Two kind of views for thesis in Scientific Computing

Published 18 April 08 05:13 AM | norman

In my earlier post, I've summarized what is Scientific Computing, area where I spent many hours these days, that I may become a distracted husband, dad and boyfriend. Smile

Here, I'd like to highlight the "content" of my reference. Materials that I've been digging. Here you go:

  • Systems of Linear Equations
  • Linear Least Squares
  • Eigenvalues and Singular Values
  • Nonlinear Equations
  • Optimization
  • Interpolation
  • Numerical Integration and Differentiation
  • Ordinary Differential Equations
  • Partial Differential Equations
  • Fast Fourier Transform
  • Random Numbers and Stochastic Simulation

I remedy these materials with two different views:

  • First view, mastering these known techniques/numerical algorithms so that I can solve problems in  various domains that need numerical solutions (the domain can be Physics, Engineering, Biology, Economics, etc). Here, I learn the "tools" so that I can use them to solve other problems.
  • Second view, looking for intrinsic issues within the techniques/numerical algorithm so that I can improve the techniques/numerical algorithms. Here, a domain problem is not necessarily needed. Here, I learn the "tools" so that I can make better "tools".

I haven't decided my thesis would be from which view of the two above. I would need to consult my mentor. The second view might be harder, I think. But then, if I have to focus on the first view, I still have no idea to solve problems in what domain. Physics/Engineering or Computer Science as I have background on it? Biology? Economics? or.... Mathematics itself!

That sounds interesting, using computing to solve problems within Math! I got the idea after I got these two books:

From the two books I was introduced to a re-emerge discipline now called Experimental Mathematics. Hmm, something to discuss with my mentor.

Btw, is there any of you familiar with Experimental Mathematics or someone doing it?

Phew! I really need to get title for my thesis.

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Comments

# gre said on July 31, 2008 09:18 PM:

It is nice to know that an Indonesian like you have passion in applied math. As I read your background, you are a physical engineer. Probably you know about Control Theory or Control Engineering. Some of Indonesians who are perhaps friends of your supervisor in Twente University have made great contributions to this field.

One of Hilbert problems (en.wikipedia.org/.../Hilbert_problem) was accidentally solved by a guy in Control and Dynamical Systems Department @Caltech. Who's know someday maybe you are one of the solver of those problems ? And of course you will be a rich person :)

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