MATH 432 - Intermediate Differential Equations

3 units (fi 6)(EITHER, 3-0-0)

Elementary existence and uniqueness theorems. Systems of equations, stability, perturbation theory. Introduction to numerical methods. Introduction to phase plane analysis. Prerequisite: One of MATH 201, MATH 334, MATH 336, or MA PH 251

MATH 436 - Intermediate Partial Differential Equations

3 units (fi 6)(FIRST, 3-0-0)

Partial differential equations as physical models. Introduction to basic generalized functions. Theory of linear and quasi-linear first-order equations: general solution, initial value problem, generalized solutions and propagation of singularities, characteristic surfaces, shock formation. Theory of fully nonlinear first order equations: complete solution and the initial value problem. Hamilton-Jacobi equation and its applications. Second order linear equations in n dimensions: classification, canonical form, characteristic surfaces and shock formation, initial and boundary value problem. Prerequisite: MATH 300 or MATH 337.

MATH 509 - Data Structures and Platforms

3 units (fi 6)(EITHER, 3-0-0)

Basic data analysis with R, SAS, and Python. Program development with Jupyter notebooks. Cloud computing, collaborative software development, docker containers, kubernets. Internet security, privacy and ethics. Technologies will be updated as new developments arise. Prerequisites: No programming skills are needed.