Category: NUS Math

The Department of Mathematics at NUS is the largest department in the Faculty of Science. We offer a wide range of modules catered to specialists contemplating careers in mathematical science research as well as to those interested in applications of advanced mathematics to science, technology and commerce. The curriculum strives to maintain a balance between mathematical rigour and applications to other disciplines.

We offer a variety of Major and Minor programmes, covering different areas of mathematical sciences, for students pursuing full-time undergraduate studies. Those keen in multidisciplinary studies would also find learning opportunities in special combinations such as double degree, double major and interdisciplinary programmes.

Honours graduates may further their studies with the Graduate Programme in Mathematics by Research leading to M.Sc. or Ph.D. degree, or with the various M.Sc. Programmes by Coursework.

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This module is primarily taken by Polytechnic Students currently enrolled in Engineering or Computing courses in NUS. Grading was primarily done through the Midterm Test and Final Examination. No marks for tutorial attendance or participation. Almost everyone got full marks during the 2 quizzes. All lectures are web-casted. Dr Ng takes special interest in helping students and his lectures are at a followable pace and he thoroughly explains everything and goes through all problems step by step to help students. He often tells jokes during his lectures and his style of teaching isn’t too dry and can keep students engaged. He always gives notes and feedback to students about the cohort’s general performance during the quiz or exam and points out the problems most students experienced or committed and how to fix them. He only streamlines the content and provides revision packages that are relevant to their future modules of study.

His midterm tests were reasonably difficult with most questions typical and a few more challenging questions. Aren’t a problem if you diligently did his revision package and tutorials. Final Examination was more tricky. His revision packages equipped you with the skills to solve all the typical problems for most topics. The tricky part came with the wording of the examination questions that most students are not used to and may not be sure what he actually wants. The question provides all the required information and what he wants clearly, but students may not be used to the unusual wording. Overall it was above average difficulty and students may struggle if they have not familiarised themselves with solving question in the revision package.

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MA6291 Topics in Mathematics I – Fundamental Solutions

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Expected grade: B

Actual grade: B+

Assessment and workload:

– 40% Project 1 (20% report, 20% presentation)

– 60% Project 2 (30% report, 30% presentation)

– No Final examination

Experience:

– This module is very difficult, especially for students with insufficient background in computer science and topics related to machine learning. The module begins with a crash refresher course on numerical linear algebra and probability. It then suddenly escalates to topics in deep learning. The main forms of deep learning were introduced, essentially neural networks, convolutional neural networks, random boltzmann machines, recurrent neural networks and approximation theory for neural networks. There is simply too much breadth.

– Prof Yang is obviously pretty knowledgeable in this area and he trivialises many things. Delivery of this module is pretty inadequate as he introduces many big ideas, but with insufficient elaboration and emphasis on the fundamentals. He also assumes a high level of mathematical background from us as he uses advanced concepts without elaboration. Prof Yang tries to encourage class participation but failed to do so, as he does not give clear directions on the kind of answer he wants. This causes the student to feel embarassed or appear dumb in front of the class, which causes a vicious cycle of people being unwilling to answer any questions he poses.

– There are no tutorials for postgraduate modules. This is a seminar style module.

– Project 1 involved us having to heavily modify a code on Github on the fundamental aspects of deep learning, and apply regularisation techniques taught. My group choose logistic regression and we wrote a report and presentation based on our experiments.

– Project 2 involved us having to pick an area of deep learning, and try to reproduce results from a research paper or come up with something revolutionary. My group choose Maxout networks and we wrote a report and presentation based on this.

– This year, Prof Yang decided to give us the power to judge our peers’ reports and presentations, and gave us the power to decide 50% of our peers’ grades. While this is a good idea because of the difference in benchmark between the professor and the student, this idea was poorly executed in my opinion. We had to give 2 groups A and 2 other groups B for the report. Next, each of us had to grade 12 other students based on their presentation skills as well as Q&A, and we were allocated 5A 5B and 2C. After all the presentations, I feel no student deserves to get C due to the effort everybody put in to prepare for the presentation. I felt so bad having to give 2 people C because it definitely will affect their final grade. In addition, Prof Yang’s Q&A is unfair because he asks questions of varying difficulties. The student who failed to answer a tough question may have gotten a bad grade from their peers because they were unable to answer to Prof Yang’s satisfaction.

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Selected topics in financial mathematics are offered.

