Posts on Math
October 27, 2005
Application season with Michael Palin via Lebesgue
It's time for those apps to get cracking again! This year I am applying to a larger base of schools... in line with my original risk theory (the number of applications is a monotonically increasing function of the number of grey hairs on my head). For now I'll keep quiet about it, and let's see how things shape up!
I also got my collection of Micheal Palin stuff from Amazon.co.uk today. I'm a big fan of his work as a travel writer/presenter. I've blogged about some of his stuff before here and here. His "Around the World in 80 Days" still has me in awe of the world! So I finally (after ages) managed to put together a collection of his out of print hardback books on each of his journeys - 80 Days, Full Circle, Pole to Pole, Sahara, Hemmingway Adventures, Great Railway Journeys, and Himalaya. I also managed to find a deeply discounted special edition DVD collection of all of them... which just made my day!
I also picked up a copy of Capinsky and Koop's book on Measure, Integral and Probability. Ziad had recommended it to me a while ago, and when I had borrowed a copy from him I realised I had finally found the perfect book to understand the fundamentals of Measure Theory... something I have been trying to do forever now. Sometimes you have to put your learning journey on hold, and wait patiently till the perfect book comes along!
Ten mintues with the book had taught me:
a. Exactly how the Indicator funciton works.
b. Why and how all finite, countable sets were null sets.
c. Why using b. the set of all rational numbers in [0,1] had measure zero.
Simple things to all you mathematically profound princes of the Economics world. Despicably elusive to bimbos like me.
Posted by vinayak at 7:32 PM
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August 4, 2005
You poor poor souls.
It's official - I will be teaching at math camp next month. I genuinely feel bad for you guys :-)
Nonetheless, as all you incoming MSc/MRes students come closer to September, make sure you enjoy yourselves while you can. I never worked as hard as I did at math camp last year. Even in my final exams I didn't study as hard. A one hour lecture, followed by a 90 minute class, and then another one hour lecture, followed by another 90 minute class - in general it's crazy rigorous. It's also one of the most useful things you will ever do next year. I used that stuff SO often it's not funny. You learn to optimize (statically, dynamically, anywayyouwantically), you learn the rudiments of phaseplane diagrams and how they work, its a really cool month if you want to take time off later in the year :)
Good luck!
July 18, 2005
Finding your way around probability, measure, and stochastic processes.
I've been scouring the world for good ways to understand the basics of probability, measure, and stochastic processes. After a long and hard search, I thought I'd share the results of my quest.
Assuming you're a beginner to this mostly painful sometimes delightful world, notation seems to be the most difficult thing to overcome. I think a great start to understanding the very basics is Kai Lai Chung's "A Course in Probability Theory". However, this book gets very tough, very fast, so you don't want to go beyond the first two chapters, and perhaps the supplement (third edition only).
At this point, you want to move over to Grimmett and Stirzaker's Probability and Random Processes (3rd Edition). This is by far the most comprehensive starter book to understanding the fundamentals. I find the beginning a little rough, which is why I would recommend Chung's introductions as a good way to overcome this. Why I like G&S is because they give you good primers to *all* common applications of stochastic processes. Take my own example; I'm working on deciphering a paper that extensively uses diffusion processes in its work. The most accessible comprehensive reference on Diffusion Processes is Karin and Taylor's "A Second Course in Stochastic Processes". However, this book was most definitely beyond my initial reach. Grimmet and Stirzaker provided a good (brownian?) bridge to help me understand those concepts better.
Once you have a basic grasp for things, Karin and Taylor provide the next gentle step, and both their "First Course" as well as "Second Course" are great ways to get an adequately firm grasp for the subject. Ross's "Probability Models" and "Stochastic Processes" are also good, but it lays more emphasis on Queueing models.
As always, for the Economist's touch, there can be no complete understanding of any of this crud without Stokey Lucas and Prescott. Its almost like a good dose of Irish Cream after a heavy meal. They rigorously and painfully (trust me) tell you how it works.
SLP's pure math equivalent (in my opinion) is Doob's "Stochastic Processes", considered one of the first comprehensive references to the subject.
Any other words of advice? Feel free to pitch in!
(I'll add links to these books soon).
Posted by vinayak at 8:32 PM
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May 23, 2005
Death and the afterlife... statistically speaking.
A long time ago Chris had written about the law of the unconscious statistician. It apparently gets better. I've been reading up on Diffusion Processes and found this in Karlin and Taylor's A Second Course in Stochastic Processes: 
Drama, murder, intrigue, Republican Party endorsements... I love this shit... I really do.
Posted by vinayak at 9:49 PM
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