Course Information

Graduate Courses in Mathematics


Courses for PhD and MSc by Research

Core Courses

Advanced courses in mathematics, covering core topics tested in the PhD Qualifying Examinations.

MAS710
Continuous Methods

4 AU | Semester 2

Abstract integration (basic topology, general Lebesgue-like integrals and measures); positive Borel measures (Riesz representation theorem for positive linear functionals); Lp-spaces; integration on product spaces; abstract differentiation; holomorphic functions.

MAS711
Discrete Methods

4 AU | Semester 1

Enumeration; graph and network algorithms; finite fields and applications; boolean algebras; polyhedra and linear programming; algorithmic complexity.

MAS712
Algebraic Methods

4 AU | Semester 1

Groups, rings, and fields; basic techniques of group theory; Galois theory.

MAS713
Mathematical Statistics

4 AU | Semester 2

Review of probability, random variables and their distributions, moments and inequalities; point estimation in parametric setting; point estimation in nonparametric setting; interval estimation and hypothesis testing.

MAS714
Algorithms and Theory of Computing

4 AU | Semester 1
Available for undergraduates

Turing machines; time complexity and space complexity; algorithm design and analysis (greedy, divide and conquer, dynamic programming); graph algorithms; network flow.

Topic Courses

Specialized courses offered based on student and lecturer interest. The precise course contents are subject to variation.

MAS720/725/740
Topics in Discrete Mathematics I/II/III

4 AU

Special topics in discrete mathematics.
MAS721/726/741
Topics in Scientific Computation I/II/III

4 AU

Special topics in scientific computation.
MAS722/727/742
Topics in Pure Mathematics I/II/III

4 AU

Special topics in pure mathematics.
MAS723(*)/728(*)/743
Topics in Probability and Statistics I/II/III

4 AU
(*) Available for undergraduates

Special topics in probability and statistics.

Seminar Courses

Seminars on new research developments in the Mathematical Sciences.

MAS790/791
Graduate Seminar - Discrete Mathematics I/II

4 AU

Seminar course in discrete mathematics.
MAS792/793
Graduate Seminar - Scientific Computation I/II

4 AU

Seminar course in scientific computing.

MAS794/795
Graduate Seminar - Pure Mathematics I/II

4 AU

Seminar course in pure mathematics.
MAS796/797
Graduate Seminar - Statistics I/II

4 AU

Seminar course in statistics.

Courses for MSc in Analytics

Compulsory Courses

MH8101
Operations Research I

1.5 AU

This course introduces a number of optimization methods commonly used in operations research. Topics covered include linear programming, nonlinear optimization, discrete optimization, dynamic programming, and heuristics.
MH8102
Operations Research II

