Live data from Hacker News

Self studying the MIT applied math curriculum (2019)

smallstepcap.com

31–40 of 52 posts

Re: Self studying the MIT applied math curriculum (2019)

#31
post #30

If anyone wants to attempt this, that's awesome. It's a lot of hard work, but I think it opens a lot of opportunities for personally and professionally. I've a Ph.D in Applied Mathematics from a traditional program, so I wanted to chime in based on some of the comments I'm seeing. As a note, this is an opinion and others may feel differently and strongly at that. To me, applied mathematics is the art of transforming…

What would you recommend on Hilbert spaces to someone who has worked through Baby Rudin?

Thanks for the insightful comment by the way.

Re: Self studying the MIT applied math curriculum (2019)

#32
post #3

I have a pretty similar background. I have an undergrad in ChemE who fell in love with machine learning research. As I didn’t had the appropriate background so I taught myself Computer science using mostly resources such as OCW and teachyourselfcs, videolectures etc. However, what stood out to me was how difficult it is to self study? Universities provide a setting which helps you learn difficult subjects over a long…

This is very well done. I've been hobby researching learning tools for the past couple years and this looks like one of the best. @ai_ia have you seen Andy Matuschak's Orbit project?

https://withorbit.com/

You both seem to be solving similar problems.

Re: Self studying the MIT applied math curriculum (2019)

#33
post #2

Is this doable for someone with less basis in math? I almost stopped studying math after two years of undergrad, when I went to a more practically-focused school. It'd be nice to get back into shape, because I've started reading research articles and always feel like I'm behind on the theory side of ML.

It helps to have good resources https://openstax.org/subjects/math

Re: Self studying the MIT applied math curriculum (2019)

#34
post #32
post #3

I have a pretty similar background. I have an undergrad in ChemE who fell in love with machine learning research. As I didn’t had the appropriate background so I taught myself Computer science using mostly resources such as OCW and teachyourselfcs, videolectures etc. However, what stood out to me was how difficult it is to self study? Universities provide a setting which helps you learn difficult subjects over a long…

This is very well done. I've been hobby researching learning tools for the past couple years and this looks like one of the best. @ai_ia have you seen Andy Matuschak's Orbit project? https://withorbit.com/ You both seem to be solving similar problems.

Thank you for your kind words.

I am familiar with Andy's Orbit project given that I am a big fan of his writing.

I even linked to his essay "Why Book's don't work"[1] in the introductory blog post[2] as well.

[1]: https://andymatuschak.org/books/

[2]: https://primerlabs.io/blog/introducing-primer/#the-problem-o...

Re: Self studying the MIT applied math curriculum (2019)

#35
post #3

I have a pretty similar background. I have an undergrad in ChemE who fell in love with machine learning research. As I didn’t had the appropriate background so I taught myself Computer science using mostly resources such as OCW and teachyourselfcs, videolectures etc. However, what stood out to me was how difficult it is to self study? Universities provide a setting which helps you learn difficult subjects over a long…

Excellent intro comic, it got me really excited about your product! I would love to try it out once you release a more advanced course. I signed up, hopefully you will send e-mail updates as you release new courses.

> I signed up, hopefully you will send e-mail updates as you release new courses.

Yes. That's why we have created guest-login for people to test out the product and if they want to get new course release updates, they can sign up.

Thank you

Re: Self studying the MIT applied math curriculum (2019)

#36
post #31
post #30

If anyone wants to attempt this, that's awesome. It's a lot of hard work, but I think it opens a lot of opportunities for personally and professionally. I've a Ph.D in Applied Mathematics from a traditional program, so I wanted to chime in based on some of the comments I'm seeing. As a note, this is an opinion and others may feel differently and strongly at that. To me, applied mathematics is the art of transforming…

What would you recommend on Hilbert spaces to someone who has worked through Baby Rudin? Thanks for the insightful comment by the way.