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This module studies the theory of probability. It covers the following topics: probability space, weak law of large numbers, strong law of large numbers, convergence of random series, zero-one laws, weak convergence of probability measures, characteristic function, central limit theorem. The course is for graduate students with interest in the theory of probability.

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This course will be an introduction to Riemann surfaces, focusing on topics such as topology of Riemann surfaces, divisors and line bundles, differential forms and Hodge theory, the Riemann-Roch theorem, period mappings, the Poincaré-Koebe uniformisation theorem. We will also discuss more advanced topics such as algebraic curves, hyperbolic geometry and discrete groups of automorphisms.

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This module is intended for graduate students interested in pursuing research in applied and computational mathematics. It provides a concise and self-contained introduction to important methods used in applied mathematics, especially in the asymptotic analysis of differential equations involving multiple scales. Major topics include scaling analysis, perturbation methods, the WKB method, the averaging method, multi-scale expansion and the method of homogenization.

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Expected grade: B+

Actual grade: A- (Pleasant surprise)

Assessment and workload:

– 10% Homework (3 homeworks, best of 2, I got 10/10 for this component)

– 30% In-class tests, open book (3 of them, best of 2, I got 25/30 for this component)

– 60% Final examination, 1 A4 sized helpsheet.

Experience:

– This module is manageable, provided that you have taken MA4269 before this. This module could be renamed Mathematical Finance 3 due to its nature. This module goes deep into the stochastic calculus parts in MA4269 that were previously skipped or discussed very briefly. The structure of the course is also similar, starting with a detailed review about probability concepts, followed by an in-depth discussion about Brownian motion. Lecture 3 onwards is where it gets more theoretical. The quadratic variation of brownian motion would be derived in a rigorous way, which is different from 4269. Stochastic integrals would then be elaborated on, along with its properties. Ito’s lemma would be used again, and in this module, if in doubt, apply Ito’s lemma. Stochastic differential equations would be introduced, followed by the Black Scholes PDE. Next, Girsanov’s theorem would be elaborated on, followed by change of numeraire. The concepts are the same as 4269 but the notation is quite different. The module ends with barrier options and pricing of exchange options, greeks.

– Prof Zhou has been teaching this module for 4 to 5 times in a row now. He is very experienced in teaching this module and even tries to inject humour into the lecture. Prof Zhou explains concepts in a clear manner and tries his best to use analogies from simpler mathematical concepts to explain the more advanced concepts in this module. The lecture notes are also quite comprehensive and I recommend reading them before attending the lecture because some parts can get a little confusing.

– There are no tutorials for postgraduate modules but Prof Zhou provides some small exercises in each set of lecture notes to practice on applying the concepts. He also assigns homework which allows us to practice the concepts learnt.

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Assessment and workload:

– 20% Midterm test, no helpsheet (I got 14/50, which was absolutely depressing)

– 80% Final examination, 1 A4 sized helpsheet.

Experience:

– This module extremely difficult. It elaborates a lot about the concepts gone through in MA3252 for linear programming, and MA3236 nonlinear programming. Proofs that were previously omitted in those 2 modules are discussed here. As somebody who has done all optimisation modules, this module is a real eye opener for me because the concepts of optimisation go pretty deep. The module starts with a very thorough discussion about convexity, convex sets and functions, then moves on to optimality conditions. Chapter 3 would be about duality and the most general form of duality, Fenchel duality, would be introduced. The following 6 chapters would be optimisation algorithms and their convergence results. The final chapter would be about nonsmooth optimisation which is really difficult but interesting. This module does complete the optimisation package in NUS.

– Prof Zhao has taught this module many times and is very experienced in teaching it. He explains the concepts in the lecture notes pretty well and in a systematic way, adding his own understanding as input when he writes the concepts on the whiteboard. He is also very approachable and keen to answer questions posed by students.

– There are no tutorials for postgraduate modules but Prof Zhao provides a list of recommended exercises to try, which were pretty useless because his test and exam uses techniques of a way higher level compared to the exercises.

– Midterm test was a bloodbath. Prof Zhao set a pretty difficult paper, at least it was really difficult to me. The level of technique needed to do the questions is very high and it is not easy to come out with those techniques in the short span of 90 minutes. The cohort didn’t fare that well, and the mean is in the low 20s out of 60 before Prof Zhao voided 1 question. Still, my coursemates, especially the Phd students, are very strong and the highest scorer got 54/60 before Q5 was void.

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