PhD Curriculum

Required Courses

First Year

  1. Foundations of Optimization
  2. Foundations of Stochastic Modeling
  3. Optimization I/Linear Programming (IEOR)
  4. Stochastic Modeling I (IEOR)
  5. Stochastic Modeling II (IEOR)

In addition, students must demonstrate proficiency in the area of real analysis at the level of Rudin, “Principles of Mathematical Analysis”, on the basis of prior coursework, an exemption exam, or by taking the “Introduction into Modern Analysis I” at Columbia.

By the End of the Third Year

  1. A graduate level course in game theory (e.g. “Micro II” offered by the Department of Economics or an equivalent course).
  2. A graduate level course on statistical inference theory (either “Statistical Inference Theory I” offered by the Department of Statistics or “Econometrics I” offered by the Economics Division).
  3. A graduate level course on advanced deterministic optimization (e.g., “Optimization II/Network Flows”, or “Integer Programming”, or “Combinatorial Optimization” offered by the IEOR Department).
  4. A graduate level course in dynamic programming.

Sample of Elective Courses

  • Tools: advanced statistical inference theory / econometrics, probability theory I (highly recommended) and II, Micro I/II (highly recommended), stochastic differential equations, Monte Carlo methods, network analysis, integer programming, ...
  • Seminars: pricing and revenue management, economics of social networks, data driven decision making, optimization and economics of online marketplaces, supply chain management, economics of queues, marketing models, computational finance, industrial organization, …

It can be useful to leverage the opportunity of being at a great university to build their methodological toolkit from other departments (e.g. Math/Stat/CS/Econ/EE/). You may consider doing this beyond what is absolutely necessary in terms of course requirements.