1.5 AU

This course is a continuation of MH8101 Operations Research I. Topics covered include Monte-Carlo simulation, queuing theory, discrete event simulation, stochastic programming, dynamic programming and optimal control, and inventory theory.
In this course, we introduce state of the art software packages such as SAS, R, IBM Business Analytics to teach students data analysis, data mining, predictive modelling, data visualization, decision optimization, and report generation. In this course, we cover topics including Python, Cplex, R, Matlab, and SAS.
In this course, we introduce state of the art software packages such as SAS, R, IBM Business Analytics to teach students data analysis, data mining, predictive modelling, data visualization, decision optimization, and report generation. In this course, we cover topics including weka, libsvm, IBM Business Analytics, Matlab, SAS, Rapid Miner and Cplex.
This course provides opportunities for students to learn cutting-edge technologies in data analytics, through interactive workshops. During workshops, the instructor will brief each topic and summarize the state of the art. Students will form groups, to conduct deep survey and present the findings to the class.
This course provides opportunities for students to learn cutting-edge technologies in data analytics, through interactive workshops. During workshops, the instructor will brief each topic and summarize the state of the art. Students will form groups, to conduct deep survey and present the findings to the class.
The probability and statistics course provides a systematic approach to understanding uncertainties. Topics covered include probability, conditional probability; random variables, joint distributions, conditional distributions and independence; probability laws, multivariate normal distribution; order statistics; convergence concepts, the law of large numbers, central limit theorem; estimation, Bayes estimators, interval estimation including confidence intervals, prediction intervals, Bayesian interval estimation; hypothesis testing, likelihood ratio tests; Bayesian tests; nonparametric methods, bootstrap.
Many of the business systems are dynamic systems in which their states change over time. This course introduces time series models and associated methods of data analysis and inference. Topics include auto regressive (AR), moving average (MA), ARMA, and ARIMA processes, stationary and non-stationary processes, seasonal processes, identification of models, estimation of parameters, diagnostic checking of fitted models, forecasting, and spectral analysis. Real-world applications for understanding characteristics of time series data in economics, finance, management and industries, and modelling and evaluating forecasts upon which decision-making would depend are emphasized with lab using SAS.
This course covers basic and advanced topics in database management systems. The first part introduces the foundation and practices in database design, including conceptual modelling, SQL, relational algebra and calculus, functional dependency and normalization. The second part covers the implementation of a database system, including indexing, query processing and optimization and transactions. Finally, a few advanced topics such as XML database, trajectory database and big data will be covered.
Data mining is the process of knowledge discovery. Topics taught include data preparation (data cleaning, outlier analysis and transformation) and statistical techniques (regression modelling, multivariate statistics, and statistical inference). Supervised and unsupervised learning techniques including decision tree induction, nearest neighbour categorisation, cluster analysis, association analysis, support vector machines, Bayesian learning and neural networks are touched upon. As well, data mining software and tools, and applications of data mining to complex data types are covered.
Professional consulting project mentored by experienced instructors to solve problems that are of great importance to the sponsoring companies. Practicum is a compulsory course.

Elective Courses

This course focuses on issues, data structures and algorithms on representation, storage, and access to very large digital document collections. Information retrieval models (including Boolean, vector space and probabilistic models), indexing and retrieval techniques, evaluation of information retrieval systems, text and web mining (content, structure and usage mining), web search (search engines, spiders, link analysis, agents), recommender systems and intelligent information retrieval, information extraction and integration are covered in this course.
Stochastic Processes. Gaussian and Markovian Processes. Markov Chains, Markov Decision Processes. Poisson Processes. Continuous-Time Markov Chains. Stochastic Modelling Applications.
Statistical Modelling and Data Analysis includes a cluster of techniques primarily developed in the biomedical sciences, but are also widely used in social sciences like economics, and in engineering. This course focuses on the statistical methods related to the analysis of survival or time to event data, introduces hazard & survival functions, censoring mechanisms, parametric and non-parametric estimation, and comparison of survival curves. The course emphasizes basic concepts and techniques as well as practical applications relevant to business, social sciences and life sciences.
Uncertainty analysis aims to quantify the overall uncertainty within a model, in order to support problem owners in model-based decision-making. Uncertainty and dependence elicitation, dependence modelling, model inference, efficient sampling, screening and sensitivity analysis, and probabilistic inversion are some of the topics covered in this course.
Techniques for measuring and managing the risk of trading and investment positions for positions in equities, credit, interest rates, foreign exchange, commodities, vanilla options, and exotic options; risk sensitivity reports, design of static and dynamic hedges, measure value-at-risk and stress tests; Monte Carlo simulations determining hedge effectiveness; case studies.
Techniques for measuring and managing the risk of trading and investment positions for positions in equities, credit, interest rates, foreign exchange, commodities, vanilla options, and exotic options; risk sensitivity reports, design of static and dynamic hedges, measure value-at-risk and stress tests; Monte Carlo simulations determining hedge effectiveness; case studies.
This course explores management, organizational, and technological issues in terms of the ways data are stored, managed and applied in businesses. Using a simulated business, the database module covers data concepts, structures, conceptual and physical design techniques, data administration and data mining. Theory and practice of database management systems are integrated through hands-on experience with the design and implementation of a business solution. By the end of the course, participants will gain critical IT skills in analysing business processes, improving these processes, developing business applications with an industry standard database and use data for business requirements.
Topics covered include structure of the web, random graph models of networks, link analysis and web search, network dynamics, network effects, power law phenomena, the small-world phenomenon, and diffusion through networks.