Laugh. I was hoping no one would ask since I don't have a great answer! We used "An introduction to Hilbert space" by Young. It's fine? There's stuff in there like Sturm-Liouville systems that I don't particularly use or care for. I also never use it as a reference.

Here's a hodgepodge of other books related to functional analysis that I like more, but don't directly answer your question. I got a lot of benefit out of "Convex Functional Analysis" by Kurdila and Zabarankin. They sort of have a high level overview of different functional analysis topics, including Hilbert Spaces, but with the ultimate goal of proving what they call the Generalized Weierstrass Theorem. Essentially, when does a function has an inf and when is it attained. Even if you don't care about optimization theory, I very much appreciated their survey of topics to get there.

I occasionally also use "Introductory Functional Analysis with Applications" by Kreyszig as a reference. I think this was the first time I saw cleanly the difference between an adjoint and the Hilbert-adjoint of an operator, which was constantly confusing to me prior to that point.

The last one I like is "Nonlinear Funtional Analysis and its Applications I: Fixed-Point Theorems" by Zeidler. He wrote, I think, five volumes, but this is the only one that I use. Anyway, he presents differentiation, Taylor theorem, and the implicit function theorem very well in function spaces. The first four chapters are great as a reference.

Since I'm listing off obscure books, for integration, I like "A Concise Introduction to the Theory of Integration" by Stroock. I actually don't like his newer book, "Essentials of Integration Theory for Analysis" as much as the older book. Anyway, I find it very dense, but well written. Essentially, I like the first five chapters, which culminates with the divergence theorem, which ultimately gives a precise description of integration by parts in more than one dimension. He also answers precisely the question about the difference between Reimann and Lebesgue integrals.

Re: Self studying the MIT applied math curriculum (2019)

#37
post #29
post #24

Earlier quoted context omitted.

I think that would be more likely to be covered in a pure math program than applied math.

> I think that would be more likely to be covered in a pure math program than applied math. Integration is pretty basic and used extensively, and I'd say it makes no sense to cover contour integrals within the scope of complex numbers and differential equations but leave out integrals.

The applied math does teach integration: the Riemann integral. Knowing about Lebesgue integration is not really necessary for most of this kind of work.

Re: Self studying the MIT applied math curriculum (2019)

#38
post #36
post #31

Earlier quoted context omitted.

What would you recommend on Hilbert spaces to someone who has worked through Baby Rudin? Thanks for the insightful comment by the way.

Laugh. I was hoping no one would ask since I don't have a great answer! We used "An introduction to Hilbert space" by Young. It's fine? There's stuff in there like Sturm-Liouville systems that I don't particularly use or care for. I also never use it as a reference. Here's a hodgepodge of other books related to functional analysis that I like more, but don't directly answer your question. I got a lot of benefit out o…

Thank you! What is that extra power that comes from considering Hilbert spaces as opposed to staying in good ol' R^n?

Re: Self studying the MIT applied math curriculum (2019)

#39
post #29
post #24

Earlier quoted context omitted.

I think that would be more likely to be covered in a pure math program than applied math.

> I think that would be more likely to be covered in a pure math program than applied math. Integration is pretty basic and used extensively, and I'd say it makes no sense to cover contour integrals within the scope of complex numbers and differential equations but leave out integrals.

Integration is covered in any calculus course, the comment I was replying to do was about Lebesgue integration which is a much more advanced topic that as far as I know is only needed for integrating functions which are so pathological that they probably don't occur in the physical world.

Re: Self studying the MIT applied math curriculum (2019)

#40
Just don't spread yourself out too thin, and know when to stop - it's super easy to burn out when taking on too much coursework, even if this extra part is self study.

The author writes that he wants to pursue a Ph.D - in that case, I'd put all my effort into pursuing what would maximize my chances at getting into such program. Unfortunately, self study is quite difficult to prove, and does not hold much weight when applying for such positions.

Post reply on HN