Ph.D in Applied Analysis
Course Work
Ph.D in Probability, Stochastic Analysis and Applications
Course work
Both Ph.ds
Course Descriptions


Students must complete the following one-semester courses prior to enrollment or during the first year of the program, in Portugal. Students must consult with their Pro Tem advisors to make sure they meet all course requirements for all universities involved.

Following the links provides an abridged description of each course:

First year

During the first year of the program, while in Portugal, a student must take 6 one semester courses, to be chosen, under supervision of the Portuguese Pro Tem advisor, from the requirements list or from the following list of recommended courses:

  • Ordinary Differential Equations (ODEs)
  • Evolution Problems
  • Optimal Control
  • Functional Integration and Applications
  • Introduction to Stochastic Processes
  • Stochastic Analysis
  • Stochastic Differential Equations
  • Stochastic Calculus in Finance

Second year

During the second year of the program, while at CMU, the student must take 6 one semester courses, which are to be chosen under supervision of the CMU Pro Tem advisor and must fall under at least one of the following general headings:

  • Complex Analysis
  • Discrete Mathematics
  • Optimization and Control
  • Probability
  • Reading and Research
  • Stochastic Analysis