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.

MH7001
Continuous Methods

4 AU

Detailed course information

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.

MH7002
Discrete Methods

4 AU
Available for undergraduates

Detailed course information

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

MH7003
Algebraic Methods

4 AU | Not offered

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

MH7004
Mathematical Statistics

4 AU

Detailed course information

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.

MH7005
Algorithms and Theory of Computing

4 AU

Detailed course information

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.

MH7006/7010
Topics in Discrete Mathematics I/II

4 AU

Special topics in discrete mathematics.

For more details, please refer to the detailed course information here:

MH7007/7011
Topics in Scientific Computation I/II

4 AU

Special topics in scientific computation.

For more details, please refer to the detailed course information here:

MH7008/7012
Topics in Pure Mathematics I/II

4 AU

Special topics in pure mathematics.

For more details, please refer to the detailed course information here:

MH7009/7013
Topics in Probability and Statistics I/II

4 AU

Special topics in probability and statistics.

For more details, please refer to the detailed course information here:

Seminar Courses

Seminars on new research developments in the Mathematical Sciences.

MH7014/7015
Graduate Seminar - Discrete Mathematics I/II

4 AU

Seminar course in discrete mathematics.

For more details, please refer to the detailed course information here:

MH7016/7017
Graduate Seminar - Scientific Computation I/II

4 AU

Seminar course in scientific computing.

For more details, please refer to the detailed course information here:

MH7018/7019
Graduate Seminar - Pure Mathematics I/II

4 AU

Seminar course in pure mathematics.

For more details, please refer to the detailed course information here:

MH7020/7021
Graduate Seminar - Statistics I/II

4 AU

Seminar course in statistics.

For more details, please refer to the detailed course information here:

 

Courses for MSc in Analytics

Compulsory Courses

 

MH6142
Database Systems

3 AU

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.
MH6151
Data Mining

3 AU

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.
MH6201
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.
MH6202
Operations Research II

1.5 AU

This course is a continuation of MH6201 Operations Research I. Topics covered include Monte-Carlo simulation, queuing theory, discrete event simulation, stochastic programming, dynamic programming and optimal control, and inventory theory.
MH6211
Analytics Software I

1.5 AU

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.
MH6212
Analytics Software II

1.5 AU

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.
MH6231
Probability and Statistics

1.5 AU

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.
MH6221
Analytics Workshop I

1.5 AU

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.
MH6222
Analytics Workshop II

1.5 AU

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.
MH6241
Time Series Analysis

1.5 AU

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.

 

Elective Courses

 

MH6191
Practicum

6 AU

Professional consulting project mentored by experienced instructors to solve problems that are of great importance to the sponsoring companies. Practicum is a elective course.
MH6301
Information Retrieval and Analysis

3 AU

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.
MH6311
Stochastic Processes for Data Science

1.5 AU

Stochastic Processes. Gaussian and Markovian Processes. Markov Chains, Markov Decision Processes. Poisson Processes. Continuous-Time Markov Chains. Stochastic Modelling Applications.
MH6321
Statistical Modelling and Data Analysis

1.5 AU

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.
MH6322
Managing Uncertainty and Dependence: From Data To Decisions

1.5 AU

The usefulness of any model depends in part on the accuracy and reliability of its output. Uncertainty analysis aims to identify and quantify the overall precision within a model, in order to support problem owners in model-based decision-making. Understanding the dependence structure between input variables is critical for modelling risks and uncertainty. Efficient sampling and estimates, model selection and validation, kernel density estimation and bandwidth selection, copulas and their applications are some of the topics covered in this course.

MH6331
Financial and Risk Analytics I

1.5 AU

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.
MH6332
Financial and Risk Analytics II

1.5 AU

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.
MH6333
Analytics in Smart City Operations

3 AU

Smart city operations have become pivotal in today's context, reflecting the current trend towards leveraging technology to enhance urban living and address city-wide challenges. Through this course, you will gain insights into applying a range of analytical tools to enhance the efficiency of various smart city operations, such as reinforcing supply chain resilience, optimizing sharing economy dynamics, and streamlining e-commerce operations. This learning experience will involve delving into modeling techniques and problem-solving strategies for these operations, benefiting students aiming to acquire mathematical models for resolving industrial challenges.
MH6341
Data Management and Business Intelligence

1.5 AU

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.
MH6351
Web Analytics

1.5 AU

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.
MH6812
Advanced Natural Language Processing with Deep Learning

3 AU

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 invent their own deep learning models using available deep learning libraries.
MH6813
Blockchain Systems I: Concepts and Principles

1.5 AU

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?
MH6814
Blockchain Systems II: Development and Engineering

1.5 AU

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.

