Mathematical, Computational and Statistical Sciences (MCS)

The Mathematical, Computational and Statistical Sciences (MCS) major offers students the opportunity to pursue traditional curricula as well as curricula that cut across disciplinary boundaries.

Requirements for a Major in MCS

Class of 2021 onwards

The MCS major requires students to complete 54 Units including a capstone project that is worth 10 Units. Students will take three core courses, four courses in one of the three focus areas, Mathematics, Computer Science, or Data Science, and at least 9 Units of electives. At least 4 Units need to be at the 4000-level in addition to the 10 Units capstone.

Core Courses

The required core courses are:

• YSC1212 Introduction to Computer Science

• YSC2209 Proof

• YSC2239 Introduction to Data Science

Focus Areas

Students need to complete four courses in one of the focus areas. Each focus area has three compulsory course and two specialist courses from which one should be completed.

Focus Area Mathematics

Class of 2021 to Class of 2023:
The compulsory courses for Mathematics are YSC3206 Introduction to Real Analysis, YSC2232 Linear Algebra, and YSC3240 Foundations of Applied Mathematics. Additionally, one of the specialist courses YSC4220 Ordinary and Partial Differential Equations or YSC3237 Introduction to Modern Algebra, is required.

Class of 2024 to Class of 2025:
The compulsory courses for Mathematics are YSC3206 Introduction to Real Analysis, YSC2232 Linear Algebra, and YSC3237 Introduction to Modern Algebra. Additionally, one of the specialist courses YSC4220 Ordinary and Partial Differential Equations or YSC4206 Mathematical Signal Processing is required.

Focus Area Computer Science

The compulsory courses for Computer Science are YSC2229 Introductory Data Structures and Algorithms, YSC3232 Software Engineering, and either (select one):

• YSC4230 Programming Language Design and Implementation

• YSC3236 Functional Programming and Proving

• YSC4231 Parallel, Concurrent and Distributed Programming

• Additionally, one of the specialist courses YSC3236 Functional Programming and Proving or YSC2244 Programming for Data Science is required.

Focus Area Data Science

The compulsory courses for Data Science are YSC2243 Probability, YSC3249 Statistical Inference, and YSC2232 Linear Algebra. Additionally, one of the specialist courses YSC4216 Machine Learning or YSC2244 Programming for Data Science is required.

Electives

At least 9 Units of elective courses are required. These courses can be selected from MCS course offerings and approved NUS courses. Recent MCS course offerings are available here. At least 4 Units must be at the 4000 level unless already taken as a focus course. 2 Unit MCS courses do not count towards the major.

Capstone

The capstone experience offers each student an opportunity to learn a subject in great depth, to apply and reflect on previous coursework, and to reach out to other disciplines. It also serves to develop further skills in technical exposition, both written and spoken.

Graduating students will enjoy the self-confidence and initiative that comes from having successfully conducted an independent research inquiry.

Sample topics include: topological field theory and physics; robotics; number theory and cryptography; survival statistics; social network analysis; computer graphics; smartphones as a distributed computing platform; neuroimaging. In addition to the project, the capstone includes a weekly seminar. Combined, the capstone bears 10 Units.

Requirements for a Minor in MCS

An MCS minor offers students the opportunity to engage with advanced topics in mathematics, computation, and statistics. This can be an excellent supplement for students pursuing a major in quantitative social sciences, natural science, philosophy, etc. We encourage students to pursue an MCS minor to enhance their major, to explore their curiosity, and to develop skills for future employment.

Class of 2021 onwards

To minor in MCS, a student must complete the 3 core courses:

• YSC1212 Introduction to Computer Science

• YSC2209 Proof

• YSC2239 Introduction to Data Science

Plus 10 Units of elective MCS courses

Students can approach MCS faculty if they need assistance to design a suitable programme of study for the minor.

Core Courses

YSC1212 Introduction to Computer Science

Computer science has improved human life dramatically in the last 50 years. This course explains how computational tasks are solved and computers are programmed. You will learn how to be a more careful and methodical thinker. Moreover, millions of people around the world enjoy programming and you can too!

