Self Studying the MIT Applied Math Curriculum • Hacker News Board

Re: Self Studying the MIT Applied Math Curriculum

#71

Post by bookofjoe » Fri, May 03, 2019, 1:51 AM UTC

tomjakubowski wrote: post #68

laserson wrote: post #65

Earlier quoted context omitted.

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…

I love Strang's conversational style. If you've ever heard him give a lecture, you hear him when reading his textbooks.

Q&A with Strang: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3060226/

Re: Self Studying the MIT Applied Math Curriculum

#72

Post by leereeves » Fri, May 03, 2019, 2:04 AM UTC

AnthonBerg wrote: post #19

mpoteat wrote: post #2

7 non soft classes in a single summer is ambitious to say the least.

True. However there is also this perspective: https://sivers.org/kimo

> In our three-hour lesson that morning, he taught me a full semester of Berklee’s harmony courses.

I don't know anything about music theory, but if a course can be completed in three hours, it's a soft course.

Re: Self Studying the MIT Applied Math Curriculum

#73

Post by dorchadas » Fri, May 03, 2019, 2:28 AM UTC

ghufran_syed wrote: post #52

hsikka wrote: post #15

Earlier quoted context omitted.

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 h…

Agreed. I'm trying to move from being a secondary mathe teacher to actually learning pure math, and proofs are the killer. I feel like I understand topics, but creating proofs kills me.

Re: Self Studying the MIT Applied Math Curriculum

#74

Post by wittedhaddock » Fri, May 03, 2019, 2:43 AM UTC

dxbydt wrote: post #48

wittedhaddock wrote: post #40

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.

You're 100% correct, the algo only handles square matrices! Typo. So, disclaimer, where m === n :) thanks!

Re: Self Studying the MIT Applied Math Curriculum

#75

Post by AlexCoventry » Fri, May 03, 2019, 2:57 AM UTC

nsfmc wrote: post #39

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…

> 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…

Pretty sure you need analysis to get far with Numerical PDEs or Calculus of Variations.

Re: Self Studying the MIT Applied Math Curriculum

#76

Post by verylongname » Fri, May 03, 2019, 3:02 AM UTC

graycat wrote: post #24

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…

Personally, I think complex analysis is important. I really like Serge Lang's book "Complex Analysis." It is supposedly a graduate level text, but the first half of it covers the basics at a level suitable for upper division undergrad class. Ahlfor's book is also really really good, but a little harder to read in my opinion.

I didn't like either Royden or Rudin. I really like Folland's book "Real analysis: modern techniques and their applications." His Fourier analysis book is also pretty good IMO.

Re: Self Studying the MIT Applied Math Curriculum

#77

Post by sandGorgon » Fri, May 03, 2019, 3:14 AM UTC

dxbydt wrote: post #56

jimmy_dean wrote: post #49

Earlier quoted context omitted.

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

How would you compare coding the matrix to strang ?

I'm going to be starting out on one of these and coding-the-matrix is very python centric (which is super helpful and practical) versus MATLAB in Strang's book.

Re: Self Studying the MIT Applied Math Curriculum

#78

Post by sus_007 » Fri, May 03, 2019, 3:33 AM UTC

sn9 wrote: post #59

hsikka wrote: post #29

Earlier quoted context omitted.

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/

Wow, I didn't know these resources existed. It's gonna help me a lot as I'm on a similar journey as the OP. Thank you very much, sn9

Re: Self Studying the MIT Applied Math Curriculum

#79

Post by whymauri » Fri, May 03, 2019, 3:45 AM UTC

tomjakubowski wrote: post #68

laserson wrote: post #65

Earlier quoted context omitted.

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…

I love Strang's conversational style. If you've ever heard him give a lecture, you hear him when reading his textbooks.

Absolutely this!

"Now this is a matrix you wouldn't want to meet in a dark alley!" - Gil

Re: Self Studying the MIT Applied Math Curriculum

#80

Post by hyperpallium » Fri, May 03, 2019, 4:08 AM UTC

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…

/aside As someone who's also refreshing maths: What's the point of investing in studying hard, if I end up forgetting? Is there some aspect of maths I should focus on, that is an enduring investment?

My feelings is that getting an intuitive understanding is key, so that it becomes part of myself... but I find proofs don't give me this (they show me that it is true, but not why it is that it is true - if that makes sense). Derivations seem important, because then I can re-derive when I forget (though, I must recall the "tricks" of the derivation, and also know the operations used). General skills can persist, if they get ongoing exercise (e.g. methodicalness, care with definitions, close reading, organization to cope with complex and multi-layered problems).

Finally - and awfully - I now think mathematics is like a language, not so much in the sense of communication, but by being full of special cases, exceptions, "abuse of notation". Becoming fluent in a language takes much practice, and may be impossible without special talent. But once achieved, is never fully forgotten, and quickly regained.