Second Year Courses

The coordinator of Second Year Mathematics courses is Prof D. Wickramasinghe, room JD G1.

Outlines of First Semester Second Year Courses

Games, Graphs and Machines MATH2301

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

Differential Equations and Applications MATH2305

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.
 

Maths Methods 1 Honours: Ordinary Differential Equations and Advanced Vector Calculus MATH2405

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.

Analysis 1 Honours: Metric Spaces and Applications MATH2320

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.

Bioinformatics and Biological Modelling MATH2307

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

Partial Differential Equations and Applications MATH2306

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. 

Maths Methods 2 Honours: Partial Differential Equations, Fourier Analysis and Complex Analysis MATH2406

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. 

Algebra 1 Honours: Groups, Rings and Advanced Linear Algebra MATH2322

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 Friday September 11, 2009