 

Courses for MSc in Financial Technology

Compulsory Courses

 

MH6800
Foundations of Statistical Modelling

1.5 AU

Basic foundation needed to understand the modeling of uncertain phenomena.

MH6801
Introduction to ​FinTech

1.5 AU

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.

MH6802
FinTech Ecosystem and Innovations

1.5 AU

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.

MH6803
Python Programming

1.5 AU

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.
MH6804
Python for Data Analysis

1.5 AU

This course builds upon the Python basics, covered in MH6803 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.
MH6805
Machine Learning in Finance

3 AU

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.

MH6806
Principles of Finance and Risk Management

1.5 AU

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

 

Prescribed Electives Course for Intelligent Process Automation Specialisation

 

MH6301
Information Retrieval and Analysis

3 AU

Information retrieval and analysis provide students with hands on experience to deal with, manage, and organize large amount semi-structured and unstructured information.
MH6812
Advanced Natural Language Processing with Deep Learning

3 AU

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.

MH6813
Blockchain Systems I: Concepts and Principles

1.5 AU

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?

MH6814
Blockchain Systems II: Development and Engineering

1.5 AU

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.

MH6815
Algorithmic Trading and Robo-Advisors

1.5 AU

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.

MH6816
Introduction to Cybersecurity

1.5 AU

This course explores cryptographic primitives, and how these are used in building secure protocols. These include symmetric key cryptography public key encryption, message integrity, authentication, secure email, secure transport (SSL), IP sec, firewall and privacy-preserving techniques such as fully homomorphic encryption and secure multiparty computation
MH6831
Quantitative Methods in Finance

1.5 AU

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.

MH6832
Reinforcement Learning for Finance

1.5 AU

This MSc course aims to introduce the theory of reinforcement learning and its applications in finance. This course will not only provide students with a comprehensive understanding of various dynamic programming (DP) and reinforcement learning (RL) algorithms, but also delve deeply into important financial trading problems. This course blends mathematics, algorithms, theory, and practice to give students a thorough understanding of this promising field.

This course is geared towards a wide-ranging audience of students from diverse academic backgrounds, including mathematics, computer science, engineering, physics, and economics, who are keenly interested in implementing reinforcement learning techniques in the field of finance. This course offers a new way to make smarter and more efficient decisions using algorithms that handle uncertainty and complexity. It also helps you understand how to tackle financial problems with DP/RL algorithms. Proficiency in these techniques is of utmost importance for finance industry professionals, particularly in the era of artificial intelligence.

 

Prescribed Elective Courses for Digital Services Specialisation

 

MH6331
Financial and Risk Analytics I

1.5 AU

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.
MH6332
Financial and Risk Analytics II

1.5 AU

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.
MH6821
Anti-Financial Crime and Compliance

1.5 AU

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.
MH6822
Regulatory Technology

1.5 AU

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.
MH6823
Financial Inclusion and Decentralized Finance

1.5 AU

This course will deep dive into the problem of financial inclusion and use of Tech as a Force of good. You will learn about how financial markets develop and how legacy systems operate but how they totally exclude the last mile. We will help you to build a solid understanding regulation, infrastructure, technology and various tools used to enhance financial inclusion especially amidst Covid-19. Explore what are the challenges towards inclusive growth and how developing markets mitigate them using Blockchain. By taking this course you will be able implement FinTech tools in your firm, propose risk averse policies and create strategies for financial development/inclusion.
MH6824
Fundamentals of FinTech Entrepreneurship

1.5 AU

This course illustrates the essential knowledge and concepts of entrepreneurship and entrepreneurial process. A deliberate emphasis on the FinTech industry context and relevant business features is ensured. Students get to appreciate and evaluate different types of entrepreneurial opportunities, challenges, risks, and uncertainty. They learn not only what is entrepreneurial mindset, but more importantly, how to develop such a mindset and attitudes to seize entrepreneurial opportunities. Moreover, they start to see that entrepreneurial opportunities are not merely found, but more than often, they should and could be shaped and created. With this acquired knowledge, the participants are motivated to learn the essential skills of business model analysis and innovation, customer development, entrepreneurial leadership, and lean startup. Practical FinTech case study and real project analysis form integrate parts of the whole teaching and learning process to ensure the relevance of the knowledge and skills in this FinTech subject domain.
MH6825
FinTech Entrepreneurial Practice

1.5 AU

This course adopts a problem-based learning approach whereby the participants need to address an entrepreneurship challenge involving real-life FinTech operation, ideation, or startup. Although there is no prerequisite, it is preferred that the participants have taken the “Fundamentals of FinTech Entrepreneurship” module prior to this course.