Courses for MSc in Financial Technology

Compulsory Courses

This course gives an overview of all the changes, which are happening now in the financial industry and discusses how some of the FinTech processes are being constructed. Each FinTech disruption concept is based on a mathematical of behaviour concept, which is backed by data, analysis and technology. This course goes into detail into some of these processes, so give an understanding as to what is the business model, skill, and future of FinTech in the financial services industry. It will also cover the recent progresses on FinTech development and applications. Although the topics may vary in order to keep pace with the FinTech development, they mainly involve case studies, practical challenges, trends, and opportunities in a FinTech career.
This course discusses the existing and future landscapes of FinTech in Singapore, from incumbent financial firms to FinTech startups. Both traditional and new players are working with policy-makers to define the ecosystem, to encourage innovation, adoption while maintaining regulatory oversight.
This course provides an introduction to the basic principles and theory of finance, terminology and commonly used tools. The course will specifically discuss the financial system, financial statements and financial statement analysis, time value of money, basic valuation of bonds and stocks, capital budgeting processes and techniques, and risk analysis
This course covers the quantitative methods to construct computer-based algorithms for automatic trading and asset management. A number of notable algorithmic trading strategies are discussed. This course also emphasizes the rationale behind the winning strategies, backtesting, automated execution and how to build robots for trading and asset management with specific goals. Moreover, the course provides a hands-on experience of implementing the financial solutions with real market data.
This is an introductory course that attempts to answer the following questions: What is blockchain? What does blockchain aim to achieve? What are the useful properties of blockchains? What are the building blocks of blockchain? What are the design principles underlying the building blocks of blockchain? What are the use cases for blockchains? What is cryptoasset and cryptocurrency? How to evaluate cryptoasset/cryptocurrency? What is Bitcoin? What is the relationship between Bitcoin and blockchain?
Python is an easy to learn higher level scripting language that can be used across many different platforms. As such, it is a common choice to code for FinTech products. This course will train the student for programming in python, with particular focus in FinTech applications.
This course builds upon the Python basics, covered in MH8811 Python Programming, to understand a more comprehensive use of Python with its famous libraries, such as Numpy, Pandas, Matplotlib, Seaborn, and Scikit-learn. This course will train the students for Python programming skills for data analysis.
Probability, conditional probability; random variables, joint distributions, conditional distributions and independence; probability laws, multivariate normal distribution; order statistics; convergence concepts, the law of large numbers, central limit theorem. Estimation, Bayes estimators, interval estimation including confidence intervals, prediction intervals, Bayesian interval estimation; Hypothesis testing, likelihood ratio tests; Bayesian tests; Nonparametric methods, bootstrap.
This course covers essential machine learning techniques in finance. The emphasis is placed on the financial applications and how can they transform the finance industry. This course will cover supervised learning, unsupervised learning, and deep learning. This course will also train the students’ soft skills through the group project on realistic data analysis problem.
Professional consulting project mentored by experienced instructors to solve problems that are of great importance to the sponsoring companies. The internship companies our students once involved with include GIC, Julius Baer, Lumiq, DBS, OCBC, Macquarie Bank, CIMB, Grab, etc.

