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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?

#81

Post by selimthegrim »

te_platt wrote: post #71
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…

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.

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

#82

Post by ny8jjang »

forkandwait wrote: post #69
enraged_camel wrote: post #64

Earlier quoted context omitted.

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.

I think setting attainable goals and working towards it helps. It is very easy to lose motivation if you don't know what you are going for..

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

#84

Post by jack_h »

gnulinux wrote: post #61
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 teache…

As someone who did study both math and CS at university I disagree. I think there are numerous courses that can more easily be self-taught[1], mostly what one would encounter in their first ~2 years in a math degree. After that things get conceptually a lot more difficult.

For me personally I didn't really need an instructor for most of my calculus courses, or ordinary differential equations, or most of the linear algebra stuff. It was a bit more difficult around real/complex analysis, non-linear dynamics, and courses of that nature. The classes that taught me the value of having an instructor were abstract algebra and topology. Those were such a massive shift away from what I had perceived math to be that an instructor being able to impart intuition, correct my own incomplete or incorrect assumptions, and generally just help guide me to a different mode of thinking was invaluable.

The problem with books/texts in this instance is they are not reactive, they have no idea what you're thinking and can't steer you in the right direction. Worse is that as the person trying to learn the subject matter you don't know where to look to get on the right track and correct your own assumptions because you don't know enough yet.

Now I'm not saying you need an instructor per se, but having some place to ask questions where someone far more knowledgeable than you can help might be a good substitute. I'm sure there are some websites like this, although I don't know of any since I graduated a long time ago.

[1]This does somewhat depend on a person's skillset going into this.

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

#85

Post by niall00c »

amsully wrote: post #47

Good advice here. If you choose the project/problem based approach I recommend https://projecteuler.net You will learn a ton solving these problems (the programming aspect is the trivial piece in most cases).

This is absolutely the right approach!

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

#86

Post by Eridrus »

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 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.

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

#87

Post by maxxxxx »

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 agree, I would not have survived math in school without being able to ask other people.

I learned programming on my own from books but I don't think I could do that with advanced math.

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

#88

Post by ghufran_syed »

I did this a few years ago, now doing an MS in math, after last formally studying math in high school, more than 20 years previously.

There is lots of advice in this thread, including long lists of books - at your level, I think that’s unhelpful. To get started with the foundations, I think it’s best to have one or two books at most, that you work through completely, then decide what to do next. Otherwise you can waste a lot of time time figuring out “what to do next” instead of actually doing math!

I would personally recommend “Engineering math” and “advanced engineering math” by Stroud. The first covers “foundation” topics like algebra, trigonometry etc, then covers the first year of math for a English engineering degree. The second book covers the second year.

Note that English engineering degrees are 3 years vs 4 in the US, but have no general education requirements, so the math covered in the two books is roughly equivalent to the 1st-3rd year of an engineering degree in the US. Both books are very much focused on calculations, not proofs, but will give you a fluency in handling mathematical calculation that is assumed when doing more proof-based courses later. And they are both designed for self-study, which is important.

The other book that I would get, and do in parallel once you have done the foundation part of the first stroud book, Chartrand, Mathematical proofs. This will teach you how to do proofs, using mainly (high school) algebra and basic number theory to start, but going on to cover some proof techniques in analysis, advanced algebra and others areas.

Once you have done those 3 books, you will have a solid basis for further study. I also agree with the comments about interacting with others studying the same material if possible.

Happy to chat sometime if you want to message me (contact info in profile)

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

#89

Post by forkandwait »

ny8jjang wrote: post #82
forkandwait wrote: post #69

Earlier quoted context omitted.

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

I think setting attainable goals and working towards it helps. It is very easy to lose motivation if you don't know what you are going for..

Depending on your background, you probably don't have enough information to pick a long-term goal anyway.

I am afraid that sounds curmudgeonly, but I have also seen students shoot themselves in the foot because they decided they didn't need a class for their not very well informed goals.

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

#90

Post by maxxxxx »

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."

I hope you are kidding to some degree. Having to hide things you want to do from your spouse doesn't sound like a good relationship.
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