On completion of each work term, the student must submit to the School of Mathematics and Statistics a written report on the work performed. Graded...
Fourier series, Fourier integrals; introduction to harmonic analysis on locally compact abelian groups, Plancherel Theorem, Pontryagin duality;...
Banach spaces and bounded linear operators, Hahn-Banach extension and separation, dual spaces, bounded inverse theorems, uniform boundedness...
Lebesgue measure and integration on the real line; sigma algebras and measures; integration theory; Lp spaces; Fubini's theorem; decomposition...
An introduction to the group representations and character theory, with selected applications. Prerequisite(s): MATH 3106, or a grade of B or higher...
Fundamental concepts in rings and modules, structure theorems, applications. Prerequisite(s): MATH 3158 or permission of the School.Lectures three...
Fundamental principles as applied to abelian, nilpotent, solvable, free and finite groups; representations. Prerequisite(s): MATH 3106 or permission...
Fields, including algebraic and transcendental extensions, Galois theory, valuation theory; Noetherian commutative rings, including Noether...
Axioms of set theory; categories, functors, natural transformations; free, projective, injective and flat modules; tensor products and homology...
Introduction to field theory, emphasizing the structure of finite fields, primitive elements and irreducible polynomials. The influence of...
Topological spaces, maps, subspaces, product and identification topologies, separation axioms, compactness, connectedness. Prerequisite(s): MATH 3001...
An introduction to homotopy theory. Topics include the fundamental group, covering spaces and the classification of two-dimensional manifolds. ...
A study of at least one modern axiom system of Euclidean and non-Euclidean geometry, embedding of hyperbolic and Euclidean geometries in the...
Introduction to differentiable manifolds; Riemannian manifolds; vector fields and parallel transport; geodesics; differential forms on a manifold;...
Dirichlet series, characters, Zeta-functions, prime number theorem, Dirichlet's theorem on primes in arithmetic progressions, binary quadratic forms. ...
Algebraic number fields, bases, algebraic integers, integral bases, arithmetic in algebraic number fields, ideal theory, class number. ...
Applications of the principles of Operations Research to practical problems in business, management, and science. Students present at least one case...
First-order partial differential equations. Classification of second-order linear partial differential equations; the diffusion equation, wave...
Theory of distributions, initial-value problems based on 2-dimensions wave equations, Laplace transform, Fourier integral transform, diffusion...
Basic concepts of dynamical systems. Vector formulation for systems. Theory of autonomous systems in one, two and higher dimensions. Limit sets,...