51–60 of 77 posts
The main thing to remember is that nobody learns mathematics to any significant depth by reading. The only way to learn it is by doing it. Doing it carefully, and in full detail, not falling into the trap of "and I understand it from there". So the biggest barriers to doing it on your own aren't source material (there is lots of that) it's a good source of correction. There is also the usual problem of self study, in…
The same could be said of programming, or anything really.
I know that many learn programming themselves but I'm curious if anyone have learn advanced mathematics this way.
What are the best ways for a non-genius, normal person to learn advanced mathematics?
I started with Basic Mathematics by Lang, Eccles book on Mathematical Reasoning, A Course of Pure Mathematics by Hardy combined with the lecture notes of MITs honors single variable calc and Polya's How To Solve It, currently doing Advanced Calculus by Loomis & Shlomo.
I would imagine if you're interested in advanced math you would go to free university seminars from visiting professors and network with whoever is there as a self learner.
I get up 3hrs before work everyday and read a chapter then do as many exercises as I can. Repeat until done, or I get stumped and skip that exercise then come back to it later.
Earlier quoted context omitted.
I'm curious why people care about articles with referral links. It's not like you're paying more if you end up buying something, is it?
It is always good to know when someone is profiting financially from a recommendation they're giving you.
Affiliate links are also a good way to compensate people for curating valuable information. So the sort of "it goes without saying affiliate links are bad" attitude is kind of a mystery to me.
The main thing to remember is that nobody learns mathematics to any significant depth by reading. The only way to learn it is by doing it. Doing it carefully, and in full detail, not falling into the trap of "and I understand it from there". So the biggest barriers to doing it on your own aren't source material (there is lots of that) it's a good source of correction. There is also the usual problem of self study, in…
This is probably the reason why there are so many more autodidact programmers than mathematicians. When programming, you know if you made an error as soon as you try to run your code. The program, by definition, must be "correct" in order to execute. The "source of correction" is the error detection built into any programming language runtime or compiler. No such "source of correction" exists for mathematics, and tha…
Earlier quoted context omitted.
> I got a minor at my undergrad just by doing stats, linear algebra and calc through multivariate. I wouldn't call this a good thing; this just seems like a sane basis for any maths work (including Comp Sci).
That's my point. It was pretty much what was required for the CS degree. The UK standard is much higher.
https://math.berkeley.edu/programs/undergraduate/minoring-ma...
The main thing to remember is that nobody learns mathematics to any significant depth by reading. The only way to learn it is by doing it. Doing it carefully, and in full detail, not falling into the trap of "and I understand it from there". So the biggest barriers to doing it on your own aren't source material (there is lots of that) it's a good source of correction. There is also the usual problem of self study, in…
By the way, did anyone else have to take engineering maths instead and feel they were somewhat lacking?
An early place where the OP dropped the ball: > and some good experience manipulating continuous functions and their derivatives. Nope. If a function is differentiable, then it is continuous, but continuity is not sufficient for differentiability. So, we can't talk in general about the derivatives of continuous functions. E.g., each sample path of Brownian motion is almost surely differentiable nowhere. Just f(x) = |…
>> and some good experience manipulating continuous functions and their derivatives. > Nope 1. "good experience manipulating differentiable functions and their derivatives" sounds weird in prose. 2. Some continuous functions are differentiable. Those ones have derivatives you can manipulate. In fact knowing when a function is not differentiable is a pretty useful skill. > The interview was in their computer group, bu…
My point is not that I was rejected but just that they had no hint that anyone at Morgan Stanley was doing applied math for automatic trading.
If you want to learn mathematics but do not have the time for a full time degree do it part time.
You are most definitely not actually going to reach the same level of mastery of mathematics as even the most mediocre graduate by studying alone. It requires a huge amount of commitment and staying focused and discipled enough is very hard when you don't have a set goal and good continuous guidance and motivation.
It is also very boring and much less productive to study alone. I'd estimate that 70% of my learning comes from the tutorial sessions. Reading the literature is just the starting point. It only counts for 10% if that. Homeworks and exams are also very useful because they make sure you have the prerequisites to move on and start learning something new.
The main thing to remember is that nobody learns mathematics to any significant depth by reading. The only way to learn it is by doing it. Doing it carefully, and in full detail, not falling into the trap of "and I understand it from there". So the biggest barriers to doing it on your own aren't source material (there is lots of that) it's a good source of correction. There is also the usual problem of self study, in…
If anyone knows a good way to check proofs by yourself, let me know. I love it, but you pretty much have to have other mathematicians tell you when you're doing something horribly wrong. By the way, did anyone else have to take engineering maths instead and feel they were somewhat lacking?
I know that many learn programming themselves but I'm curious if anyone have learn advanced mathematics this way.
I did have some very good (and very patient) instructors early on. But at some point when I had the chance to read and understand the basics of discrete math and intermediate calculus in-between my semesters (undergraduate was a bit broken up for me, I was a deployed military reservist), I guess I found it interesting enough at that point to go deeper and change my major.