Math Theoretical Physics / Mathematics - Books, Career prospects

[qwsdcnjkio]

Hi, last month I graduated with a BSc in Physics and have decided to take a break for a while to decide my next move. Also, having left Uni, its made me realize that I actually have to decide on a future career, something I've kind of put off until now, and how much I enjoy Physics.
I'm pretty sure now that I would really like to study for a Masters in a few years time, I'm slightly unsure what at the moment, but i think it will proberly be in Theoretical Physics or a Mathematics type course. Though I think I'm going to wait a bit longer and go with the flow and not set anything in concrete yet.
Anyway, since leaving Uni I've been trying to keep learning, and have been trying to complete as many problems in as many books as possible. Which brings me to my first question. I want to buy some books so that I can learn as much Mathematics as possible to prepare me for a possible future career in Theoretical Physics or some kind of Mathematicall Modelling. Basically I would like to start from the very basic of mathematics so that I can get my foundations sterdy and work my way up. So I was wondering if anyone here can direct me to what books I should get?
My second question is what kind of jobs are available that I could use this knowledge for? I was thinking there must be loads, since you can apply mathematcis to almost anything.

Thanks for your time and reading this, I look forward to any help anyone would like to give.

 

[qwsdcnjkio]

I've also read the post on becomming a mathemitician, and am unsure which books to choose from the suggested list. Also, the main maths book I'm working from right now is a big fat one on Calculus by Finney/Weir/Giordano. (Also, does anyone know of any programs downloadable for free form the internet that enable you to write equations etc? Thanks!)

 

[SeReNiTy]

A neat little book I'm working through at the moment is Calculus on Manifolds by M.Spivak. Also try his comprehensive introduction to diff geometry as well if you want to learn more about differential forms and so forth.

As with physics, i can only reccomend the Feynman Lectures for a intuitive understanding while some more standard textbooks for problems.

 

[fliptomato]

My second question is what kind of jobs are available that I could use this knowledge for? I was thinking there must be loads, since you can apply mathematcis to almost anything.

To poorly paraphrase a part of Feynman's Surely You're Joking, Mr. Feynman: when Feynman was an undergrad, he asked his math professor "I'm interested in majoring in mathematics. But what's the point of learning higher mathematics if not just to learn even higher mathematics?" Feynman's professor responded by saying "If you have to ask, then you shouldn't major in mathematics."

Something I can paraphrase a little more accurately, Andrei Linde, one of the big names in inflationary cosmology, once told his freshman physics course the following story (in a delightful Russian accent): "The physics department once asked me to talk to prospective physics students. So I told them: 'When you wake up in the morning, if you can think of doing anything else other than physics, then you should do that instead."

Those who go into theoretical physics or pure mathematics are interested in the physics.mathematics itself as a career, not necessarily any applications. With the possible exception of condensed matter theory (and even then, maybe not), theoretical physicists tend to work on topics that are far removed from applications. Anyway, it's no surprise that theorists get the label of the "primadonnas" of physics.

That being said, the greatest skill one gets in theoretical physics/mathematics isn't any particular application (though a few exist), but learning creative ways to think critically. (Though path integral methods in quantum field theory have been applied to the stock markets by 'quants'.) I've heard string theory grad students say that "There's nothing wrong with a graduate education where the worst case scenario is ending up a millionaire on Wall Street."

Anyway, I don't have any good suggestions for math books, but here are my suggestions for physics books:

* Quantum Mechanics: Griffiths (for a first course), Shankar (especially good for self-study), Sakurai (the classic text)
* Statistical/Thermal Physics: Reif (the "standard text," has a reputation for being wordy, but is pretty good if you have the patience to read straight through.)
* Quantum Field Theory: [after having read the QM texts] Zee, Greiner, Peskin (perhaps in that order!)

Whatever you end up reading for your self-study, the two more important things are:

1. Work out problems on your own, you don't really "learn" anything until you have to apply the knowledge to solve a problem.
2. It helps immensely to have people to talk to. If only to ask questions or bounce ideas off of.

Best wishes,
F.

 

[fliptomato]

Oh, one more thing you can do with a theoretical physics PhD, apparently: you can win big in poker tournaments!

http://www.pokernews.com/news/2006/8/wsop-final-table-updates-binger.htm"
http://cosmicvariance.com/2006/08/10/world-series-poker-theorist/"

Michael Binger, a recent Ph.D in particle phenomenology, just won $4.1 million after finishing 3rd at the World Series of Poker!