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


The ICTI program in Applied Analysis has certain basic course requirements which students are expected to complete during the program, or have completed prior to entering the program. Students should consult with their (temporary) advisors to make sure that they meet the course requirements.

First Year

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

  • Ordinary Differential Equations (ODEs)
  • Sobolev Spaces
  • Calculus of Variations
  • Optimal Control
  • Numerical Analysis
  • Dynamical Systems
  • Stochastic Analysis
  • Second year

    The student must take at least 6 one semester courses that fall under at least one of the following general headings:

    • Numerical Analysis
    • Probability
    • Analysis
    • Ordinary Differential Equations and Dynamical Systems
    • Ordinary Differential Equations
    • Calculus of Variations
    • Stochastic Analysis

    Third and later years

    It is expected that the student will follow advanced courses and research seminars.