Analysis
Philosophy and goals
The Master’s Program in Applied Analysis provides rigorous training in core areas of modern analysis, including real and complex analysis, functional analysis, partial differential equations, and the calculus of variations. Students develop a strong theoretical foundation together with practical skills in mathematical modeling, enabling them to analyze complex systems arising in science and engineering. The program equips students with the mathematical tools needed to study fluid flows and nonlinear solids, optics and wave phenomena, composite materials, and electrochemical systems, bridging advanced analytical theory with real-world applications.
The course pathways are below.
Track: Applied Analysis
Recommended Pathways of Courses
Year 1:
Math 5041-2 Concepts of Analysis or 8041-2 Real Analysis
Math 5045 ODE
Math 8051 Complex Analysis
Math 5057 Applied Differential Equations and Optimization
Math 5058 Fundamentals of Mathematical Modeling
Year 2
Math 8141-2 PDE I and II
Math 9041 Functional Analysis or Math 9043 Calculus of Variations
Math 9996 MS Thesis research
All courses can be replaced by the electives below
Math 5001 Linear Algebra
Math 8052 Intermediate Complex Analysis
Math 9042 Fourier Analysis and Distribution theory
Math 9044 Harmonic Analysis
Math 9210 Topics in Applied Mathematics
Math 9400 Topics in Analysis
Math 9991 MS research
Math 9995 MS Capstone project
Track: Theoretical Analysis
Philosophy and goals
The track in Theoretical Analysis is aimed as students who are primarily interested in theoretical aspects of analysis. In this track the students can focus on the study of PDE, Harmonic analysis, Calculus of Variations, Functional Analysis, and many more.
Recommended Pathways of Courses
Year 1:
Math 5041-2 Concepts of Analysis or 8041-2 Real Analysis
Math 5045 ODE
Math 5001
Math 8051 Complex Analysis
Math 8141 PDE I
Year 2
Math 8142 PDE II
Math 9041 Functional Analysis
Math 9044 Harmonic Analysis or Math 9043 Calculus of Variations
Math 9996 MS Thesis research
All courses can be replaced by the electives below
Math 8052 Intermediate Complex Analysis
Math 5057 Applied Differential Equations and Optimization
Math 5058 Fundamentals of Mathematical Modeling
Math 9042 Fourier Analysis and Distribution theory
Math 9210 Topics in Applied Mathematics
Math 9400 Topics in Analysis
Math 9991 MS research
Math 9995 MS Capstone project