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NUS Math Module Review: MA5233 Computational Mathematics

Expected grade: B

Actual grade: A- (Pleasant surprise)

Assessment and workload:

– 45% Homework (3 x 15% each, I got 12.86/15 for the 1st, 13.5/15 for the 2nd, 12/15 for the 3rd one)

– 25% Programming assignment (I got 23/25, a miracle for a failed code which gave me a singular coefficient matrix -_-)

– 30% Final examination, closed book, no helpsheet.


– This module is pretty difficult. When I took this module, I was expecting it to be a combination of MA3227, MA4255 and MA4230, which it is, but Prof Cai brings it to a new level. The module essentially covers the following topics: Linear systems of equations, nonlinear system of equations, numerical methods for ODEs and PDEs as well as basic concepts in Finite element methods, which include stuff about Sobolev spaces that I do not understand. Prof Cai motivates the methods using the Poisson equation and the convection diffusion equation a lot, so it would be good to have an intuition of those 2 PDEs before taking this module under him.

– Prof Cai is quite a decent lecturer. He uses the whiteboard to teach and is very systematic in explaining concepts. It is amazing that he can write and talk at the same time. Prof Cai derives many things from scratch and explains to us the physics motivations for the equations he uses. His notes however, are very brief, with gaps and jumps in logic that require listening attentively in class to fill up those jumps. The only grouse I have is that the module becomes very Physics-oriented, to which I am unable to appreciate the methods taught because of the inability to understand the 2 PDEs mentioned above. Prof Cai is also very hardworking and grades everything personally and gives good feedback to students for every question.

– There are no tutorials for postgraduate modules. Prof Cai gives us 3 extremely tedious and difficult homework assignments to do, some of which contain his past year exam questions which are very difficult. Other than that, no other questions are given.

– The programming assignment is extremely tedious. In the undegraduate sense, this single programming assignment can be an FYP in itself. Prof Cai gives us 4 reference papers and asks us to reproduce numerical results in those academic papers using whatever methods you like. As somebody who isn’t fantastic at programming, I struggled a lot to get my program to finally work, only to yield a singular matrix for the linear system. That being said, Prof Cai gives marks based on the effort put in for the report. I was able to elaborate in great detail about the possible reasons why my program failed, maybe that’s the reason why I was given 23/25.

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