For Additional Mathematics, please make one of the following three choices:

• probability choice: please take MATH 8651, MATH 8652 and MATH 8659
• numerical analysis choice: please take MATH 8651, MATH 8441 and MATH 8442
• differential equations choice: please take MATH 8651, MATH 5587 and MATH 5588

Note that MATH 8651 (a probability course) is required in all three choices.

These courses are offered by the School of Mathematics, and are recommended to those students in our program who wish to enhance their knowledge of mathematics beyond the level covered in the regular FM courses.

WARNING: Courses listed on this website may have prerequisites; see the syllabi to check on those. If you have any question about whether you are ready to take a certain course, please speak to the course instructor and/or your advisor.

NOTE: Completion of these "with additional Mathematics" requirements also also fulfills the requirements for a Master's level minor in Mathematics. If you wish to obtain that minor, you'll need to get the signature of the Mathematics DGS on your degree program form.

MATH 8651 Theory of Probability Including Measure Theory 3 credits
Syllabus

Probability spaces. Distributions/expectations of random variables. Basic theorems of Lebesque theory. Stochastic independence, sums of independent random variables, random walks, filtrations. Probability, moment generating functions, characteristic functions. Laws of large numbers.

MATH 8652 Theory of Probability Including Measure Theory 3 credits
Syllabus

Conditional distributions and expectations, convergence of sequences of distributions on real line and on Polish spaces, central limit theorem and related limit theorems, Brownian motion, martingales and introduction to other stochastic sequences.

MATH 8659 Stochastic Processes 3 credits
Syllabus

In-depth coverage of various stochastic processes and related concepts, such as Markov sequences and processes, renewal sequences, exchangeable sequences, stationary sequences, Poisson point processes, Levy processes, interacting particle systems, diffusions, and stochastic integrals.

MATH 8441 Numerical Analysis and Scientific Computing 3 credits
Syllabus

Approximation of functions, numerical integration. Numerical methods for elliptic partial differential equations, including finite element methods, finite difference methods, and spectral methods. Grid generation.

MATH 8442 Numerical Analysis and Scientific Computing 3 credits
Syllabus

Numerical methods for integral equations, parabolic partial differential equations, hyperbolic partial differential equations. Monte Carlo methods.

MATH 5587 Elementary Partial Differential Equations I 4 credits
Syllabus

Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks.

MATH 5588 Elementary Partial Differential Equations II 4 credits
Syllabus

Heat, wave, Laplace's equations in higher dimensions. Green's functions, Fourier series, transforms. Asymptotic methods, boundary layer theory, bifurcation theory for linear/nonlinear PDEs. Variational methods. Free boundary problems. Additional topics as time permits.