Georgia Institute of Technology School of Mathematics | Georgia Institute of Technology | Atlanta, GA

Pass/Fail only. A course for graduate students in Mathematics to help prepare for the written comprehensive exams in Algebra and Analysis. Offered Summer 2017.

In 2017, the course was split into two sections: MATH 8802 ALG and MATH 8802 ANA.

Review of linear algebra and ordinary differential equations, brief introduction to functions of a complex variable.

Volterra and Fredholm linear integral equations, relation to differential equations, solution methods, Fourier, Laplace and Mellin transforms, applications to boundary value problems and integral equations.

Geometry, convergence, and structure of linear operators in infinite dimensional spaces. Applications to science and engineering, including integral equations and ordinary and partial differential equations.

Topics include L^p, Banach and Hilbert spaces, basic functional analysis.