Physical phenomena
There’s a wide range of physical phenomena out there, barring even quantum and relativistic effects, that are utterly fascinating. Take cavitation, for example– imagine that under non-esoteric conditions you can form bubbles that when they collapse radiate with black body termperature equal to the sun’s! Almost enough to make you want to be a physicist, or a mechanical engineer. But then, you realize you’d rather just daydream about cool ways to exploit those phenomena than do the grunt work of gathering data and formulating theories to explain and properly harness them.
I just got back from the latest departmental colloqium talk, given this week by Richard Tsai from UT Austin. It was a nice talk, about path planning and visibility optimization, reminiscent more of the style of computer scientists’ or engineers’ talks than mathematicians; that is, he used nice pictures and got his point across with few references to equations for justification. Of course, this was in large part possible because of his subject matter, so I can’t say it was better than the talks before it, which flew over my head… just that I enjoyed it more.
In the course of agonizing over my stochastic processes midterm, I realized that a really good book on probability would be one that approached it from applications to gambling, the way the field originally developed, and took it from the basics all the way up through its modern, starvedly rigorous heights, all the while applying it to the solution of interesting/challenging problems. I.e., it’s slightly useful when you motivate martingales by mentioning their usefulness in modeling fair games, but it’s enlightening when you show me that usefulness. Anyone know of any such book?
Possibly relevant posts:
- Real Analysis and Fourier theory (3/4/2005)
- Fractal River Basins (7/12/2007)
- Demographics in Technical Fields (8/24/2005)
Steven Shreve has a nice set of lecture notes on ‘Stochastic Calculus and Finance’ which motivates much of the standard material on probability theory and stochastic processes by its application to the pricing of financial assets. [This has historical significance too. Louis Bachelier’s 1900 thesis on ‘The Theory of Speculation’ developed results about random walks five years before Einstein’s celebrated paper on Brownian motion.] Shreve’s notes do not require any prior knowledge of finance.
Thanks, but unless I’m mistakened, Shreve’s taken his notes down. I’ll try to find his books at the library.
Oops, should have checked the link before posting. Here is one that works.
The new template looks good.
The notes are actually still up on the web. See http://www.cs.cmu.edu/~chal/Shreve/shreve.pdf.
There is actually a nice book in Milikan called “How to gamble if you must: Martingale (or stochastic) inequalities”. You may want to google or amazon it to find out about the authors. It seems to fit in with all your criteria. However personally I find the book a bit too technical.
This may seem a bit random, but I’ve seen you around at the stochastic processes course. Can I make friends with you? - you seem to have a lot of nice thoughts.
Sure, I’m always in the market for friends; say hello next class.
I almost bought a book in the bookstore, “Discrete Gambling and Stochastic Games”, which partially bills itself as an introduction to the ideas in that book, and it seemed pretty sophisticated already, so I don’t think I’m ready for that level quite yet.