on?

I'm studying CS and Biology, and I'm currently researching disentangling object representations using brain inspired auto encoders

Re: Self Studying the MIT Applied Math Curriculum

#52
post #15

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?

As someone who also went back to study math after not doing it for a long time, I would recommend doing a book that focusses on teaching how to prove things, using the math you already know. Most upper div math courses either assume you know how to prove things, or try and teach it in passing while also teaching the topic itself (classically linear algebra and calc 3 were taught this way, though now many places now have separate "proof" classes instead)

I would strongly recommend Chartrand and Zhang's "Intro to mathematical proofs", once you know how to prove things, every other more advanced math class you take will be much easier than it would have been otherwise.

[Edit] In particular, do the book, including the chapters on "proofs in calculus" and "proofs with real and complex numbers" before doing real analysis - you'll enjoy it much more that way! [/Edit]

I went through most of this book a few years ago, now about to finish my MS in math :)

Re: Self Studying the MIT Applied Math Curriculum

#53

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…

> Most students would be taking one or two of these in 12 - 16 weeks while doing nothing else but being a student. From my experience (at MIT in the 80s and 90s): The usual student takes 3 technical courses and one humanities course per term. From my own history: I took 18.03 in one term with two EECS courses and a humanities course, and then 18.04 the following term, also with two EECS courses and a humanities cours…

> From my experience (at MIT in the 80s and 90s): The usual student takes 3 technical courses and one humanities course per term.

My experience (in the 80s) was the same. There were a couple of semesters where I had to take 4 technical courses; I had no desire to repeat the experience. :-)

Re: Self Studying the MIT Applied Math Curriculum

#54
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…

The PSET posted is for Statistics for Applications. I was wondering why it looked so different from when I went through it a couple years ago haha

Re: Self Studying the MIT Applied Math Curriculum

#55
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…

When taking Lin Alg in undergrad, I attended the first 3 classes. My friend then showed me the youtube series from Strang; I never went to class again and learned it all.

I partially credit Strang for getting me an A in Linear Algebra. His lectures and the book from David C Lay that I thought was pretty good.

Re: Self Studying the MIT Applied Math Curriculum

#56
post #45

It’s awesome to see more & more devs getting interested in math & stats as machine learning, optimization & sequential testing (what you folks call a/b test) becomes more mainstream. The obvious benefits are, much of math literature is currently written for consumption by math grad students & profs, so all of this will get a much needed rewrite. I foresee a surge in material like Jeremy Kun’s popular “math for progra…

The Coding The Matrix textbook is exactly the type of book you've described that is tailored for programmers. I've read only the first few chapters and found it a joy even if a little wordy in some parts. https://codingthematrix.com/

it’s a good undergrad book. also on that page he says lights out game is a “linear algebra problem”. It’s actually not. incidentally I worked on Lights out for my thesis, and my advisor made a whole career out of lights out! That game relates to Fibonacci polynomials, studied in Combinatorics - https://www.unf.edu/~wkloster/fib.html

Re: Self Studying the MIT Applied Math Curriculum

#57
post #48

Earlier quoted context omitted.

So grateful something mentioned this man. Strang is just amazing. When I first moved to Cambridge, his corresponding book was a relatively expensive prospect, and I was rather serious about 18.06, so ascertaining its book was very important to me. He was gracious enough to gift me a copy that I still have and cherish to this day. Some real moments of thrilling discovery happened for me, it was exhilarating, though tr…

> general inversion of any MxN matrix ??! is there such a thing ? only nonsingular square matrices can be inverted. a general mxn matrix may have a “left inverse” or a “right inverse”, but i don’t think your code is computing that.

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Re: Self Studying the MIT Applied Math Curriculum

#58
post #15

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?

Analysis requires a certain level of mathematical maturity to motivate, follow, understand, and appreciate. This level is roughly acquired after having taken undergraduate coursework in ODEs, linear algebra, or abstract algebra.

Re: Self Studying the MIT Applied Math Curriculum

#59
post #29

While at it pick up Julia, another MIT product. esp for applied math it's invaluable compared with python or matlab. Juno is a nice ide, it's gotten a lot better over the last two months.

I've been meaning to invest some time into learning Julia. I'll definitely try my hand soon

The newest iteration of 18.06 [0] is using this textbook [1] that incorporates usage of Julia in a companion book.

[0] https://github.com/mitmath/1806/blob/master/summaries.md

[1] http://vmls-book.stanford.edu/

Re: Self Studying the MIT Applied Math Curriculum

#60
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...

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