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Self Studying the MIT Applied Math Curriculum

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Re: Self Studying the MIT Applied Math Curriculum

#41

Post by vecter »

afarrell wrote: post #33
mkl wrote: post #22

Can someone please explain how MIT course numbers work? I get that "18" means maths, but why do specific courses sometimes have two digits after the "." and sometimes three, and if the level of study is encoded in it, why does it seem to jump to starting with "6"?

There is no strict system after the “.” however the 3-numeral course numbers tend to be advanced/grad classes. There are some smaller patterns within each major but nothing knits those together. 6.82x tend to be systems classes like networks or OS. But 17.828 isn’t like an intro to constitutional law and 6.42 isn’t Causes and Prevention of Software Project Failure.

This is misleading and false when it comes to Course 18. Math classes numbering has much more structure.

18.XYZ where Z >= 5 are grad classes.

    X = 1 is Analysis
    X = 2 is Mathematical Physics
    X = 3 is Applied Mathematics
    X = 4 is Theoretical Computer Science
    X = 5 is Logic
    X = 7 is Algebra
    X = 9 is Topology

Re: Self Studying the MIT Applied Math Curriculum

#42

Post by _mhr_ »

martincmartin wrote: post #38

Is there a place to find answers to textbook questions? I get that this is discouraged, because it means paying students can cheat. But for people who are self studying, there are many times you think you understand, but you're not sure and would like to see. In particular, I'm hoping to self study the Structure and Interpretation of Classical Mechanics, but can't find the answers anywhere.

Try slader.com

Re: Self Studying the MIT Applied Math Curriculum

#43

Post by yeahman »

martincmartin wrote: post #38

Is there a place to find answers to textbook questions? I get that this is discouraged, because it means paying students can cheat. But for people who are self studying, there are many times you think you understand, but you're not sure and would like to see. In particular, I'm hoping to self study the Structure and Interpretation of Classical Mechanics, but can't find the answers anywhere.

If you post a serious attempt to math stack exchange, they are usually very helpful in telling you if you are right, or where you went wrong.

Re: Self Studying the MIT Applied Math Curriculum

#44

Post by hamburglar1 »

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…

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.

Re: Self Studying the MIT Applied Math Curriculum

#45

Post by dxbydt »

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 programmers” book that so many of you loved on HN. Much of math lit is imo unnecessarily dense & terse. Speaking as a phd student, I really appreciate atleast 1-2 numerical examples with answers, not just plain theory. Maybe if there was a Linear Algebra for programmers text with some code in python to accompany the theorems, it would be a huge hit among applied ML researchers & programmers. Graduate linear algebra is actually quite hard & very few phd students pass the linalg quals in their first attempt ( Grad linear algebra, not basic shit like matrix algebra, linear maps & decompositions). This material should imo be rewritten ( “dumbed down” ) so regular folk can also sample some of the magic.

In my previous work at an adtech corp, I built a whole bidding algorithm straight from Strang’s linear algebra book (the chapter on Lagrange optimizers). It’s still running, 5 years & counting. I once joked if they gave a nickel out of every dollar that algorithm made to Prof Strang, he’d be a multimillionaire.

Re: Self Studying the MIT Applied Math Curriculum

#46

Post by jpmattia »

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…

> 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 course.

I would guess that 3 math courses at one time (and taking nothing else seriously technical) would constitute a pretty full load for most people. Much beyond that probably impacts how much is being truly absorbed for the long term.

Re: Self Studying the MIT Applied Math Curriculum

#47

Post by barry-cotter »

hsikka wrote: post #3
mpoteat wrote: post #2

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

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?

Re: Self Studying the MIT Applied Math Curriculum

#48

Post by dxbydt »

wittedhaddock wrote: post #40
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…

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.

Re: Self Studying the MIT Applied Math Curriculum

#49

Post by jimmy_dean »

dxbydt wrote: 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/

Re: Self Studying the MIT Applied Math Curriculum

#50

Post by adamnemecek »

commandlinefan wrote: post #14

I’ve been doing more machine learning for work, and I’ve realized a) how much calculus is involved in it and b) how much calculus I had forgotten since I took the courses as an undergraduate almost 30 years ago. I happen to still have my old calculus textbook (I couldn’t sell it back to the bookstore back then), so I dusted it off and started working through all the problems. I’m about halfway through right now, and…

Look into dual numbers and automatic differentiation, it's like Calculus on steroids.
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