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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?

#91

Post by te_platt »

selimthegrim wrote: post #81
te_platt wrote: post #71

Earlier quoted context omitted.

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…

I don’t know what PhD program your brother was looking at but ideally candidacy committees won’t pass you unless you chose the problem or made it your own. Where your brother is right is that forming such a ideal committee is mostly politics.

I think you are right on both points. There were more details and his answer was just a quick way to say:

He didn't care about the status of having a PhD

He didn't need a PhD to advance his career

He was having fun doing math stuff anyway

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

#92

Post by QuercusMax »

Eridrus wrote: post #86
selimthegrim wrote: post #81

Earlier quoted context omitted.

I don’t know what PhD program your brother was looking at but ideally candidacy committees won’t pass you unless you chose the problem or made it your own. Where your brother is right is that forming such a ideal committee is mostly politics.

I don't know about math, but in CS, a lot of funding comes from specific grants, so you'll be working on something related to what your advisor got grant funding for.

Regardless of grants, etc., your general area of work is going to be based on what the faculty members' focuses are. But in any case, you'll probably still be doing your own sub-piece of some larger effort. You wouldn't choose an advisor at random, so this isn't really relevant.

I mean, if you're interested in astrophysics, you shouldn't go to a school where the Physics department is focused on nuclear physics!

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

#93

Post by burtonator »

I'm actually building an app specifically for this use case:

https://getpolarized.io/

Polar is basically a personal knowledge repository.

The idea is that you use Polar for all of your education. Either official education or continued learning.

Every textbook or technical paper should go into Polar.

You can then annotate the textbooks directly including text highlights, comments, etc.

It supports spaced repetition systems like Anki so you can continually review what you've learned and NEVER forget anything.

It doesn't make sense to pursue a PhD or spend 6-12 months researching a topic to just forget 80% of it due to bit rot.

The reason I named it Polar is that it's meant to 'freeze' all of your knowledge so that you never forget it - ever.

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

#95

Post by empath75 »

sweeneyrod wrote: post #80
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.

I dunno, it's worked for me. I have a problem I want to solve, then learn the tools I need to solve it. Not just math, but just as a software developer.

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

#96

Post by febin »

Hey, I am also on the same boat. I have been trying different things lately. I have gone through a lot of courses and a lot of books, but most of these experts have the curse of knowledge. They don't know how it is like to not know. They skip things that seems obvious to them. But, for begineers not having such information can be frustruating and feels like the author/lecturer is moving fast.

I recently stumbled upon this book "The Language of Mathematics: Utilizing Math in Practice" I have been reading this book for a while and the author takes a different approach in teaching maths. I am slowly beginning to learn how to forumulate a real world problem into mathematical model and then solve it. More importantly, I am able to read and understand mathematical expressions better through this book. This book has raised my hopes in learning and apply math. I would recommend you to give it a shot on this before you go through any other courses.

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

#97

Post by oarabbus_ »

madhadron wrote: post #20

There's a set of basics that you will want no matter which direction you go: calculus/real analysis, linear algebra, differential equations/dynamical systems, and sets, groups, rings, and lattices. Calculus: learn to extract qualitative information about a function (it goes up here, has a maximum there, goes down there, oscillates with an increasing period, goes to this value at infinity...) and to numerically comput…

Most engineers I know have not learned set theory or groups/rings/lattices. They still seem to be doing pretty well.

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

#98

Post by School-Cotton »

madhadron wrote: post #20

There's a set of basics that you will want no matter which direction you go: calculus/real analysis, linear algebra, differential equations/dynamical systems, and sets, groups, rings, and lattices. Calculus: learn to extract qualitative information about a function (it goes up here, has a maximum there, goes down there, oscillates with an increasing period, goes to this value at infinity...) and to numerically comput…

Basic topology is also important.

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

#99

Post by hprotagonist »

forkandwait wrote: post #72
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.

group sessions keep you honest and help you work through high level stumbling blocks. You're expected/obligated to do a fair amount of solo pick-and-shovel work in between.
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