How to Learn Advanced Mathematics Without Heading to University

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 &quot;and I understand it from there&quot;.<p>So the biggest barriers to doing it on your own aren&#x27;t source material (there is lots of that) it&#x27;s a good source of correction. There is also the usual problem of self study, in that you don&#x27;t have a roadmap and can waste time easily.<p>That said though, one advantage if you are diligent is that you probably by necessity learn techniques of checking your work (formally and informally) earlier than typical students, which is a good thing.

I&#x27;ve been getting into math recently and found <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;user&#x2F;professorleonard57" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;user&#x2F;professorleonard57</a> Professor Leonard&#x27;s videos are excellent, clear and he injects just enough humour to keep it from been too dry.

Learn it in a group. Mathematics is a social activity. Meeting even once a week to discuss the material you&#x27;re trying to learn will vastly improve the learning rate for everyone involved.

There is no reason to shun university.<p>If you want to learn mathematics but do not have the time for a full time degree do it part time.<p>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&#x27;t have a set goal and good continuous guidance and motivation.<p>It is also very boring and much less productive to study alone. I&#x27;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.

An early place where the OP dropped the ball:<p>&gt; and some good experience manipulating continuous functions and their derivatives.<p>Nope. If a function is differentiable, then it is continuous, but continuity is not sufficient for differentiability. So, we can&#x27;t talk in general about the derivatives of continuous functions.<p>E.g., each sample path of Brownian motion is almost surely differentiable nowhere.<p>Just f(x) = |x| is continuous but not differentiable at x = 0.<p>Maybe the OP advice is okay in England, but here in the US I would advise people wanting to learn to f&#x27;get about the OP and get better advice.<p>For job opportunities in <i>quantitative trading</i>, I tried that on Wall Street here in NY, and got nowhere. I came with a Ph.D. from a world-class US research university with my dissertation research on stochastic optimal control, which should have put my resume near the top of any stack. My favorite prof was a star student of E. Cinlar at Princeton and, thus, about the best there is for mathematical finance. I came with a long, solid background in software, peer-reviewed publications in mathematical statistics, optimization, and artificial intelligence.<p>I had a good background in second order stationary stochastic processes, power spectral estimation, and the fast Fourier transform -- no interest.<p>Got nowhere. That was before I heard about James Simons.<p>One interview was by a guy who recruited for Goldman Sachs, and he didn&#x27;t have a clue about my background.<p>Another interview was at Morgan Stanley: The interview was in their computer group, but I indicated that I&#x27;d like to get into quantitative trading -- they acted like they had never heard of any such thing.<p>I got the impression that only a very tiny fraction of the people on Wall Street had good backgrounds in measure theory and stochastic processes based on measure theory, that my resume never got in front of any such person, and that the other people didn&#x27;t know measure theory, anything about Brownian motion, power spectra, time series analysis, etc. and were looking to hire people like themselves.<p>Candidate Lesson: Study all the math you want, but don&#x27;t expect Wall Street to be interested.

A single book is enough to learn mathematics:<p>Riley, Hobson, Bence: Mathematical Methods for Physics and Engineering: A Comprehensive Guide<p>It has a whopping 1300 pages, but it has everything you need. And if that is not enough for you get<p>Cahill: Physical Mathematics<p>This will give you advanced topics like differential forms, path integrals, renormalization group, chaos and string theory.

I know that many learn programming themselves but I&#x27;m curious if anyone have learn advanced mathematics this way.

Amazing how thorough the Math curriculum is in the UK! I got a minor at my undergrad just by doing stats, linear algebra and calc through multivariate. I think I was just 2-3 courses shy of a BA in the subject.<p>I&#x27;m curious how many people have met self-trained mathematicians in real life. I know there are storied examples, but is it feasible? (Compared to say - self-trained programmers or writers)

Any one know any books or resources that concentrate on invariant programming? Translating recursive code into properly tail recursive or iterative code can be pretty difficult.

It&#x27;s cute that quants think what they do is advanced, isn&#x27;t it?