Ph.D. Model Program: Applied Mathematics

The overall set of courses must constitute a coherent, rigorous program appropriate for a Ph.D. specifically in the field of Applied Mathematics, and the faculty recommend that students take Applied Math graduate courses to the greatest extent possible and relevant.

Listed here are examples of courses the Applied Math faculty have identified as appropriate for Ph.D. Program Plans in Applied Math.  Note that the list is not exclusive, and each student’s individual plan requires review and approval by the CHD.

Examples of courses for students studying machine learning and artificial intelligence:

  • AM 216 Inverse Problems in Science and Engineering

  • AM 221 Advanced Optimization

  • CS 234r Topics on Computation in Networks and Crowds

  • CS 280r Advanced Topics in Artificial Intelligence

  • CS 281 Advanced Machine Learning

    • or CS 181 Machine Learning if more appropriate given the student’s background

  • ES 250 Information Theory

  • Other Computer Science or Engineering Sciences courses relevant to the student’s research

 

Examples of courses for students studying computational math, inference, and prediction

  • AM 207 Advanced Scientific Computing: Stochastic Methods for Data Analysis, Inference and Optimization

  • AM 231 Decision Theory

  • AC 209a/b Data Science 1/2

  • CS 205 Computing Foundations for Computational Science

  • ES 255 Statistical Inference with Engineering Applications

  • 200-level Statistics courses appropriate for the student’s area of research

 

Examples of courses for students with an interest in physical modelling and applications:

  • AM 201/202 Physical Mathematics I/II

  • AM 203 Introduction to Disordered Systems and Stochastic Processes

  • AM 205 Advanced Scientific Computing: Numerical Methods

  • AM 207 Advanced Scientific Computing: Stochastic Methods for Data Analysis, Inference and Optimization

  • AM 216 Inverse Problems in Science and Engineering

  • AM 225 Advanced Scientific Computing: Numerical Methods for Partial Differential Equations

  • AP 225 Introduction to Soft Matter, or other Applied Physics courses

  • ES 220 Fluid Dynamics

  • ES 240 Solid Mechanics

  • Other Applied Physics, ES or FAS technical courses relevant to the student’s research

    • Examples of Statistical Mechanics courses: AP 284, Physics 262

    • Examples of Electromagnetism courses: AP 216, Physics 232

    • Examples of Solid State Physics courses: AP 295a/b

 

Examples of courses for students with an interest in biological modelling and applications

  • AM 203 Introduction to Disordered Systems and Stochastic Processes

  • AM 205 Advanced Scientific Computing: Numerical Methods

  • AM 217 Instabilities and Patterns in Soft Matter and Biophysics

  • CS 289 Biologically-inspired Multi-agent Systems

  • Math 243 Evolutionary Dynamics

  • MCB 199 Statistical Thermodynamics and Quantitative Biology

 

Examples of courses for students with an interest in economics:

  • AM 207 Advanced Scientific Computing: Stochastic Methods for Data Analysis, Inference and Optimization

  • CS 236r Topics at the Interface between Computer Science and Economics

  • Econ 2020a/b Microeconomic Theory I/II

 

Note that taking “G-level” courses at MIT is certainly an option, as MIT offers a different course selection than is available at SEAS and Harvard.  Examples of MIT courses taken by Applied Math PhD students include 2.29, 6.252J, 6.851, 8.334, 16.920, 18.1021,18.335J, 18.336.