Self Studying the MIT Applied Math Curriculum • Hacker News Board

Re: Self Studying the MIT Applied Math Curriculum

#81

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Re: Self Studying the MIT Applied Math Curriculum

#82

Post by Eldandan » Fri, May 03, 2019, 6:32 AM UTC

hyperpallium wrote: post #80

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 se…

The payoff is indeed learning the intuition, but also learning how to prove things and learning how to learn math. The content itself is only as important as whatever field you're in, or whatever application you're studying that requires that specific mathematics. But the "thinking like a mathematician" and knowing how to learn new math is the valuable skill you'll gain.

Re: Self Studying the MIT Applied Math Curriculum

#83

Post by miguelmota » Fri, May 03, 2019, 6:34 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

A good quote from Sivers' post:

> He taught me “the standard pace is for chumps” — that the system is designed so anyone can keep up. If you’re more driven than most people, you can do way more than anyone expects. And this applies to all of life — not just school

Re: Self Studying the MIT Applied Math Curriculum

#84

Post by mikorym » Fri, May 03, 2019, 6:59 AM UTC

This is a cool thing to do. I followed a slightly similar path in that my undergraduate degree did biochemistry up to 3rd year, but at the expense of third year pure math courses. (I had a kind of applied PDEs and modelling course but applied to biological problems like gene flow, disease modelling and population modelling.)

I ended up doing honours in bioinformatics, but then took a year to do third year pure math (and the honours course in lattice theory and topology). After this I ended up doing what I really wanted to, which was an MSc in pure mathematics.

I also did probably the first 1/3 of Strang's course (even though I had already done linear algebra formally in my original course). I think online math courses are a mixed bag and it could even be that it works better when you have an idea already of why you want to do it and the applications thereof. Applications need not imply applied math—you can apply mathematics to other branches of mathematics.

The more difficult thing for me is to independently find research topics and subtopics. Mentorship in mathematics is very important.

Re: Self Studying the MIT Applied Math Curriculum

#85

Post by mikorym » Fri, May 03, 2019, 7:14 AM UTC

leereeves wrote: post #72

AnthonBerg wrote: post #19

Earlier quoted context omitted.

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.

I think that music theory lends itself to a pace that can be dramatically increased and at the same time learnt successfully.

I don't think math works like this. I specifically decreased my pace when doing math courses that I hadn't done in undergraduate and I am glad that I took that approach. I now see any problem (given enough time) as more of a research question than just a box to tick.

Re: Self Studying the MIT Applied Math Curriculum

#86

Post by usgroup » Fri, May 03, 2019, 7:26 AM UTC

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 agree with this comment and would supplement as follows:

whatever you intend to learn, consider how you're going to retain it. I'm quite sure that I've forgotten a lot more maths than I know. I'm not sure about the utility of forgotten maths. You may think it rehydrates well, but it doesn't. It won't be as hard to relearn but it'll be hard. So consider, for whatever you learn, are you going to be using it? Are you going to be building upon it? Is it just a tourist expedition? These are all fine reasons but they each have different implications.

Re: Self Studying the MIT Applied Math Curriculum

#87

Post by usgroup » Fri, May 03, 2019, 7:30 AM UTC

behnamoh wrote: post #27

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…

This guy did something similar: completing a 4-year MIT undergrad CS degree in just one year! https://www.scotthyoung.com/blog/myprojects/mit-challenge-2/

It'd be more believable if he did it in 3 years :)

Re: Self Studying the MIT Applied Math Curriculum

#88

Post by HAL9000Ti » Fri, May 03, 2019, 7:32 AM UTC

behnamoh wrote: post #27

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…

This guy did something similar: completing a 4-year MIT undergrad CS degree in just one year! https://www.scotthyoung.com/blog/myprojects/mit-challenge-2/

Scott Young is a publicist - his goal is to sell, sell, sell. Completing a world-renowned 4-year curriculum in 1 years time is impossible. (He also admitted to reading the solutions instead of doing the problem sets)

Re: Self Studying the MIT Applied Math Curriculum

#89

Post by c0vfefe » Fri, May 03, 2019, 10:47 AM UTC

usgroup wrote: post #86

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 agree with this comment and would supplement as follows: whatever you intend to learn, consider how you're going to retain it. I'm quite sure that I've forgotten a lot more maths than I know. I'm not sure about the utility of forgotten maths. You may think it rehydrates well, but it doesn't. It won't be as hard to relearn but it'll be hard. So consider, for whatever you learn, are you going to be using it? Are you…

I think most of us are highly invested in the value of easily-rehydratable knowledge, because an incredible amount of the first third of our lives is spent learning facts that we'll forget. If we admitted there might be a better way, we'd have to do the hard and thankless work of institutional overhaul in our schools.

Re: Self Studying the MIT Applied Math Curriculum

#90

Post by c0vfefe » Fri, May 03, 2019, 10:51 AM UTC

joflicu wrote: post #37

One question for all the self-learners here (I have immense admiration). Do these courses inform your day to day job in some way? Or is this for personal knowledge (even more impressive)? How do you find the damn time? Need some suggestions. My goals are infinite and my time is so short.

I hope you get some good answers, but just consider that you'll never achieve satisfaction by having infinite goals (in any part of life). All the tips and self-discipline in the world might only take you from X to 10X, and somewhere down the line you'll have to learn to be okay with that. The alternative is to have the health of your life & the lives of those around you be consumed by ambition and its pursuit.