All required coursework must be passed with a grade of B or better. Here are Institute requirements for the Ph.D. degree.

#### Core Courses

The ACO core curriculum consists of the following one-semester courses:

*Computing*

- CS 6515 - Introduction to Graduate Algorithms or CS 6520 Complexity or (for CoC students only) CS 7545 Machine Learning Theory (CoC students must select one of the latter two)
- CS 6550 - Design and Analysis of Algorithms

*Industrial and Systems Engineering *

- ISyE 7661 - Theory of Linear Inequalities
- ISyE 7686 - Advanced Combinatorial Optimization

*Mathematics*

- Math 6014 - Graph Theory
- Math 6121 - Algebra I (Students with home in ISyE or CoC may substitute Math 6112 Advanced Linear Algebra)
- Math 7018 - Probabilistic Methods in Combinatorics

**Note on CS 6515 vs. CS 6520 or CS 7545.** The corresponding question on the comprehensive examination will be based on CS 6515. Math and ISyE students should take CS 6515, unless they know the material. CS students are expected to already know the material of CS 6515.

#### Additional Course Requirements

Each student must complete at least 15 semester hours of course work at the 6000 or higher level in addition to the courses that constitute the program core. The following courses are required, depending on the student's home department:

*Computing *

- Two theory courses at the level of 7000 or above

*Industrial and Systems Engineering *

- ISyE/Math 6761 - Stochastics I
- ISyE 6663 - Nonlinear Optimization
- CS 7545 - Machine Learning Theory (applies only to students who matriculated in 2019 or later)

*Mathematics *

- Math 6337 - Real Analysis I
- Math 6338 - Real Analysis II is not required but is strongly encouraged
- Two of the following three:

Math 6112 - Advanced Linear Algebra

Math 6321 - Complex Analysis

A 6000 level or above topology/geometry course

#### Minor Field of Study

Each student must satisfy the Institute's requirement of a minor program of study of at least 9 hours of course work chosen to the satisfaction of the Coordinating Committee and the student's home department. Courses in the ACO core curriculum may not be used as part of a minor program. Students with home in the School of Mathematics are encouraged to do a minor in machine learning.

#### Responsible Conduct of Research

Each student** **must complete two forms of RCR training: On-line training and In-person training. Mathematics students may find it best to satisfy the in-person training requirement by taking Math 6001 Introduction to Graduate Mathematics, while computing students may want to take CS 7001 Introduction to Graduate Studies.