Graduate
Courses
MATxxxS refers to courses for the M.Sc.
programme
Course
Description
This
course provides a solid foundation in the Lebsegue integration theory and
basic techniques in analysis. Topics included sigma-algebra of sets, measure
theory, Lebsegue integration theory, convergence theorems, Lp-spaces and
differentiation. Students taking this course are expected to have knowledge
in advanced calculus and elementary analysis.
This
course provides more advanced topics in real analysis. Topics include signed
measures, Hahn decomposition theorem, Lebesgue decomposition theorem, product
measures, Fubini theorem, measure and topology, Riesz representation theorem.
Students taking this course are expected to have knowledge in MAT5011 or
equivalent.
MAT5031 Complex
Analysis I
This
course is intended to provide a solid and advanced training in the basic
techniques and theorem of complex analysis. Topics include: properties
of holomorphic functions, complex integration, conformal mappings, singularities
and residues. Students taking this course are expected to have knowledge
in advanced calculus and elementary analysis.
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MAT5032
Complex Analysis II
This
is a continuation of MAT5031; advanced topics in complex analysis will
be selected from: Schwarz lemma, Riemann mapping theorem, Picard theorem,
Weierstrass theorem and Mittag Leffler theorem, analytic continuation and
introduction to Riemann surfaces. Students taking this course are expected
to have knowledge in advanced calculus and elementary analysis.
MAT5051 Abstract
Algebra I
This
course is intended to provide a solid background knowledge in abstract
algebra. Topics include group theory, Sylow's theorems, structure of finitely
generated abelian groups, rings and ideals, polynomial rings, principal
ideal domain (PID), modules, fields, Galois theory. Students taking this
course are expected to have knowledge in a first course in algebra.
MAT5052 Abstract
Algebra II
This
is a continuation of MAT5051. Topics include fields, cyclic extensions,
separable extensions, integral ring extensions, integral Galois extensions,
Noetherian rings and modules, localization, Hilbert basis theorem, primary
decomposition. Students taking this course are expected to have knowledge
in MAT5051 or equivalent.
MAT5070 Topology
of Manifolds
This
course is an introduction to several basic topological invariants for manifolds.
Major topics are: differentiable manifolds and maps, Sard's Theorem, degree
of maps, fundamental group, covering space, homology group. Students taking
this course are expected to have knowledge in elementary analysis.
Series
of projects in pure or applied mathematics focusing on a central theme.
Prerequisite: permission of the instructor.
This
course is designed for the M.Sc. Degree Programme in Mathematics. The course
is intended to provide an introduction to linear structures and various
concepts of limits/convergence in analysis especially in the context of
Euclidean/Hilbert/Banach spaces as well as the Lebesgue integration spaces.
MAT572S Discrete
Mathematics
This
course is designed for the M.Sc. Degree Programme in Mathematics. The course
is an introduction to discrete mathematics; topics will be chosen from:
set theory, number theory, algebraic structures, graph theory and combinatorics.
MAT573S Complex
Analysis and Its Applications
This
course is designed for the M.Sc. Degree Programme in Mathematics. The course
is intended to provide an introduction to the analysis and applications
of analytic functions on the complex plane. Emphasis will be placed on
the understanding and appreciation of the theory as well as its wide range
of usage. It includes the study of integrals, residues, series expansion,
and conformality of analytic functions; transforms and their use in differential
equations.
MAT574S Algebra
and Geometry
This
course is designed for the M.Sc. Degree Programme in Mathematics. The course
studies polynomial rings of one and several variables, their ideals and
the associated varieties. The Hilbert basis theorem and Groebner bases
algorithms are included.
MAT580S Guided
Studies II
Series
of projects in pure or applied mathematics focusing on a central theme.
This course is a continuation of MAT570S. Prerequisite: permission of the
instructor.
MAT581S Mathematics
for Logistics
This
course is designed for the M.Sc. Degree Programme in Mathematics. The course
provides the basic mathematical tools for logistics. Topics include: Linear
and nonlinear programming, resource allocation problem, shortest route
problem, inventory and production problem, cargo loading problem, equipment
replacement problem, reliability problem, max flow problem, decision tree
analysis, production theory, maintenance and reliability theory.
