Degrees Offered
Ph.D in Mathematics, M.Sc. in Mathematics, M.Sc. in Applied Mathematics
Graduate Courses
Math 550. Ordinary Differential Equations
Comprehensive Exam course. Linear and nonlinear systems and their dynamical behavior.
Math 551. Dynamical Systems Theory
Discrete and continuous dynamical systems, in finite and infinite dimensions.
Math 553. Partial Differential Equations
Comprehensive Exam course. Classical theory of the wave, diffusion and potential equations.
Math 554. Linear Analysis and PDEs
Spectral theory for differential operators, distributions, Fourier transforms, Sobolev spaces, and semigroup theory. Applications to elliptic, parabolic and hyperbolic partial differential equations, including the potential, diffusion, wave and Schroedinger equations. Aimed at engineering and mathematics students.
Math 555. Nonlinear Analysis and PDEs
Topics in nonlinear PDEs.
Math 556. Methods of Mathematical Physics, I
Math 557. Methods of Mathematical Physics, II
Aimed at engineering and applied mathematics students. Emphasizes functional analysis and applications to ordinary and partial differential equations arising in science and engineering.
Math 595. Topics in Mathematics
Advanced topics course.
Our course structure is undergoing revision in 2009-2011. Under consideration is a proposal to modify Math 550-551 into a sequence in Dynamical Systems, with applications to ordinary and partial differential equations. Math 556 might become a course in Methods of Applied Mathematics; we are trying out that applied mathematics course as a section of Math 595 offered in Spring 2010. The previous material of Math 556 is substantially covered in Math 554, whose syllabus was recently updated. Finally, we are proposing to allow students to take Math 555 more than once, since the material changes from year to year.
Associated Courses
Math 552. Numerical Methods for PDEs
Taught by Computer Science.
Math 559. Asymptotic Methods
Taught by Mechanical Science and Engineering.