Are there any readings or books on math theories that can make me better understand the course?

[Yitong Zhou]

This course makes me strongly realizes how bad my math is. I always encounter a situation where real analysis and linear algebra are combined together, also maybe adding some stochastic or probability theory. My problem is that what I have learnt before is purely real analysis or purely linear algebra and abstract spaces. I find it quite hard to rethink a calculus or a probability distribution under vector space.

For example, normal distribution, calculus of f(x) seems all fine. But a multivariate distribution makes me confusing and struggling, and especially like how could you solve a vector calculus gradually on every dimension to finally get a multivariate CDF. And like how to calculate the  Fourier Transform of k(x,x') on a R x R space, just way beyond imagination. Even do a gradient partial on the inner product of two vectors seems not so natural and obvious.

Could anyone recommend some books or chapters to read to better prepare these problems on math?

Thanks,

Yitong

[Alex Smola]

hi yitong,

i guess serge lang's book is good. then there's bolobas' book on real analysis. let me see whether we can offer a basic calculus class as one of the tutorials. also, maybe one of the students can chip in what their favorite book for these subjects was (i could recommend some very nice german and italian ones but that probably wouldn't be terribly useful).

apologies for us assuming this as background - barnabas and i are teaching our first class. and we thought that these topics had been taught before. in particular given that this was listed as prerequisite. 

let's see what we can do.

cheers,

alex

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http://www.youtube.com/playlist?list=PLZSO_6-bSqHQmMKwWVvYwKreGu4b4kMU9 (YouTube playlist)
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