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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?

#31

Post by mywittyname »

calebm wrote: post #6

I've been following a breadth-first-based-on-my-interests approach for the last several years. It's not been very systematic, but it's been a lot of fun. I think math is essentially clear thinking, and it's best when it's explored from curiosity. A couple resources I would recommend would be: * A book called "Who Is Fourier? A Mathematical Adventure", which touches on a pretty good variety of math topics. It's aimed…

3B1B is amazing at explaining concepts. Lots of commenters in his videos studies math/cs/physics and tell stories about finally understanding a topic they misunderstood in university.

His videos, I think, are best consumed twice: once before you explore a topic, so that you go in with a solid overview and know the key things to look out for; and again after you've studied in depth, when you are able to predict what he will say next, which reinforces you learning.

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

#32

Post by [deleted] »

imbusy111 wrote: post #3

Look at any undergraduate course curriculum at your university of choice and just follow that. Some of them might even have lecture notes and exercises published. As a maths undergraduate, I attended around 10 classes per year - you go see who the instructor is and then just read the lecture notes at your own time at home. Then go take the exam at the end and that's it. That sums up my 3 years of undergraduate studie…

[deleted]

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

#33

Post by konschubert »

padthai wrote: post #12

If we are talking about content you can find plenty of advice here or elsewhere. But do yourself a favor and pay a tutor and/or find a study group. As in writing, dancing, etc. you cannot evaluate your own work good enough. You will not improve your math watching youtube videos and reading books. You need to produce stuff that pass the "sniff test" to your colleagues.

Let me add to that.

It you don’t have somebody challenging you and checking your work, you will likely plateau very quickly unless you are especially gifted.

You will Hit walls of concrete and walls of glass.

You will misunderstand concepts and not notice it.

Your proofs will have logical gaps and you won’t notice it.

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

#34

Post by drablyechoes »

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.

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

#35

Post by dhnsmakala »

klibertp wrote: post #28
jackallis wrote: post #9

Earlier quoted context omitted.

this is an excellent recommendation. it did not work for though. i was not the one that was at the advanced level and the one that was got bored rather quickly with us minions. Happend 5 different times. if you could find one who willing, this recommendation will def help.

Other people's help is indeed one of the most effective ways to learn. My problem with that is simply finding such people - given my extremely introverted disposition it's much harder for me than for normies - and also what you say, ie. finding people who would not quit after three sessions. Then I thought, why can't I just buy the time of someone competent? There are many students who tutor high school kids, shouldn…

Definitely, plenty of PhD students looking to make some extra money. I saw requests like this on grad student email lists frequently.

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

#36

Post by syntaxing »

Is there a particular reason why you want to learn upper level mathematics? I have a pretty decent math background and I personally found majority of math boring (particularly linear algebra). The only reason why I did so well in Math is because I know I needed a strong math foundation to do the fun stuff (like fluid dynamics). Without this purpose, I would of passed my math courses in college but definitely would not of excelled in it.

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

#37

Post by nobody271 »

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 would do three hours of math straight, sitting in my car. Then sometimes in the evening I would do a first pass over a section that I knew I would have to really think hard about the next day that way I had sort of taken the first layer of difficulty off.

Why in my car? Because I simply cannot sit at home and focus enough to study math. I've tried the library but it's too restrictive on what you're allowed to do "oh f*! that's how you do that" doesn't generally go over well in public places. Plus I feel very safe in my car. I can be relax which makes learning a lot easier.

I always take one day off a week (for me that's Tuesday) but aside from that I don't skip.

Get your books at half price books. Math book reviews on Amazon are almost always wrong. I usually have to try two or four books before I find one I can understand. I would just get a book and read it in your car. You don't need the pressure of following along with a schedule where you fall behind and miss out on a topic. You also don't want to miss a topic just because the teacher chose not to include it. Some of the coolest topics/examples don't get covered when you take a course because they don't have the time.

Also, when you get done with a book go through it again and take good notes on note cards that you can review on your drive to work or while you are waiting around. You'll find yourself going back to them over and over again.

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

#38

Post by abnry »

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't have to learn everything about mathematics, because that is in fact impossible.

My advice is to FIRST construct a bunch of projects, tasks or goals that require knowledge.

It could be something like (a) implement a machine learning algorithm to do X from scratch (b) implement a simple physics engine (c) try to verify a number theory conjecture (d) be able to solve all the exercises in a book (e) be able to write up a compelling description/theorem/problem in math (d) numerically solve the quantum mechanics equations of a certain system

Spend some time on material that will inspire you first to help get these goals. Numberphile on YouTube, or any of Brady Haran's videos, is a good place to start. But make the goals your own and make them personal.

Math is not a spectator's sport. Make sure to DO mathematics, not just LEARN mathematics.

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

#39

Post by jdefr89 »

scarecrowbob wrote: post #29

I had math through some introductory calculus when I was an undergrad 20 years ago, but I let my skills lapse. But I want to understand enough math so that I can do some more complex electronics projects and some statistics / ML / intelligence analysis. This level of math, as I recall, is more or less the math core of the undergrad engineering program I dropped out of in favor of a philosophy degree (cause I am dumb…

That sounds like an awesome path dude, keep at it.

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

#40

Post by foo101 »

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?

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