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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.
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…
> 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... I don't see the utility of re-doing calculus or linear algebra if the author is already strong in both. having (somehow) completed many of these requirements for my 18c degree, i would say that analysis is not necessary if your interest is actually applied math. There's a great line in ru…
If you start reading research papers in applied math, there’s a ton of measure theory and functional analysis there.
More generally, both introductory real analysis and introductory complex analysis are assumed basic foundational background for pretty much any kind of research mathematics, applied or otherwise.
I’m also not sure I would recommend trying to self-study them though. Some expert guidance/feedback is pretty helpful for someone starting out.
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.
Why is Julia better than MATLAB or Python? Most applied mathematicians I know are in MATLAB all the time.
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...
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…
[1]: https://www.amazon.com/Linear-Algebra-Learning-Gilbert-Stran...
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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.
Suggestion: Set aside complex variables and do measure theory instead. For the Fourier and Laplace transforms, cover those via measure theory. For measure theory, H. Royden, Real Analysis and the first half of W. Rudin, Real and Complex Analysis. Then take a course in graduate probability which is based on measure theory. Good authors are Loeve, Neveu, Breiman, Chung, among others. So, learn about the cases of conver…
Incredible, thank you for the guidance! I'll look into these topics more carefully
A good course in statistics, e.g., with sufficient statistics, needs graduate probability, and with a grad probability course can do elementary statistics easily in the footnotes. E.g., the proof I worked out for the Neyman-Pearson lemma is quite general but based on the Hahn decomposition based on the Radon-Nikodym theorem (Rudin gives von Neumann's cute proof) in measure theory. The grown up approach to conditional probability is based just on the Radon-Nikodym theorem of measure theory.
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…
Strang just published a new book called "Linear Algebra and Learning From Data" [1] which I only just started but find to be quite enjoyable so far. It's simultaneously conversational but also quite terse (similar to "All of Statistics"). There are many advanced and very contemporary applications covered in the book, with a focus towards machine learning. [1]: https://www.amazon.com/Linear-Algebra-Learning-Gilbert-St…
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Why is Julia better than MATLAB or Python? Most applied mathematicians I know are in MATLAB all the time.
I mean julia is much younger. The main strengths are that it's open source, it's a much nicer language, you can actually ship things in it (good luck doing that in matlab), package manager, etc etc. Matlab is legit not great.
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I mean julia is much younger. The main strengths are that it's open source, it's a much nicer language, you can actually ship things in it (good luck doing that in matlab), package manager, etc etc. Matlab is legit not great.
Ah ok. The reason I like MATLAB is cause I want a “numerical experiment” and I don’t want to have to learn a lot to get it to run