Not offered 2007-2008
MATH 401 Functional Analysis with Applications to Mathematical Physics (Q)
Functional analysis can be viewed as linear algebra on infinite dimensional spaces. It is a beautiful and classical area of mathematics and it also provides the rigorous mathematical background for some areas of theoretical physics (especially quantum mechanics). We will introduce infinite-dimensional spaces (Banach and Hilbert spaces) and study their properties. These spaces are often spaces of functions (for example, the space of square integrable functions). We will consider linear operators on Hilbert spaces and we will study their spectral properties. A special attention will be dedicated to various operators arising from mathematical physics-especially the Schrödinger operator.
Format: lecture. Evaluation will be based on homeworks and exams.
Prerequisites: Mathematics 301 or 305 or permission of instructor. No enrollment limit (expected: 15).

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