Postgraduate Courses

This course is an introduction to analysis and its applications. Countable and uncountable sets, metrics, norms, open sets, closed sets, continuity, homeomorphisms, connectedness, complete metric spaces, totally bounded sets, fixed points, compact metric spaces, uniform continuity, category, the Baire Category Theorem, sequences of functions, pointwise and uniform convergence, the space of bounded functions.

This course is a continuation of MAED 5021. It covers the space of continuous functions, the Stone-Weierstrass Theorem, functions of bounded variation, the Riemann-Stieltjes Integrals, Fourier Series, Lebesgue measure, measurable functions, Lebesgue integrals, Convergence in measure, Lp spaces, differentiation.

This is a course which develops the rigorous definition of real and complex numbers, and various aspects of polynomials.

This course reviews the notion of groups, rings and homomorphisms and quotient constructions. Applications are then described for finite fields and number theory, and coding theory.

This course develops group theory and presents applications. Among the applications covered are the use of group theory to show the impossibility of expressing the roots of a general polynomial in terms of radicals, and the use of finite fields in random number generation, construction of orthogonal Latin squares, and the finite Fourier transform. Other applications are connections of group theory with Rubik’s Cube and uses of Lie groups.

This course is about important ideas in the development of geometry. Topics include logic and axiomatic system, projective geometry, Hilbert’s axioms, hyperbolic models, geometric transformations, hyperbolic trigonometry.

Topics in combinatorics including counting combinations and counting permutations, generating functions, and enumerative combinatorics. Inclusion-exclusion principle, Polya’s theory of counting, graph theory and applications.

This course illustrates how to use statistical and probabilistic techniques with an open source statistics package R to analyze data, especially in education.

This course covers ways to teach strategies and techniques to students to solve mathematical problems as they appeared in mathematical competitions. It covers many techniques, including transformation methods for solving geometry problems, and graph theoretical methods for solving combinatorial problems.

This course introduces a selection of topics from interdisciplinary mathematics, which may include mathematical physics, mathematical biology, image processing, etc.

This course introduces various case studies drawn from different areas of science to illustrate the use of computers as a problem-solving tool. Each integrates physical principles and mathematical models, as well as numerical techniques and computer implementations, into a coherent perspective.

In this course, the student will do a project in an area of mathematics under the guidance of a faculty member. The project either surveys a topic or describes an investigation completed by the student.