Study notes « Random Thoughts

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Computer graphic course

I accidentally found a very interesting course from Berkeley today. The title is Mesh Generation and Geometry Processing in Graphics, Engineering, and Modeling by Jonathan Shewchuk.

Add comment November 6, 2008

A site collection of “lets”

I found this from when browsing randomly on Nuit Blanche. It has nice collection of links to curvelets, ridgelets, and so on.

Add comment June 22, 2008

Useful Tools

Just found a list of good tools suggested in Nuit Blanche.

The list may be a bit dated but many of the tools are still very useful.

Add comment June 22, 2008

Protected: Network coding and capacity bound

Enter your password to view comments December 17, 2007

A not so rigorous introduction to finite fields

Field is meant to extend the most basic set of mathematical operations: addition, subtraction, multiplication, and division beyond real number. As subtraction and division are really inverse operations of addition and multiplication, we actually only need to consider the latter two. The set of all real numbers are closed under addition and multiplication. In the sense, any sum of two real numbers is real and so as their multiple. Moreover, associative law holds for both operations. That is, for any real numbers $x$ , $y$ and $z$ , $x+(y+z) = (x+y)+z$ . Further, both $+$ and $\times$ operations are commutative, i.e., $x + y = y + x$ and $x \times y = y \times x$ .

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Add comment December 12, 2007

About method of types

Question:

I was confused on the proof of Theorem 11.1.3 in yersterday’s class. And I am still confused after review the book and your notes many many times.

I think that one of key points of Theorem 11.1.3 is that, under any source distribution $Q(x)$ , the upper bound and the lower bound is true for all possible types $P$ . (Theorem 11.1.4 express $P$ and $Q$ seperately and use the conclusion of Theorem 11.1.3. Obviously, the bounds for the size of a type class $T(P)$ should be free from the souce distribution $Q(x)$ .)

However, during the proof of Theorem 11.1.3, we always assume $P$ is the same as the source distribution.
(In our text book, the author always use the notation $P^n(T(P)$ ) and related theorems and corollary which are only applicable for $P=Q$ the source distribution)