Graduate Courses in Mathematics
- PhD and MSc by Research
- MSc in Analytics
- MSc in Financial Technology
Courses for PhD and MSc by Research
Advanced courses in mathematics, covering core topics tested in the PhD Qualifying Examinations.
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.
Enumeration; graph and network algorithms; finite fields and applications; boolean algebras; polyhedra and linear programming; algorithmic complexity.
Groups, rings, and fields; basic techniques of group theory; Galois theory.
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.
Turing machines; time complexity and space complexity; algorithm design and analysis (greedy, divide and conquer, dynamic programming); graph algorithms; network flow.
Specialized courses offered based on student and lecturer interest. The precise course contents are subject to variation.
Seminars on new research developments in the Mathematical Sciences.
Seminar course in scientific computing.
Courses for MSc in Analytics
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.
Courses for MSc in Financial Technology
Basic foundation needed to understand the modeling of uncertain phenomena.
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 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.
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
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 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?
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.
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.
Prescribed Elective Courses for Digital Services Specialisation
Unrestricted Elective Courses
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.
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 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.