In this course, the participants form teams of different expertise to collaborate, adapt, learn, and contribute actively while making progress along the way. Each member is expected to apply the entrepreneurial knowledge and skills to make sense of the identified or assigned FinTech business challenge and develop a viable solution, which needs to be translated into a minimum viable product (MVP) or prototype developed by each team. The participants are highly motivated and facilitated to develop relevant core soft skills (collaboration, problem-solving, decision-making, networking, negotiation, and presentation) with key stakeholders including clients, users, partners, advisors, and inventors in the FinTech ecosystem.

The level of entrepreneurial mindset, skills, and attitudes will be reflected and demonstrated through the actions taken by participants and by their final presentation of the MVPs or solution prototypes.

MH6826
Investment and Portfolio Management

1.5 AU

Advancements of Big Data, artificial intelligence, and machine learning to evaluate investment opportunities, optimise portfolios, and mitigate risks are affecting not only quantitative asset managers but also fundamental asset managers who make use of these tools and technologies to engage in hybrid forms of investment decision making. This course provides students with a critical understanding of techniques used for investments and portfolio management. Students will be able to implement trading strategies and portfolio construction methods in a wide range of assets.
MH6827
Financial Data Management and Business Intelligence

1.5 AU

This course aims to get students familiar with concepts, technologies, and best practices for data management and business intelligence widely used in financial industry. It provides comprehensive coverage of technical topics including relational data model, SQL data language, dimensional data model, and related tools. Students will also learn why business intelligence is critical for modern financial business, how to manage data using relational database, and hands-on experience of creating dashboard for business intelligence initiatives.
MH6833
Microeconomics and Macroeconomics

1.5 AU

Introducing Microeconomics and Macroeconomics to a fintech course is essential as it provides a foundational understanding of economic principles that impact financial technologies. Microeconomics offers insights into market dynamics, consumer behaviour, and cost structures, enabling fintech professionals to develop user-centric solutions and efficient pricing strategies.

Macroeconomics, on the other hand, equips them with knowledge about economic indicators, monetary and fiscal policies, and overall economic trends, aiding in better financial decision-making and investment strategies. Together, these disciplines ensure a well-rounded comprehension of the economic environment in which fintech operates, fostering more informed and strategic business practices.

 

Unrestricted Elective Courses

 

MH6838
Practicum

3 AU

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.

 

Courses for MSc in Modelling and Simulation

Compulsory Courses

 

MH6501
Fundamentals of Modelling and Simulation

3 AU

This  course  provides  a  comprehensive  overview  of  modelling  and simulation principles and techniques, divided into four key sections. The  first  section  establishes  a  foundational  framework,  introducing primary  continuous  and  discrete  approaches  in  an  accessible manner. The second section offers a rigorous exploration of systems theory,  covering  models  as  system  specifications,  formalism integration,  and  simulators  in  sequential,  parallel,  and  distributed forms. The third section emphasizes the fundamental role of systems morphisms,  focusing  on  perfect  and  approximate  morphisms  for model  abstraction  and  system  representation.  Finally,  the  course delves  into  DEVS-based  modelling  and  simulation,  exploring  its application  in  high-tech  systems  design,  integration  with  other formalisms, and support for collaborative modelling and simulation.
MH6502
Numerical Linear Algebra and Differential Equations

3 AU

This  course  integrates  the  theoretical  foundations  and  practical applications of numerical linear algebra and differential equations. It begins  with  an  in-depth  study  of  linear  algebra  methods,  covering matrix  algebra,  linear  systems,  spectral  theory,  vector  and  matrix norms, and both direct and iterative numerical methods. The second part focuses on numerical techniques for solving ordinary and partial differential  equations,  including  finite  difference,  finite  element,  and spectral  methods.  Emphasis  is  placed  on  discretization  schemes, stability,  convergence,  and  error  estimation.  Various  types  of differential equations, including elliptic, parabolic, and hyperbolic, are explored  with  applications  in  modeling  and  simulation  of  physical phenomena.
MH6503
Stochastic Modelling and Simulation

