Temple University 3 credits MATH
Functional Analysis provides the foundation for high-dimensional geometry, analysis, and probability. This course introduces the fundamental concepts and methods of functional analysis, with an emphasis on concrete examples. Topics include the Baire Category Theorem and its applications, particularly to Banach space theory principles such as the Uniform Boundedness Principle, the Open Mapping Theorem, and the Closed Graph Theorem. The course also explores different notions of convergence, weak topology, duality, and convexity. In addition, it introduces linear operator theory, including spectral theory for compact operators, self-adjoint operators, Fredholm theory, and their applications.
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