Introduces functional analysis with an emphasis on Banach and Hilbert spaces. The necessary theory of Banach Algebras and the functional calculus are developed for the spectral theorem for bounded self-adjoint operators on Hilbert space. Various applications and extensions presented. Simplicial and Singular Homology, The Lefschetz Fixed-Point Theorem, Cohomology, Duality in Manifolds. All graduate students in the department enrol each year.
Students attend the regular department colloquia.
After the first year in their program, they are expected to join the regular seminar series in their area of specialization. MATH 994 Research Students writing a Master's thesis must register for this course. MATH 996 Research Students writing a Ph.D. thesis must register for this course.