Students are encouraged to discuss second year course selection with potential advisors, the ACM Director and instructors of particular courses as part of their planning for their Ph.D. Candidacy Examination and choosing their areas of dissertation research. Students are encouraged to take courses throughout their graduate study. Note that in addition to regular courses many advanced topics are taught intermittently as special topics courses, e.g., MAD 5932 Topics in Computational Mathematics, MAP 5932 Topics in Applied Mathematics, MAD 6408 Advanced Topics in Numerical Analysis, MAP 6437 Advanced Topics in Applied Mathematics, and seminars such as MAD 6939 Advanced Seminar in Scientific Computing. Each of these may have several sections per semester and groups of students are encouraged to make requests for such courses on topics in which they are interested. Also, given the broad nature of the areas of interest for ACM students, courses associated with the Biomathematics and Financial Mathematics Programs as well as other departments, e.g., Statistics, Scientific Computing, and Computer Science may also be of interest and the courses offered in those departments should be consulted each semester.

Second year and other advanced courses in the Department of Mathematics and other departments include but are not limited to:

- MAD 5738 Numerical Solution of Partial Differential Equations I
- MAD 5739 Numerical Solution of Partial Differential Equations II
- MAD 5745 Spectral Methods for Partial Differential Equation
- MAD 5757 High Order Finite Difference Methods for Computational Acoustics and Fluid Dynamics
- MAP 5395 Finite Element Methods
- MAP 6437 Advanced Partial Differential Equations
- MAD 5305 Graph Theory
- MAP 5932 Numerical Linear Algebra
- STA 5106 Computational Methods in Statistics I
- STA 5107 Computational Methods in Statistics II
- STA 5635 Applied Machine Learning
- STA 6468 Advanced Topics in Probability and Statistics
- Shape and Functional Data Analysis
- ISC 5305 Scientific Programming
- ISC 5307 Scientific Visualization
- MAP 5207 Optimization
- MAD 5420 Numerical Optimization
- MAD 5427 Numerical Optimal Control of Partial Differential Equations
- ISC 5308 Computational Aspects of Data Assimilation
- MAP 5107 Mathematical Modeling
- MAP 5431 Introduction to Fluid Dynamics
- MAP 5513 Wave Propagation Theory