PhD Courses in Decision, Risk and Operations


Required Courses
Highly Recommended Courses

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.

Highly Recommended Courses

  1. A graduate level course in microeconomic theory (e.g., “Micro I” offered by the Department of Economics)
  2. “Probability I” course offered by the Statistics Department.

Elective Courses

  1. Revenue Management
  2. Logistics and Distribution
  3. Inventory Management
  4. Supply Chain Management
  5. Competition and Coordination in Supply Chains
  6. Â Monte Carlo Methods
  7. Computing for Business Research
  8. Game-Theoretical Models in Operations
  9. Marketing Models
  10. Experimental Design and Analysis
  11. Finance Theory
  12. Computational Finance
  13. Stochastic Differential Equations
  14. Probability-II