Time  TTH 10:3012 
Location  Wean 4623 
Instructor  Gary
Miller [mail  Wean 7130  82631] office hours: ? 
Secretary  Charlotte
Yano [mail  Wean 7120  87656] 
TA  TBA 
Textbooks None  
Web page  Scientific Computing 
Other references 

Scientific computation is the broad field concerned with the design and analysis of numerical algorithms. The simplest examples are solving a linear system of equations or finding the eigenvalue and eigenvectors of a matrix. These numerical algorithms are central to design, testing, and understanding of enumerable physical objects. The design of building, ships, artificial organs, to ink jet printers all use these algorithms. Numerical algorithms also appear in other parts of science and engineering. Google uses eigenvectors of graphs to rank pages on the Internet. Eigenvectors are used to partition large graphs for storage over multiple machines.
On the other hand computer science algorithm theory is playing a larger role in the design of new faster numerical algorithms. As an example in the 1970's researcher showed how efficient algorithms for Gaussian elimination could be expressed as a purely graph theoretic problem. This formulation dramatically changed how we view Gaussian elimination and how we design algorithms for it.
More recently, the focus has been on iterative system solvers. Here again, at least for some very important special cases, the problem can be expressed in graph theoretic ways. In this case understanding eigenvalues of graphs plays an important role.
In this class we shall cover both classic numerical algorithms as well as show the interplay with
combinatorics, graph theory, and spectral graph theory.