Stage 3 courses

This course is for people interested in thinking about the social, cultural, political, economic, historical, technological and theoretical ideas that influence mathematics education, who want to understand the forces that shaped their own mathematics education or who are interested in teaching. Students will develop their ability to communicate ideas in essay form.

Recommended Preparation
Students should have at least 45 points from courses in mathematics or statistics.

Availability: S2C
Points: 15
Coordinator: Judy Paterson

This course includes the study of some topics occurring in the history of mathematics which facilitate understanding of modern mathematics. Topics include concepts of number, geometry, algebra and differential and integral calculus.

Corequisites
At least 30 points at Stage III in mathematics is required.

Availability: S2C
Points: 15
Coodinator: Garry Tee

Logic addresses the foundations of mathematical reasoning. It models the process of mathematical proof by providing a setting and the rules of deduction. This course builds a basic understanding of first order predicate logic, introduces model theory and demonstrates how models of a first order system relate to mathematical structures. The course is recommended for anyone studying high level computer science or mathematical logic.

Prerequisites
COMPSCI 225 or MATHS 255 or PHIL 222 is required.

Availability: S2C
Points: 15
Coordinator: Sina Greenwood

This is a framework for a unified treatment of many different mathematical structures. It concentrates on the fundamental notions of groups, rings and fields. The abstract descriptions are accompanied by numerous concrete examples. Applications include symmetries, geometry, coding theory, cryptography and many more. This course is recommended for those planning graduate study in pure mathematics.

Prerequisites
MATHS 255: Principles of Mathematics or MATHS 328: Algebra and Applications, or an A- pass in MATHS 253: Advancing Mathematics 3 is required.

Availability: S2C
Points: 15
Coordinator: Eamonn O'Brien

Combinatorics is a branch of mathematics that studies collections of objects that satisfy specified criteria. An important part of combinatorics is graph theory, which is now connected to other disciplines including bioinformatics, electrical engineering, molecular chemistry and social science. The use of combinatorics in solving counting and construction problems is covered using topics that include algorithmic graph theory, codes and incidence structures, and combinatorial complexity.

Prerequisites
MATHS 255, or COMPSCI 225 and a B+ in either MATHS 208 or 250 is required

Availability: S1C
Points: 15
Coordinator: Jamie Sneddon

The goal of this course is to show the power of algebra and number theory in the real world. It concentrates on concrete objects like polynomial rings, finite fields, groups of points on elliptic curves, studies their elementary properties and shows their exceptional applicability to various problems in information technology including cryptography, secret sharing and reliable transmission of information through an unreliable channel.

Prerequisites
MATHS 255, or B+ pass in COMPSCI 225 and one of MATHS 208, 250, 253 is required.

Availability: S1C
Points: 15
Coordinator: Arkadii Slinko

This is a standard course for every student intending to advance in pure mathematics. It develops the foundational mathematics underlying calculus, it introduces a rigorous approach to continuous mathematics and fosters an understanding of the special thinking and arguments involved in this area. The main focus is analysis in one real variable with the topics including real fields, limits and continuity, Riemann integration and power series.

Prerequisites
MATHS 253 and 255, or 253 and a B+ in MATHS 260 is required.

Availability: S1C
Points: 15
Coordinator: Tom ter Elst

By selecting the important properties of distance many different mathematical contexts are studied simultaneously in the framework of metric and normed spaces. This course examines carefully the ways in which the derivative generalises to higher dimensional situations. These concepts lead to precise studies of continuity, fixed points and the solution of differential equations. This is a recommended course for all students planning to advance in pure mathematics.

Prerequisites
MATHS 332 is required.

Strongly recommended
MATHS 253: Advancing Mathematics 3 and MATHS 255: Principles of Mathematics is strongly recommended.

Availability: S2C
Points: 15
Coordinator: David Gauld

Calculus plays a fundamental role in mathematics, answering deep theoretical problems and allowing us to solve very practical problems. This course extends the ideas of calculus to two and higher dimensions, showing how to calculate integrals and derivatives in higher dimensions and exploring special relationships between integrals of different dimensions. It also extends calculus to complex variables.

Prerequisites
MATHS 253: Advancing Mathematics 3 is required.

Availability: S1C, S2C
Points: 15
Coordinator: Robert Chan

Partial differential equations are used to model many important phenomena in the real world, such as heat flow and wave motion. This is an introductory course on methods of solution for linear partial differential equations in one, two and three dimensions.

Prerequisites
MATHS 260: Differential Equations and MATHS 253: Advancing Mathematics 3 or equivalent, or PHYSICS 211 is required.

Availability: S1 C
Points: 15
Coordinator: Vivien Kirk

Techniques such as variational methods, Green’s functions and perturbation analysis are a crucial part of the applied mathematician’s toolbox. This course covers a selection of such advanced topics in detail, and is suitable for those students intending to advance in applied mathematics or physics.

Prerequisites
Either MATHS 260: Differential Equations and MATHS 253: Advancing Mathematics 3 or equivalent, or PHYSICS 211 is required.

Recommended Preparation
MATHS 340 and 361 is recommended.

Availability: S2C
Points: 15
Coordinator: Jari Kaipio

Much of modern research in applied mathematics, physics and engineering relies heavily on the construction and numerical solution of mathematical models. This course covers the theory and practice of such computational approaches, including the computation of solutions to ordinary differential equations (ODEs) and partial differential equations (PDEs), the study of first order PDEs and bifurcations in ordinary differential equations. Matlab is used extensively.

Prerequisites
MATHS 260: Differential Equations and MATHS 270: Numerical Computation is required.

Availability: S2C
Points: 15
Coordinator: Steve Taylor

Semester 2 2011 study guide (external link)

This course is suitable for Finance majors who want to learn more about the more mathematical aspects of the subject and for Statistics or Mathematics majors wanting to learn about Finance.

Topics studied include
Mean-variance portfolio theory, options, arbitrage and put-call relationships, introduction of binomial and Black-Scholes option pricing models, compound interest, annuities, capital redemption policies, valuation of securities, sinking funds, varying rates of interest, taxation, duration and immunisation, introduction to life annuities and life insurance mathematics.

Assessment
Final exam is 75% and coursework 25% or Final exam is 100% and coursework is 0%. There is one test worth 15% and the assignments are worth 10%. Students must obtain at least 50% in final exam to pass.

Prerequisites
15 points in Stage 2 statistics and 15 points in Stage 2 mathematics is required.

Availability: S2 C
Points: 15
Coordinator: Robert Chan