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Ask HN: How to self-study mathematics from the undergrad through graduate level?

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Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#61

Post by gnulinux »

drablyechoes wrote: post #34

It is really hard to truly self-study in mathematics. Going through the opencourseware and reading textbooks (working as many exercises as you can, of course) will get you only so far. It is important to have someone (ideally with a PhD-level education in mathematics) who you can meet with to guide your study, correct mistakes and answer questions.

I strongly disagree actually. I think mathematics is the best field to self-study. There is nothing in mathematics that cannot be explained on the paper. There are many textbooks that are very good that in most universities professors won't be that good anyway. I went to UC Berkeley to study mathematics (ended up studying CS though) which is supposed to be a top department, but most of my textbooks were better teachers than my professors. I still prefer reading textbook to people explaining me math. I don't even think I understand math when people explain me. I need to first teach it to myself. Then occasionally people offering different perspectives is very beneficial, which, again, can be done on paper.

I don't think you need a PhD level educator. You need mathematical maturity. Mathematics follows a very specific logical structure that needs you to shift the way you think. Human brain simply doesn't work the way mathematics needs it to work. But this is a constant time overhead. Once you understand how to approach mathematical problems, I can't see why you cannot learn everything from a textbook.

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#62

Post by madhadron »

abnry wrote: post #38

Here's my personal opinion about how you should approach this. It's all well and good to want to cover undergraduate math courses. When you are actually enrolled in a university, you will have enough inertia and motivation to complete the courses. However, when you are self-studying you are doing it all on your own. It's hard to be as thorough and cover everything. And so I ask, what really is your goal here? You don…

This is really good advice, and I thinking about suggesting the same thing. I've accepted that there are some basics that you have to have in place before you can really get traction and learn what you need to learn for specific projects.

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#63

Post by commandlinefan »

nobody271 wrote: post #37

Hello, I have actually done this. I learned Algebra up to a good amount of Vector Calculus over the course of four years mostly through self-study. I would leave for work an hour early and either sit in my car or go into a Starbucks and do math. Doing time before work is important. That's when you are at your best. Then after work I would sit in my car and do math for an hour. Then on the weekends, in the morning, I…

Bet you weren't married at the time. I'm trying to re-learn calculus myself, and I have to hide it from her because she gets mad at me when I try to do calculus problems: "why are you doing this? Are you doing this for work? You don't have to do this. There's no reason for you to be doing this."

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#64

Post by enraged_camel »

forkandwait wrote: post #57
abnry wrote: post #38

Here's my personal opinion about how you should approach this. It's all well and good to want to cover undergraduate math courses. When you are actually enrolled in a university, you will have enough inertia and motivation to complete the courses. However, when you are self-studying you are doing it all on your own. It's hard to be as thorough and cover everything. And so I ask, what really is your goal here? You don…

Personally, I think this is bad advice, because without an undergrad+ background, the projects above will either be impossibly frustrating or you will make up some crackpot bullshit. Plus, the undergraduate curriculum is its own reward.

Nah, a good way to learn new skills is to pick a destination and then figure out what steps you need to take to get there. This type of “top-down” learning can help one stay motivated through the most frustrating road blocks. This is especially important for self-learning, because unlike an undergrad setting, the person is on their own and can’t rely on peers.

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#65

Post by mindcrime »

ducttapecrown wrote: post #55
mindcrime wrote: post #17

Earlier quoted context omitted.

You will not become good at math watching youtube videos and reading books. That depends on exactly what you mean by "become good at math". If you're talking about "becoming a mathematician" and doing original research in pure math, then you're probably right. But if one means "learning existing math well enough to apply it to a problem", I would argue that one can learn this stuff just using books, videos, etc. At l…

I'm sure padthai meant that you need to do math to learn math, not just read or watch videos.

I'm sure padthai meant that you need to do math to learn math, not just read or watch videos.