3 AU

This course provides a comprehensive overview of probability theory, stochastic  processes,  and  their  application  in  modelling  and simulation. Designed for graduate students, it begins by reinforcing key concepts in probability theory and statistical methods, including probability  distributions,  statistical  inference,  hypothesis  testing, regression analysis, and data visualization. Students then  focus on various stochastic models, such as Markov chains, queuing systems, random walks, and stochastic differential equations, with a focus on understanding  the  probabilistic  foundations  and  their  relevance  in real-world  systems.  Computational  tools  like  Monte  Carlo  methods and  simulation  software  are  used  to  analyse  and  simulate  these processes. The course spans applications in fields such as finance, engineering, biology, and telecommunications. By the end, students will be equipped to model, analyse, and simulate complex systems with  stochastic  components,  enabling  them  to  make  informed decisions in uncertain environments and excel in advanced research and professional work.
MH6504
Mathematical Programming and Optimisation

3 AU

This course is focused on mathematical programming techniques and optimisation  methods  used  to  solve  real-world  problems.  Topics covered include linear programming, integer programming, nonlinear programming,  convex  optimisation,  and  combinatorial  optimisation. Students will learn about fundamental optimisation algorithms such as simplex method, branch and bound, gradient descent, and dynamic programming.  The  course  emphasizes  both  theoretical  foundations and practical applications, with hands-on experience in modeling and solving  optimisation  problems  using  software  tools  like  MATLAB, Python,  or  specialised  optimisation  solvers.  Through  lectures, assignments, and projects, students will gain the skills necessary to formulate  and  solve  optimisation  problems,  analyse  solution optimality, and interpret results in diverse fields. 
MH6505
Machine Learning and Artificial Intelligence: Principles and Techniques

3 AU

This course provides students with a comprehensive introduction to the core principles and techniques of machine learning and artificial intelligence. The course covers essential topics such as supervised and unsupervised learning, classification and regression algorithms, model  evaluation  and  validation,  and  feature  selection  and engineering. Students will gain a deep understanding of how machine learning algorithms work, how to apply them to real-world problems, and  how  to  critically  evaluate  their  performance.  This  course  also delves  into  various  artificial  intelligence  (AI)  techniques  and  their applications,  including  problem-solving  methods,  knowledge representation,  natural  language  processing,  computer  vision,  and robotics. 

 

Prescribed/Unrestricted Elective Courses

 

MH6541
Discrete Mathematics, Algorithms and Applications

1.5 AU

This  graduate-level  course  explores  discrete  mathematics  and algorithms with a focus on their applications in various fields. Topics include  foundational  concepts  in  logic,  set  theory,  graph  theory, combinatorics, and discrete probability. The course covers algorithmic techniques  such  as  sorting,  searching,  dynamic  programming,  and approximation  algorithms.  Applications  span  combinatorial optimization,  network  analysis,  and  computational  geometry. Students  will  gain  a  comprehensive  understanding  of  theoretical principles  and  practical  methods  for  solving  complex  problems. Learning  outcomes  include  mastering  core  concepts  in  discrete mathematics  and  their  algorithmic  applications,  designing  and analysing  algorithms  for  solving  practical  problems,  and  applying discrete mathematical techniques to real-world challenges in various domains.  
MH6542
Programming Languages and Software Development

1.5 AU

This  graduate-level  course  focuses  on  equipping  students  with proficiency  in  Python  and  C  programming  languages  essential  for tackling  coding  tasks  in  their  future  careers.  Students  learn  key concepts,  syntax,  and  best  practices  for  writing  efficient  and maintainable code, along with software development practices such as design patterns, version control, and testing. Emphasis is placed on writing robust  code and understanding compiler design, runtime systems,  and  software  engineering  principles.  Through  hands-on coding  assignments  and  projects,  students  will  gain  practical experience in solving realistic problems using Python and C.  
MH6543
High-Performance Computing and Simulation: MPI, OpenMP and CUDA

