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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?

#71

Post by te_platt »

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…

My oldest brother had a real love of mathematics and got a masters degree but never even applied to a PhD program. When I asked him about it he just said he was tired of working on other people's problems.

He had a quiet programming position in a large company that gave him time to work on personal projects. Among other things he volunteered at the local schools teaching "fun" math. I guess I'm just agreeing with you about finding something that inspires you and go with it.

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

#72

Post by forkandwait »

hprotagonist wrote: post #2

The hard but maximally useful thing to do, in my opinion, is to regularly meet with at least two other people and a blackboard and beat your heads against it together for about 3 hours at a stretch. Do this at least weekly--and preferably more often. Self study in between meetings is obligatory. One of those people should be at about your level. The other should be farther along. All three of you should trust each ot…

I always got more from working problems on my own with an occasional consult from peers or a teacher. A danger is that you think your group sessions substitute for working problems.

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

#73

Post by nobody271 »

commandlinefan wrote: post #63
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."

Gosh, that sounds terrible. Like it sounds like she doesn't even want to understand. Okay, you can study math if you give me three hours of "free time" and then she goes off shopping while you watch the kids after your math break lololol. Sorry man, that sounds like hell.

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

#74

Post by sedeki »

Check out Open University (https://www.open.ac.uk), they have a undergraduate (BSc) up to graduate (MSc and PhD) level programmes in Mathematics, and they take distance-learning seriously.

That’s what I would do if I were you. Learning this stuff on your own will be very difficult. I can’t even imagine the amount of discipline needed...

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

#75

Post by natalyarostova »

Lots of good points here. I can't speak to the graduate level, but for the undergrad level I think the trick is to find textbooks that don't suck (most good textbooks are free, or are old enough no one cares about copyright, and a million pdfs are online, or you could get it used for $15. Most bad textbooks are price gouging undergrads).

Then just put the time in with deliberate practice. I tried self-studying math for a year, and often skipped the harder practice problems, thinking just reading the textbook and examples is sufficient. That's actually entirely useless. You are't learning math (or anything worth learning) unless you spend 6 hours on a Saturday working through some hard problem that makes you so frustrated that you ask God why he made you such an idiot. If you spend enough time doing that you can actually learn something.

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

#77

Post by abnry »

foo101 wrote: post #40
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…

Is this sentence incomplete or am I missing the context of the word "compelling" here? > be able to write up a compelling Can someone clarify what this means?

By mistake I swapped lines in my post when composing it. It is fixed now.

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

#78

Post by madrafi »

Just follow MIT Open Courseware for curriculum as for how to learn either the lectures or textbooks, lectures are good for initial understanding but then you'll need a textbook to go over the definitions,theorems and very important EXERCICES . you might want to take it easy don't try to put everything in some sort of timeline like (I am going to do all undergraduate in 1 year) that's really stupid as may be advertised on the internet. Your real goal ,as you're taking this endeavor ,is to understand it by making it your own, get a feel for it.I cannot describe it but you'll know . Best of luck in your quests .

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

#79

Post by abnry »

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.

This is fair. That's why you need to make the goals your own and make sure they are doable. And sometimes, an unreachable goal will still help you learn and value the fundamental material.

Like, if you are into Rubik's cubes, that's going to make learning group theory a lot more fun and motivating.

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

#80

Post by sweeneyrod »

netvarun wrote: post #68

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…

An approach might work well for a Fields medallist but less so for normal people.
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