YSC2209 Proof

Mathematicians and computer scientists write proofs: convincing arguments, combining clear and concise language, computations and symbolic manipulation, illustrations and tables.

By reading, writing, and revising proofs, students will be prepared for modern topics in analysis, algebra, geometry, and theoretical computer science. Students will write proofs that utilise direct deduction and proof by contradiction, complicated logical structures with cases, and mathematical induction.

Students will acquire a thorough knowledge of naïve set theory, including sets and functions, equivalence relations and classes, cardinal and ordinal arithmetic. Topics in discrete mathematics will include the combinatorics of finite structures such as graphs and trees.

YSC2239 Introduction to Data Science

Data science has revolutionised modern life and technology using a broad spectrum of methods from mathematics, statistics and computer science.

Intrinsically, mathematical and statistical techniques are married to modern computing power to provide accurate and complex tools to capture real life phenomena. In this course we develop an introduction to methods used in data science, at a level requiring basic mathematics and statistics.

Sample Electives

This is a small subset of electives offered by the MCS major.

YSC2232 Linear Algebra

A first course in linear algebra of finite-dimensional real and complex vector spaces, balancing theoretical and computational material. The course covers vectors and linear transformations, building geometric intuition, algebraic aptitude, and computational proficiency.

Topics include spaces and subspaces, linear maps, linear independence and spanning, basis, and representations by coordinates and matrices. The theory of linear operators is developed, including eigenvalues and eigenvectors, self-adjoint operators, the spectral theorem, and the singular value decomposition.

Some topics from numerical linear algebra, especially implementation of algorithms and assessment of their efficiency are included. Applications to statistics, economics, engineering, and science are presented.

YSC2244 Programming for Data Science

With the growing influence of data science, the Statistics and Mathematics domains now require specific skills in programming, using domain-specific systems and libraries.

This course introduces common tools for data science programming. This includes a high-level language (i.e. Python), several statistics/AI libraries (i.e. numpy, sklearn), and database systems (i.e. SQL). In addition, we will create awareness of best practices in programming such as control versioning, testing, and continuous integration.

YSC2252 Multivariable Calculus

Calculus is the study of rates of changes and provides a framework for modelling systems and to find the effect of changing conditions of the systems being investigated. However, some of the most interesting systems cannot be modelled using just one variable.

The aim of this course is to extend the knowledge of calculus (YSC1216) to more complex systems, studying the rate of change, volumes and optimisation for functions in more than one variable. This course gives the needed tools to apply knowledge of advanced calculus in Physical Sciences, Life Science, Economics and Statistics.

YSC3232 Software Engineering

This course will teach principles of software engineering and object-oriented programming as well as User Interfaces (UI) and Android. In this course, students will first learn about the Java language and the object paradigm (field encapsulation, object, polymorphism), as well as useful tools for software development (e.g, version control, debugging).

The next part of the course will focus on how to write code properly and work on larger scale projects using MVC framework. Finally, the last part of the course will cover UI in Java, Threads, synchronisation, and Android Programming.

YSC4216 Machine Learning

Machine learning is a collection of techniques where computers can learn from data without being explicitly programmed. For instance, when we train a programme using human-face image data, it should be able to locate faces in an image; yet, if we train the same programme using flower data, it should be able to locate flowers in an image, without explicitly changing the programme itself.

This course particularly will focus on statistical machine learning, which relies heavily on probabilistic and statistical analysis. Programming skill in python is compulsory.

YSC4231 Parallel, Concurrent and Distributed Programming

This course will cover main concepts and programming paradigms for developing parallel concurrent and distributed systems, which is vital for implementing high-performance applications in areas such as machine learning, cloud computing, and databases—areas with an extremely high demand for well-trained software engineers.

The course contents will include both practical (about 70%) as well as a theoretical component, giving the students the basis to design concurrent algorithms, reason about their correctness, as well as to be able to design experiments for estimating the performance of the designed algorithms.