1.5 AU

The course provides an introduction to modern computing platforms, focusing on top supercomputers and accelerators. Students delve into parallel  architectures,  performance  metrics,  programming  models, and  software  development  challenges.  Through  case  studies  of scientific and engineering simulations, students gain insights into real-world  applications  of  parallel  computing.  Hands-on  experience  is provided  through  programming  exercises  involving  multicore processors,  graphics  processing  units  (GPUs),  and  parallel computers.  Key  topics  include  multithreaded  programmes,  GPU computing,  computer  cluster  programming,  C++  threads,  OpenMP, CUDA, and MPI. By the end of the course, students acquire a deep understanding  of  high-performance  computing  principles  and techniques.
MH6544
Bayesian Modelling and Statistical Learning

1.5 AU

This  course  provides  a  comprehensive  introduction  to  Bayesian modelling and statistical learning.  Students begin by mastering key Bayesian concepts, including prior distributions, likelihood functions, and  posterior  distributions,  learning  to  build  and  interpret  Bayesian models  for  various  data  types.  The  course  then  transitions  to statistical  learning,  covering  topics  such  as  supervised  and unsupervised learning, linear regression, classification methods, and advanced  techniques  like  neural  networks  and  ensemble  methods. Practical  exercises  and  case  studies  are  integrated  throughout, enabling students to apply these methods to real-world datasets. By the end of the course, students will be equipped to tackle complex problems  in  machine  learning,  data  science,  and  decision-making under  uncertainty,  with  a  strong  foundation  in  both  Bayesian  and statistical learning approaches.
MH6545
Computational Imaging: Methods and Applications

1.5 AU

This  course  provides  a  comprehensive  exploration  of  the mathematical  foundations  underlying  various  imaging  techniques used in medical, seismic, non-destructive testing, and other industrial applications. Students will study key mathematical concepts such as Fourier  transforms,  wavelets,  inverse  problems,  and  optimisation methods, which are crucial for image reconstruction and analysis. In addition to traditional techniques, the course incorporates advanced topics  in  neural  networks,  focusing  on  their  application  to  imaging. Students will explore how neural networks are used to enhance image reconstruction,  handle  large  datasets,  and  improve  image  quality across different modalities. Through theoretical lectures and practical exercises,  students  will  develop  the  skills  to  model,  analyse,  and implement  both  conventional  and  neural  network-based  imaging algorithms,  enhancing  their  ability  to  tackle  complex  imaging challenges across various fields.
MH6546
Time Series Analysis and Signal Processing

1.5 AU

This course offers an integrated approach to time series analysis and digital signal processing, appealing to students across diverse fields like  engineering,  healthcare,  finance,  and  data  science.  It  provides both theoretical foundations and practical applications, covering key topics  such  as  time  series  modelling,  stationarity,  autocorrelation, ARIMA models, and forecasting methods. Additionally, students will explore essential signal processing techniques, including the discrete Fourier  transform,  wavelet  transform,  and  spectral  estimation methods. By the end, students will gain skills applicable not only in engineering  and  healthcare  domains  but  also  in  finance,  for  tasks such as stock price forecasting and risk analysis, and in data science for analysing complex datasets and developing predictive models.


Relevant  courses  at  NTU:  AI6123  Time  Series  Analysis  offered  by MSc in Signal Processing and Machine Learning

MH6547
Simulation of Physical, Biological, and Chemical Systems

3 AU

This  course  provides  a  comprehensive  foundation  in  physical, biological,  and  chemical  sciences,  along  with  their  practical applications across various sectors. The physical foundations cover computational  mechanics,  thermodynamics  and  heat  transfer,  and electromagnetics and wave propagation. In the biological domain, the course  delves  into  computational  biology  for  modelling  biological systems,  systems  biology  and  bioinformatics,  and  applications  in genomics,  proteomics,  and  metabolic  networks. The  chemical foundations  include  computational  chemistry  techniques  such  as molecular  dynamics and  quantum  chemistry,  chemical  kinetics and reaction dynamics, and material science with molecular simulations. Additionally,  the  course  addresses  interdisciplinary  applications  in environmental  modelling  and  simulations,  biomedical  engineering, and chemical engineering processes and simulations.
MH6548
Modelling and Simulation in Materials Science and Engineering

3 AU

This course explores key modelling and simulation techniques used to  predict  material  behaviour  at  various  scales.  Students  will  learn computational  methods  like  molecular  dynamics,  finite  element analysis, and phase-field modelling to study the mechanical, thermal, and  electrical  properties  of  materials.  Applications  include nanomaterials, polymers, metals, and ceramics. students will develop the skills to perform simulations, interpret results, and apply findings to  real-world  engineering  problems.  By  the  end  of  the  course, students will be equipped with the knowledge to use computational tools effectively in materials research and development.

