Singapore

The study of ordinary differential equations (ODEs) has been a centerpiece in both pure and applied mathematics, such as in mathematical analysis, dynamical systems and mathematical modeling. The aim of this course is to give a thorough treatment on the fundamental theory of ODEs and the methods of solving ODEs. Major topics: Review of first order equations, Basic theory of linear differential equations, Variation of parameters, Principle of superposition, Wronskian, Abel's formula, Adjoint and self-adjoint equations, Lagrange and Green's identities, Sturm's separation and comparison theorems, Linear differential systems, Series solutions of second order linear differential equations, Method of Frobenius, Initial value problems, Lipschitz condition, Picard's method of successive approximations, Existence and uniqueness of solution, Gronwall’s inequality, Continuous dependence on initial value.

This course is a continuation of MA2001 Linear Algebra I intended for second year students. The student will learn more advanced topics and concepts in linear algebra. A key difference from MA2001 is that there is a greater emphasis on conceptual understanding and proof techniques than on computations. Major topics: Matrices over a field. Determinant. Vector spaces. Subspaces. Linear independence. Basis and dimension. Linear transformations. Range and kernel. Isomorphism. Coordinates. Representation of linear transformations by matrices. Change of basis. Eigenvalues and eigenvectors. Diagonalizable linear operators. Cayley-Hamilton Theorem. Minimal polynomial. Jordan canonical form. Inner product spaces. Cauchy-Schwartz inequality. Orthonormal basis. Gram-Schmidt Process. Orthogonal complement. Orthogonal projections. Best approximation. The adjoint of a linear operator. Normal and self-adjoint operators. Orthogonal and unitary operators.

The objective of this course is to familiarize students with the fundamentals of computing devices. Through this course students will understand the basics of data representation, and how the various parts of a computer work, separately and with each other. This allows students to understand the issues in computing devices, and how these issues affect the implementation of solutions. Topics covered include C programming language, data representation systems, combinational circuits, sequential circuits, assembly language, processor datapath and control, pipelining and cache.

This course introduces mathematical tools required in the study of computer science. Topics include: (1) Logic and proof techniques: propositions, conditionals, quantifications; (2) Relations and Functions: Equivalence relations and partitions, partially ordered sets, well-ordering principle, function equality, Boolean/identity/inverse functions, Bijection; (3) Mathematical formulation of data models (linear model, trees, graphs); (4) Counting and Combinatorics: Pigeonhole Principle, Inclusion-Exclusion Principle, Number of relations on a set, number of injections from one finite set to another, Diagonalization proof: An infinite countable set has an uncountable power set; Algorithmic proof: An infinite set has a countably infinite subset, subsets of countable sets are countable.

This course provides students with an understanding of the basic laws and concepts of thermodynamics for applying to analyze chemical engineering problems. The basic definition, applications and limitations of chemical engineering thermodynamics are first introduced followed by a review of basic laws, properties and concepts of thermodynamics. The application of basic concepts of energy conversion is extended to refrigeration and liquefaction processes. The development and discussion of thermodynamic property relations for systems of constant and variable compositions are covered in detail. The developed property relationships together with the basic laws are then applied to the analysis of the various equilibrium.

This course provides students with basic concepts of material and energy balances in chemical engineering processes. It also gives a comprehensive introduction to different analytical and problem solving methods. In particular, steady state material and energy balances, including recycles, phase changes and reactions, form the core structure of the course. Other topics include simultaneous material and energy balances, unsteady state balances and the introduction and application of Matlab in solving balance problems. All fundamental concepts are amply illustrated with relevant process examples. This course is targeted at level one or two engineering and science students.

The first part covers: classification of fluids and their properties, fluid statics, dimensional analysis and model theory, the integral and differential forms of the fundamental conservation equations, boundary layer theory, flows with pressure gradient, viscous flows, flows in closed conduits, and fluid machinery. This second part covers: three modes of heat transfer (conduction, convection and radiation), both steady and unsteady states for heat conduction, convective heat transfer and heat transfer with phase change, radiative heat transfer, heat exchangers and their design, analogies between heat and momentum transfer.

This module offers students a way to approach theatre and performance through the matrix of gender. Students will be exposed to selected discourses on feminism, masculinity, transgenderism. This module will focus on the issues of language, body, theatricality and performativity and explore how the gender discourses can inform the students’ engagement with these issues, particularly in relation to aesthetics and embodiment. Incorporating a critical, examination of selected play-texts, this module will lead students to develop a project where they can either construct a creative response to a play or a devised reflection on their process of researching gender in theatre.

This module provides a study of how the literary and performance traditions associated with Shakespeare's work are mobilized and transformed by the visual cultures of contemporary cinema. Through the intersections between the mediums of the dramatic text, theatre and film, the course examines central issues that shape Shakespeare's currency and circulation in the cinema: the values attached to authenticity and performance traditions, the Shakespearean actor, the appropriation and parody of the "universality" of Shakespeare, and the transformation of the meaningfulness of his plays through visuality and spectacle.

This module focuses on the classical theatre forms of India, China, and Japan. Each tradition is examined within its socio-cultural context. Textual analysis of classical scripts from Sanskrit drama, Chinese opera, and Japanese theatre will also be conducted. Students' learning experience is often constructed in stimulated theatre settings to promote their creativity and to provide them with a working knowledge of performing arts. Students interested in theatre studies, South Asian studies, Chinese studies, and Japanese studies may particularly benefit from this module.