Size and shape in topology and analysis, compactness, connectedness, limit sets, theory of dimension, fractals and self-similarity. Three lectures;...
Inversion formulae, systems of distinct representatives, block designs and other configurations; other topics. Three lectures; one term ...
Graphs, trees, bipartite graphs, connectivity, graph colouring, matrix representations, applications. Three lectures; one term Prerequisite(s): One...
Analytic functions, Cauchy's theorem, Cauchy's integral formula, residues, zeroes of analytic functions; Laurent series, the maximum principle. Three...
An introduction to the history of mathematics, including interaction with other phases of culture, with special emphasis on the past three centuries....
Metric spaces, compactness. Spaces of continuous functions, functions of several variables, inverse and implicit function theorems. Lebesgue...
Precise topics will vary; consult the department for current information. Possible topics include: functional analysis, measure theory, harmonic...
Review of multivariable calculus, basic properties of manifolds, differential forms, Stokes' theorem, de Rham cohomology and applications. Three...
Precise topics will vary; consult the department for current information. Possible topics include: differential geometry, riemannian metrics,...
Field extensions, splitting fields, normality and separability, Galois extensions, finite fields, solvability by radicals, cyclic extensions,...
Precise topics will vary; consult the department for current information. Possible topics include: algebraic geometry, algebraic number theory. Three...
Topics to be selected from the theory of ordinary differential equations, bifurcation and stability, and partial differential equations. Three...
First order logic, deduction systems, completeness and compactness theorems, model theory. Three lectures; one term Prerequisite(s): MATH 3E03
Precise topics will vary; consult the department for current information. Possible topics include: axiomatic set theory, computability theory, model...
A project in pure or applied mathematics to be carried out under the supervision of a faculty member from the Department of Mathematics. A written...
Approximation error; methods for ordinary differential equations, stiffness; iterative methods for boundary value problems; weighted residuals;...
Precise topics will vary; consult the department for current information. Possible topics include: fundamental group and covering spaces, cell...
Directed reading in areas of mathematics of interest to the student and the instructor. Prerequisite(s): Permission of the Chair of the Department...
Conformal maps, analytic continuation, harmonic functions, the Riemann mapping theorem, Riemann surfaces. Three lectures; one term Prerequisite(s):...