MAT582S Modeling
and Optimization of Supply Chains
This
course is designed for the M.Sc. Degree Programme in Mathematics. The course
provides an introduction to model-building and optimization methods for
supply chains. Topics include: Modeling techniques; optimization methods
for transportation, storage, handling, and scheduling; inventory models;
demand processes and prediction; review policies for single-item and single-location
problems; multi-item models with constraints; multi-echelon and multi-indenture
models.
MAT583S Financial
Mathematics
This
course is designed for the M.Sc. Degree Programme in Mathematics. The course
is an introductory course on Financial Mathematics. Topics include probability,
hedging, arbitrage, vanilla options, binomial models, the Black-Scholes
formula, exotic options, Monte Carlo methods and binomial methods.
MAT6011/6012
Topics in Mathematics I/II
Usually,
more than one section with various topics selected from advanced pure mathematics
will be offered. The selection of the topics depends on the field of interest
of the instructor. Prerequisites: permission of the instructor.
MAT6021/6022
Topics in Differential Geometry I/II
Various
topics selected from differential geometry. The selection of the topics
depends on the field of interest of the instructor. Prerequisites: permission
of the instructor.
MAT6031/6032
Topics in Algebra I/II
Various
topics selected from algebra. The selection of the topics depends on the
field of interest of the instructor. Prerequisites: permission of the instructor.
MAT6041/6042
Topics in Partial Differential Equations I/II
Various
topics selected from partial differential equations. The selection of the
topics depends on the field of interest of the instructor. Prerequisites:
permission of the instructor.
MAT6051/6052
Topics in Complex Analysis I/II
Various
topics selected from complex analysis (one or several variables). The selection
of the topics depends on the field of interest of the instructor. Prerequisites:
permission of the instructor.
MAT6061/6062
Topics in Number Theory I/II
Various
topics selected from number theory. The selection of the topics depends
on the field of interest of the instructor. Prerequisites: permission of
the instructor.
MAT6071/6072
Topics in Topology I/II
Various
topics selected from topology. The selection of the topics depends on the
field of interest of the instructor. Prerequisites: permission of the instructor.
MAT6081/6082
Topics in Functional Analysis I/II
Various
topics selected from functional analysis. The selection of the topics depends
on the field of interest of the instructor. Prerequisites: permission of
the instructor.
MAT6111/6112
Topics in Applied Mathematics I/II
Usually,
more than one sections with various topics selected from advanced applied
mathematics will be offered. Prerequisites: permission of the instructor.
MAT6121/6122
Topics in Numerical Analysis I/II
Various
topics selected from numerical analysis. The selection of the topics depends
on the field of interest of the instructor. Prerequisites: permission of
the instructor.
MAT6131/6132
Topics in Optimization Theory I/II
Various
topics selected from optimization theory. The selection of the topics depends
on the field of interest of the instructor. Prerequisites: permission of
the instructor.
MAT6141/6142
Topics in Applied Partial Differential Equations I/II
Various
topics selected from applied partial differential equations. The selection
of the topics depends on the field of interest of the instructor. Prerequisites:
permission of the instructor.
MAT7010 Graduate
Seminars
Usually,
more than one section will be offered. The contents of the seminars depend
on the field of interest of the instructor. This course may be taken again
for credit with the instructor's consent. Prerequisites: permission of
the instructor.
This
course is offered to part-time research postgraduate students in Mathematics.
Series of advanced research in pure or applied mathematics focusing on
a central theme. A high degree of originality is expected in this research.
Moreover, this research preferably leads to a research thesis. This course
may be taken again for credit with the instructor's consent.
This
course is offered to full-time research postgraduate students in Mathematics
and part-time Ph.D. students who are in Ph.D. post-candidacy status. Course
description is the same as MAT803R.
This
course is offered to full-time Ph.D. students in Mathematics who are in
the Ph.D. post-candidacy status. Course description is the same as MAT803R.
MAT700T Ph.D.
Thesis Project
(not
for students admitted in 2004-05 and thereafter)
Series
of advanced projects in pure or applied mathematics focusing on a central
theme. A high degree of originality is expected in these projects. Moreover,
these projects preferably lead to a doctoral thesis. This course may be
taken again for credit with instructor's consent