I don’t think i want to make this weekly. I shall write as and when i feel like it and that should be more frequent than 1/week i hope. Today is the first day of school. I am taking far less classes now, but strangely not strangely, i think i am going to learn more.

I don’t think i am taking any class on stochastic calculus. The reason: i heard the person teaching this class is very theory oriented and probably won’t provide any applications. Bad. I am a simple person. I need to see some applications amidst the theory building. Instead I plan to take another standard algorithms class (i took one such grad class back at berkeley. but basically i just slogged thru the homework and forgot everything that wasn’t tested in hw/test. Perhaps about 20% of this class i might already know, but it would be a good review. I’m starting from ground zero essentially. We talk about fibonacci heaps which i didn’t study the last time. Amortized analysis is like magic. You come up with some brilliant potential function and the key idea is a_i=c_i+\Phi_i-\Phi_{i-1} where c_i is the actual cost incurred. Looking at a_i, you sometimes overcount, sometimes undercount, but in the end, \sum c_i =\sum a_i - \Phi_k-\Phi_0 \leq \sum a_i is all that matters and we can look at a_i the amortized cost of every operation instead, and blithely ignore the actual cost c_i. A link I find useful is www.cs.duke.edu/courses/fall05/cps230/L-11.pdf.

Another class I want to take is combinatorics: the probabilistic method. This is cool. I learn some basics as an undergrad but this class i hope is going to go beyond that. Simple tricks like the union bound (P(\cup A_i) \leq \sum P(A_i)) and linearity of expectation can be used to obtain powerful bounds. That’s all for now. Tomorrow I’ll be attending two classes on commutative algebra and computational algebra, one of which will use the book i am supposed to be reading (Cox, Little, O’Shea). Kleiman is teaching both courses. I hope he’s a thorough and considerate prof and I hope (too) that these can turn out to be useful for me in future. It’s about the connecting the dots, right Steve?

I have to make an effort to attend seminars too. CS seminars to find applications for what i’m learning. Math seminars to gather more tools. It ain’t easy trying to bridge these two sides.