Sure, I'm just saying that it kinda depends on what part of math one is referring to. I think sometimes in these discussions on HN, we overload the term "math" to mean both "calculation" or "applied math", and "pure math" or "math research" and it can be unclear which is being referred to in a given statement.

I believe you can learn the former - "applied math" - (at least up to a certain level) just by reading books, and watching videos (and doing exercises, of course). But for the latter - "pure math" - I agree that you need other people, since you can't easily verify your own proofs.

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#66

Post by forkandwait »

I suggest you get the syllabi from a state college, and then follow that. "work through" the books : copy each page of exposition by hand, try to do the examples and proofs before looking, do all or most of the problems with answers, and get ready for a long journey.

I find a page of math textbook takes about 30 minutes (at least) to really work it over until you understand it.

Personally, I don't much like working in groups or watching video lectures. To learn math, you have to be able work problems by yourself, so you might as well just do that.

David Morin has some great self study books:

http://www.people.fas.harvard.edu/%7Edjmorin/book.html

I have a math BA from a regional state college, usually scored in the top 5 on the tests, and I am self teaching physics / me /ee about 5 hours per week after work.

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#67

Post by scottlocklin »

Just take community college courses. Work lots of problems. Ignore the grand theorems unless you're going to be a math major (in which case you should go to college).

Applied math; if you deal with matter it will generally be linear algebra and differential equations. Vector math important also, and Calc-3 is inadequate; junior level classical physics mechanics book is how I learned stuff like action angle and rotating frames of reference.

If you deal with electronics/signal processing you'll need some kind of Hilbert space course to get you through Greens functions, Laplace transforms and so on.

And for computer science/machine learning/OR: just be really good at linear algebra.

(Applied obv) linear algebra is the highest leverage thing you can do.

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#68

Post by netvarun »

As an alternative I would suggest a top-down approach. Start with the theorems/results you truly wish to understand and work backwards.

There was a great quote from an interview of Peter Scholze (one of last year's Fields' Medallists), which has really changed how I view learning:

At 16, Scholze learned that a decade earlier Andrew Wiles had proved the famous 17th-century problem known as Fermat’s Last Theorem, which says that the equation xn + yn = zn has no nonzero whole-number solutions if n is greater than two. Scholze was eager to study the proof, but quickly discovered that despite the problem’s simplicity, its solution uses some of the most cutting-edge mathematics around. “I understood nothing, but it was really fascinating,” he said.

So Scholze worked backward, figuring out what he needed to learn to make sense of the proof. “To this day, that’s to a large extent how I learn,” he said. “I never really learned the basic things like linear algebra, actually — I only assimilated it through learning some other stuff.”

[1]https://www.quantamagazine.org/peter-scholze-and-the-future-...

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#69

Post by forkandwait »

enraged_camel wrote: post #64
forkandwait wrote: post #57

Earlier quoted context omitted.

Personally, I think this is bad advice, because without an undergrad+ background, the projects above will either be impossibly frustrating or you will make up some crackpot bullshit. Plus, the undergraduate curriculum is its own reward.

Nah, a good way to learn new skills is to pick a destination and then figure out what steps you need to take to get there. This type of “top-down” learning can help one stay motivated through the most frustrating road blocks. This is especially important for self-learning, because unlike an undergrad setting, the person is on their own and can’t rely on peers.

Well, we disagree. Plus, taking on some crazy problem without background saps motivation as well.

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#70

Post by 40acres »

abnry wrote: post #38

Here's my personal opinion about how you should approach this. It's all well and good to want to cover undergraduate math courses. When you are actually enrolled in a university, you will have enough inertia and motivation to complete the courses. However, when you are self-studying you are doing it all on your own. It's hard to be as thorough and cover everything. And so I ask, what really is your goal here? You don…

I think this is good advice. I tried to read parts of CLRS a few years ago but could not wrap my head around the work. The mathematical prerequisites needed for CLRS gave me an end point to guide my self learning to focus on specific areas: algebra (linear and elementary), calculus 1, combinatorics / probability, discrete math, propositional logic.
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