How to Learn Advanced Mathematics Without Heading to University – Part 3

Many textbooks provide much the same structure as in universities. However, I have had a lot of success in attempting to read far above my level, and satisfying the dependencies that I need along the way.

Somewhere in the OP or its links is a statement that in 1997 or so the world of finance was really hot for quants.

Net: What I found was not "hot" but ice cold.

In contrast, early in my career around DC, for applied math for US national security and NASA, in one two week period I went on seven interviews and got five offers. In four years, my annual salary increased by a factor of 4 to six times what a new, high end Camaro cost. That was "hot".

When I went for my Ph.D. in applied math, I'd read E. O. Thorpe who had, basically an early but basically correct version of the Black-Scholes option pricing model. In the back of his book, he mentioned measure theory. So, I dug into Royden's Real Analysis, and in grad school I got a really good background in measure theory, probability, and stochastic processes from a star student of E. Cinlar, long in just those topics and the mathematics of operations research and mathematical finance at Princeton.

In more detail, about 1992 to 2000, after my Ph.D., I tried to get into finance in NYC as a quant. My Ph.D. dissertation research was in stochastic optimal control, with careful attention to measure theory and the relatively obscure topic of measurable selection and with a lot of attention to real world modeling, algorithms, and software. I had a good background in multivariate statistics and time series techniques, an especially good background in advanced linear algebra and numerical linear algebra (e.g., numerically exact matrix inversion using only double precision machine arithmetic and based on number theory and the Chinese remainder theorem), double precision inner product accumulation and iterative improvement, etc.

So, I sent nicely formatted resume copies, in total 1000+.

I have held US Federal Government security clearances at least as high as Secret; never arrested; never sued; never charged with worse than minor traffic violations; never bankrupt; good credit; physically normal; healthy; never used illegal drugs or used legal drugs illegally; married only once and never divorced; etc.

Results:

(1) I got an interview at Morgan Stanley, but all they wanted was software development on IBM mainframes (where I had a good background at the time) with no interest in anything mathematical.

(2) I got a lunch with some guy who claimed to be recruiting for Goldman Sachs, but, except for the free lunch and what I had to pay for parking in Manhattan, that went nowhere.

(3) I had a good background in optimization, published a nice paper in JOTA that solved a problem stated but not solved in the famous paper in mathematical economics by Arrow, Hurwicz, and Uzawa.

So, for mathematical finance, I got a reference to

Darrell Duffie, Dynamic Asset Pricing Theory, ISBN 0-691-04302-7, Princeton University Press, Princeton, New Jersey, 1992.

and dug in: The first chapters were heavily about the Kuhn-Tucker conditions, that is, the topic of my JOTA paper. By the end of the chapter, I'd found counterexamples for every significant statement in the first one or two (IIRC) chapters. I had to conclude that Duffie was not a good reference for anything good!

(4) Headhunters: I tried them, especially the ones claiming to be interested in technical work, computing, etc. They were from unresponsive down to insulting. It wasn't clear they had any recruiting requests.

(5) In those days, getting names and mailing addresses of hedge funds was not so easy. But I did get some lists and mailed to them. Got next to nothing back. I didn't hear about James Simons until well after year 2000.

(6) Right, there was Black-Scholes. Well, of course, that was Fisher Black at Goldman Sachs. So I wrote him and enclosed a copy of my resume. I got a nice letter back from him saying that he saw no roles for applied mathematics or optimization on Wall Street.

So, I gave up on trying to be a quant on Wall Street!

So that was 1992-2000, 8 years, 1000+ resume copies, and zip, zilch, and zero results.

Curious that the OP thinks that 1997 was a "hot" year for applied math on Wall Street.

Now I'm an entrepreneur, doing a startup based on some applied math I derived, computing, and the Internet! To heck with Wall Street: If my startup is at all successful, I will make much more money than I could have on Wall Street. And I don't have to live in or near the southern tip of Manhattan and, instead, live 70 miles north of there in the much nicer suburbs!

Lesson: Take the OP with several pounds of salt!

Is this a USA, it sounds like they're most concerned that you pay for the lower level courses rather than that you get a properly warranted degree.

Do they accept credits from any other institutions? Isn't there a national agreement on accepting credits for certified degrees?

I would partially agree. Yes, it's stupid if you have enough time "and" money to go to university and study math. Otherwise, if you have enough time, this plan might work for you. But, I wouldn't consider it a wise move, because science/math graduates are already struggling to find jobs in/out-side the academia, and a math degree from a decent university goes a long way in landing you a job.

I think, math, unlike CS, is not a "skill" you use in your everyday work. Whoever does math/science has to dedicate much of their life to it. CS you can learn on the internet, by MOOC's, or just by reading books about it. Math on the other hand, simply doesn't work like that.

To be clear, by math, I mean "advanced" mathematics as the title indicates. Elementary (and intermediate) math is required to learn no matter what.

I agree wholeheartedly! Math is the queen of the sciences, or the silent language of the world around us.

Learning math outside of high school has also helped me identify 'snake oil' statistics in my industry and challenge the validity of information I've been presented as fact.