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NUS Math Module Review: MA4229 Approximation Theory

Assessment and workload:

– 5% from participating in class twice and attending tutorial class 6 times. (I got 5/5)

– 25% Midterm test, 1 A4 sized helpsheet (I got 41/50)

– 70% Final examination, 1 A4 sized helpsheet.


– This module pretty difficult. MA3209 Mathematical analysis 3 is strongly recommended before doing this module because a lot of concepts build up from MA3209. It also doesn’t help that Prof Tang is quite a specialist in analysis related stuff, so the module becomes quite analysis-focused. That being said, this module is quite an eye opener for me. This module covers normed spaces, inner product spaces, uniform approximation, polynomial approximation and splines, with the last 2 topics being covered in MA2213 but this module goes deeper into the theory. I found the 1st 3 chapters to be pretty difficult because of the lack of MA3209, I find that I’m unable to fully appreciate the beauty of the concepts sometimes.

– Prof Tang has taught this module many times and is very experienced. His lectures have a very good pace, and he is very rigourous in his mathematical explanation. Prof Tang is also quite approachable in helping students. Prof Tang also gives us a little bit of welfare by printing the tutorials for us. Prof Tang prefers to use handwritten notes, but his handwriting is pretty neat.

– Tutorials are taught by Prof Tang himself. Again, he has taught this module many times so he is very experienced in teaching the tutorials. I like that he tries to get students to participate in class and present their solutions on the whiteboard. In that way, we get to see different kinds of solutions to certain proving questions or computational questions. Prof Tang then carefully evaluates the students’ different method and gives feedback about it on the spot. However, I find his 5% class participation a little too stingy.

– Midterm test was on the manageable but tedious side. Practice makes perfect, especially on the tutorial questions, especially the fourier series.

– Final exam turned out to be considerably more manageable than what the 2016/17 students faced. Prior to this exam, I was already assuming that I will do badly since Prof Tang has a reputation for setting difficult exams, especially when this is my first time doing a module with him. He set about 65 marks worth of computational questions, some of them similar to the midterm test. However, there were 2 parts of proofs that I simply do not know how to work out. Again, tutorial questions are important, I strongly recommend doing the tutorial questions and understanding the concepts before taking the exam.

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