Mathematical Analysis I

Academic Year 2022 - 2023
Semester 1

NUSMods Description

This module is a continuation of MA1100. The main objective is to further develop the student’s mastery of the mathematical language, concepts, and methods. The focus here is more on the analytic and topological notions such as convergence and continuity, which are essential for a rigorous treatment of mathematical analysis. The student’s ability to read and write mathematical proofs is also further developed in this module. Main topics: real numbers, sequences and series of real numbers, metrics in Euclidean spaces, open and closed sets, continuous functions, compact sets, connected sets, sequences of functions. Major applications include: intermediate value theorem, extreme value theorem.


This module is taught by Prof An Xinliang. There was a midterm and a final with some assignments along the way. I did very well for midterm (close to full marks) and I think I did ok for finals – But I got a B+ for this module. Imagine the bell curve yourself.

I was actually quite stressed about this module as it is known to end lives of mathematicians. Topics were abstract and involved some creativity and insight to solve. The tutorial sessions were the most abysmal I have ever known. My tutor was so dead and there were barely any people in the class. Not more than 5 people I swear. I remembered being 1 of 3 people who turned up.

I think this module is also wasted. The prof made the exams too easy (and too much regurgitation) such that it is too easy to score. It does not really test us on our true understanding of analysis at all. I have friends who scored higher than me for midterms with a B/B- for this module.

I think if they intend to rush Chapter 11 (Topology) towards the end of the semester, I suggest they just drop it and move it to MA3210 Mathematical Analysis II or MA3209 Metric and Topological Spaces. For revision, I literally just memorised all the topology proofs without understanding them. It was taught too fast and I did not have enough time to really internalise the concepts. Topology is elegant until this prof (or this module rather) destroyed its reputation for me.