How to Learn Advanced Mathematics Without Heading to University
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Re: How to Learn Advanced Mathematics Without Heading to University
#2It's cute that quants think what they do is advanced, isn't it?
Re: How to Learn Advanced Mathematics Without Heading to University
#3It's cute that quants think what they do is advanced, isn't it?
It's cute that the article is littered with Amazon referral links to textbooks.
Re: How to Learn Advanced Mathematics Without Heading to University
#4It's cute that quants think what they do is advanced, isn't it?
I don't know any successful quants that claim what they do is "advanced" in any fashion.
Re: How to Learn Advanced Mathematics Without Heading to University
#5I know that many learn programming themselves but I'm curious if anyone have learn advanced mathematics this way.
Re: How to Learn Advanced Mathematics Without Heading to University
#6I 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?
Re: How to Learn Advanced Mathematics Without Heading to University
#7I know that many learn programming themselves but I'm curious if anyone have learn advanced mathematics this way.
One famous, although admittedly not particularly recent, example of a mathematical autodidact is Srinivasa Ramanujan (https://en.wikipedia.org/wiki/Srinivasa_Ramanujan).
Re: How to Learn Advanced Mathematics Without Heading to University
#8I 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?
That depends primarily on your favoured learning style. MOOCs are certainly changing the available resources and lecturers are publishing freely available notes for particular courses on their home pages.
Unfortunately some textbooks can be expensive, but some are more reasonably priced. Unfortunately, the more "niche" the mathematical area becomes, the harder it becomes to find freely available sources.
I personally prefer a mix of video lectures and textbooks. Being able to watch video lectures, with the ability to pause and rewind, is a very useful feature that is not available in live lectures!
Re: How to Learn Advanced Mathematics Without Heading to University
#9An 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) = |x| is continuous but not differentiable at x = 0.
Maybe the OP advice is okay in England, but here in the US I would advise people wanting to learn to f'get about the OP and get better advice.
For job opportunities in quantitative trading, 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.
I had a good background in second order stationary stochastic processes, power spectral estimation, and the fast Fourier transform -- no interest.
Got nowhere. That was before I heard about James Simons.
One interview was by a guy who recruited for Goldman Sachs, and he didn't have a clue about my background.
Another interview was at Morgan Stanley: The interview was in their computer group, but I indicated that I'd like to get into quantitative trading -- they acted like they had never heard of any such thing.
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't know measure theory, anything about Brownian motion, power spectra, time series analysis, etc. and were looking to hire people like themselves.
Candidate Lesson: Study all the math you want, but don't expect Wall Street to be interested.
Re: How to Learn Advanced Mathematics Without Heading to University
#10I 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?
It is very easy to get most mathematics textbooks online, through slightly unsavoury means. It is far more difficult to figure out which textbooks are worth reading---this is a process that requires trial and error, and browsing through recommendations (math.stackexchange and mathoverflow.net have many good textbook recommendation questions, with many excellent answers).
Also, it is very easy to audit courses at universities! Get out there, ask the professor if you can audit the courses (make friends with them too!), and enjoy yourself a stress-free, and money-free, quality education.