MSI Second Year Courses
Second Year Courses
The coordinator of Second Year Mathematics courses is Prof D.
Wickramasinghe, room JD G1.
Outlines of First Semester Second Year Courses
This course is designed to show some of the interdependence of
mathematics and computing, and is designed for students in both
computer science and mathematics. Topics covered include Foundations,
Grammars and Automata, Graph Theory, Game Theory. Of relevance to (but
certainly not only) IT students
This course demonstrates the modelling process in the context
of differential equations and case studies from a number of areas such
as population dynamics, economics, electric circuits, mechanical
systems, fluid flow, physics and astrophysics. Analytic methods from
the elementary theory of differential equations and calculus will be
provided to allow for the analysis of the various models being
investigated. Numerical approximation methods will also be studied and
applied to real life problems, such as the orbits of stars in the
Galaxy.
The first course is an analysis of differential equations and
examples in areas such as population dynamics, economics, electric
circuits, mechanical systems, fluid flow, physics and astrophysics.
Laplace transform and numerical methods are also treated. It is
recommended (but not only!) for Engineering Students
The second course provides a more in depth exposition of the
theory of differential equations, Laplace transforms, and additionally
vector calculus. Applications will be related to problems mainly from
the Physical Sciences. It is recommended (but not only!) for Physics
and Maths students. MATH2405 is an HPC.
An introduction to modern analysis. The philosophy of the
course is that abstract mathematical notions play a fundamental role in
mathematics itself and in applications to areas such as physics,
economics and engineering. A main stream course for students interested
in fundamental mathematics and applications. This is an HPC.
The course concerns applications of mathematical, statistical
and computational methods to problems in molecular biology. Relevant
biological material will be explained as the course progresses.
Outlines of Second Semester Second Year Courses
In physics, economics and engineering, we frequently encounter
quantities (for example energy) that depend on many variables
(such as
position, velocity, temperature). Usually this dependency is expressed
through a partial differential equation, and solving these
equations is
important for understanding these complex relationships.
In
this course we will study first and second order partial differential
equations. We will develop the requisite vector calculus
and multivariable calculus along the way. The solution methods
studied
in this course will include the method of
characteristics, separation
of variables, Fourier series and Fourier transforms.
This
course will be useful for majors in economics, mathematical finance,
engineering and physics. We will illustrate the theory
with examples
from these disciplines.
Many
physical processes such as vibrating strings, diffusion of heat and
fluid flows are well modeled by partial differential equations and/or
integral equations. This course provides an introduction to methods for
solving and analysing standard partial differential equations and
integral equations, including an introduction to complex analytic
techniques.
This
course will be useful for majors in economics, mathematical finance,
engineering and physics.
Introduction to modern algebra: groups, rings, linear algebra,
set theory. A main stream course for students interested in fundamental
mathematics and applications. This course is an HPC.
Other Courses
Suitably qualified students may be allowed to do third year
courses and/or special topics second year courses. Please contact the
Department.
Note for Computer Science students
Honours students also taking Computer Science are advised to
take MATH2320
and MATH2322
rather than the discrete mathematics and algebraic systems options
MATH2301 and MATH2303.
Advice should be sought from the year coordinator to ensure
that you
make the most appropriate choice of courses to complement other
subjects or to serve as prerequisites for Third Year Mathematics
topics.
This page was updated on Monday November 19, 2007
