At the beginning I took this course because I was interested in doing parallel programming that scientific computing usually requires. But, I get much more than that: I learn how to visualize mathematics, which is very important if you have ever read Richard Feynman's Surely You're Joking, Mr. Feynman! Mathematics is not to be read as fancy symbols, it is meant to express precise semantics of what one has in his/her mind and to understand precisely what one has in his/her mind.

It was given implicitly in the beginning of the course in HW1 that

Xtl + Xbl | Xtr + Xbr
----------+----------
Xtl - Xbl | Xtr - Xbr

Xtl + Xtr | Xtl - Xtr
----------+----------
Xbl + Xbr | Xbl - Xbr

is what the following terms in the 2D FFT formula in HW4 actually means:

I_m/2 |  I_m/2     I_n/2 |  I_n/2
------+-------  X  ------+-------
I_m/2 | -I_m/2     I_n/2 | -I_n/2

But, without visualizing the symbols and the operations as well as grasping the semantics, I failed to understand the connection until I had my oral exam at the end of the semester.

The given lecture materials are here: http://docs.google.com/leaf?id=0B66kEP2FWgm_MjQ5YWI2OGEtNzkyNS00NjI4LTli...

I archive my lecture notes here: http://docs.google.com/leaf?id=0B66kEP2FWgm_MmY2OWU4MjQtZDQ2MS00MzE3LTlj...