Relevant courses at NTU: MS7240 Modelling of Materials offered by MSc in Materials Science and Engineering

MH6549
Modelling and Simulation in Medicine and Healthcare

3 AU

This course focuses on computational techniques to solve challenges in medicine and healthcare. Students will learn methods to simulate biological systems, including tumour growth, cardiovascular function, and  disease  mechanisms.  The  course  covers  systems  biology  and bioinformatics,  with  applications  in  genomics,  proteomics,  and metabolic  networks.  It  also  includes  modeling  and  simulation  for biomedical  engineering,  such  as  medical  devices,  physiological processes, and imaging. Techniques like finite element analysis and machine  learning  for  healthcare  analytics  are  introduced.  Through practical exercises and projects, students will gain skills to apply these models to real-world medical challenges, preparing them to advance medical research and healthcare innovation.

NTU  Relevant  courses:  MD7103  Biomedical  Imaging and MD7113 Computational Neuroscience by Lee Kong Chian School of Medicine.

MH6550
Modelling and Simulation in Economics and Finance

3 AU

This  course  explores  modelling  and  simulation  techniques  for analysing  economic  and  financial  systems.  Key  topics  include stochastic  processes,  econometric  modelling,  and  financial  risk management.  Students  will  learn  to  apply  numerical  methods  for simulating economic behaviours, asset pricing models, and portfolio optimisation.  The  course  covers  Monte  Carlo  simulations,  agent-based  modelling,  and  the  use  of  machine  learning  algorithms  for predictive  analytics  in  finance.  Emphasis  is  placed  on  practical applications,  including  market  risk  assessment,  economic forecasting, and financial decision-making. 

NTU Relevant courses: MH6831 Quantitative Methods in Finance by MSc in Financial Technology,  AE6201 Macroeconometric Modeling and Forecasting by MSc in Applied Economics and Numerical Methods for Financial Instrument Pricing by MSc in Financial Engineering. 

MH6551
Modelling and Simulation in Data Science and Computing Engineering

1.5 AU

This  course  provides  an  in-depth  exploration  of  modelling  and simulation  techniques  essential  for  data  science  applications. Students  will  learn  advanced  methodologies  for  constructing  and analysing predictive models, including statistical modelling, machine learning  algorithms,  and  simulation  techniques.  The  course  covers key areas such as data preprocessing, feature selection, and model validation, with a focus on applications in big data, anomaly detection, and  optimisation.  Students  will  gain  hands-on  experience  with simulation  tools  and  software,  learning  to simulate  complex  data scenarios  and  validate  model  performance.  Case  studies  and practical  projects  will  enable  students  to  apply  these  techniques  to real-world data science problems, preparing them to solve challenges in various domains.
MH6591
Graduate Research Practicum

3 AU

The  “Graduate  Research  practicum”  is  a  key  component  of  the programme supervised by a faculty advisor, with weekly consultations lasting  at  least  4  hours  per  week.  These  research  projects  are designed  to  immerse  students  in  advanced  concepts  and  skills relevant  to modelling and  simulation.  Projects  can  be  conducted  in university laboratories, local research institutes, or approved industrial sites for supervised industrial projects. The assessment will focus on research performance evaluated by the project supervisor, as well as project  report  and  oral  presentation  assessed  by  appointed examiners. Students are required to select either MH6591 or MH6592 or may choose not to enrol in either course. 
MH6592
Graduate Professional Internship Practicum

3 AU

This is a 10-week internship training at local industries with project scopes relevant to modelling and simulation. Internship projects will be primarily arranged by the School’s programme management team, although self-sourced projects are permitted pending approval from the academic Programme Director. The internship performance will be jointly evaluated by the organization supervisor and an appointed faculty  supervisor.  Assessment  criteria  include  work  performance (50%,  evaluated  by  the  internship  supervisor),  project  report  (25%, evaluated  by  the  faculty  supervisor),  and  oral  presentation  (25%, evaluated  by  the  faculty  supervisor).  The  faculty  supervisor  will conduct at least one site visit to discuss the progress of the student's work  with  the  organization  supervisor  and  to  moderate  the assessment  of  work  performance.  The  outcome  of  the  internship assessment  will  be  graded.  Students  are  required  to  select  either MH6591 or MH6592 or may choose not to enrol in either course.