Prescribed Electives for Artifical Intelligence Specialisation

In this course, students will learn state-of-the-art deep learning methods for Natural language processing (NLP). Through lectures, practical assignments and projects, students will learn the necessary tricks for making their deep learning models work on practical problems. They will learn to implement, and possibly to invent their own deep learning models using available deep learning libraries.
This course covers basic and essential quantitative methods in finance. A number of mathematical and statistical techniques are introduced. This course emphasizes the applications of the quantitative methods in two important areas in finance: asset management and derivative pricing.
This course builds upon the basic blockchain knowledge discussed in the introductory course to understand the most popular blockchain networks: Ethereum. It covers the mechanics of Ethereum and how it aims to become a global computer through its artifact smart contracts. We will learn one of the languages for smart contract: Solidity and use this to code smart contracts. With these tools, we explore the processes and principles of building decentralized apps on the Ethereum platform.

Prescribed Electives for Operations and Compliance

Techniques for measuring and managing the risk of trading and investment positions for positions in equities, credit, interest rates, foreign exchange, commodities, vanilla options, and exotic options; risk sensitivity reports, design of static and dynamic hedges, measure value-at-risk and stress tests; Monte Carlo simulations determining hedge effectiveness; case studies.
Techniques for measuring and managing the risk of trading and investment positions for positions in equities, credit, interest rates, foreign exchange, commodities, vanilla options, and exotic options; risk sensitivity reports, design of static and dynamic hedges, measure value-at-risk and stress tests; Monte Carlo simulations determining hedge effectiveness; case studies.
Financial Crime Compliance and Regulatory Compliance are probably at the top of nearly every financial institution’s risk review process and have become the key strategic imperatives for all board members. This course provides a robust training in Know your customer (KYC) and Customer Due Diligence (CDD) processes by drawing on cutting-edge experience of what world’s leading financial institutions are doing, have done, and must still do. In addition, this course covers the incorporation of the new technologies into the KYC and CDD processes.
Regulations are essential to ensure good governance in the finance industry. FinTech aiming to replace existing financial services will be subject to the same regulations. RegTech, short for regulatory technology, aims to simplify the compliance process, providing large savings in face of rising compliance costs. This course introduces the myriad of financial regulations, both for traditional financial services as well as new regulations introduced to cover novel FinTech services. The potential of RegTech for cost reduction will also be discussed.
Representation, storage, and access to very large digital document collections: issues, data structures and algorithms. Information retrieval models including Boolean, vector space and probabilistic models. Indexing and retrieval techniques. Evaluation of information retrieval systems. Text and Web mining: content, structure and usage mining. Web search: search engines, spiders, link analysis, agents. Recommender systems and intelligent information retrieval. Information extraction and integration.

Unrestricted Electives

These courses introduce a number of optimization methods commonly used in operations research. Nonlinear optimization, discrete optimization, stochastic optimization, queuing theory, inventory theory, dynamic programming, simulation, applications.
These courses introduce a number of optimization methods commonly used in operations research. Nonlinear optimization, discrete optimization, stochastic optimization, queuing theory, inventory theory, dynamic programming, simulation, applications.
Many of the business systems are dynamic systems in which their states change over time. This course introduces time series models and associated methods of data analysis and inference. Topics include auto regressive (AR), moving average (MA), ARMA, and ARIMA processes, stationary and non-stationary processes, seasonal processes, identification of models, estimation of parameters, diagnostic checking of fitted models, forecasting, and spectral analysis. Real-world applications for understanding characteristics of time series data in economics, finance, management and industries, and modelling and evaluating forecasts upon which decision-making would depend are emphasized with lab on using SAS.
This course explores management, organizational, and technological issues in the ways data are stored, managed and applied in businesses. Using a simulated business, the database module covers data concepts, structures, conceptual and physical design techniques, data administration and data mining. Theory and practice of database management systems are integrated through hands-on experience with the design and implementation of a business solution. By the end of the course, participants will gain critical IT skills in analysing business processes, improving these processes, developing business applications with an industry standard database and use data for business requirements.
This course explores cryptographic primitives, and how these are used in building secure protocols. These include symmetric ciphers, cryptographic hashes, one-time pads, public key cryptography and pseudorandom number generators.