- Algebra and Algebraic Geometry
- Analysis
- Applied Mathematics
- Combinatorics
- Computer Science
- Differential Equations
- Financial and Actuarial Mathematics
- Geometry & Topology
- Logic and Foundations
- Mathematical Biology
- Mathematical Physics
- Mathematics Education
- Number Theory
- Probability Theory
- Research Training Grant
- Named Postdoctoral Fellows

#### Advanced Courses Taught by Postdoctoral Fellows

To illustrate the breadth and depth of teaching experience Michigan post-docs typically gain, we include in this appendix a list of advanced undergraduate and graduate courses taught by post-docs in our group in the past 5 years. Often individual instructors taught the same course more than once, though we do not indicate those statistics here. RTG fellows are indicated with an asterisk.

All advanced courses (with the exception of topics courses) at Michigan are assigned a permanent faculty “Course Coordinator” who is responsible for maintaining the institutional memory regarding content and expectations for these courses. This provides one source of support for our post-docs teaching these courses for the first time. For advanced graduate courses (especially topics courses), post-docs also receive considerable mentoring from their faculty mentors and others in our group who have a stake in the course.

**Advanced Undergraduate Courses for Math Majors.**

- Math 312: Applied Modern Algebra taught by post-docs Carl Miller*, Julianna Tymozcko, and Nick Ramsey.
- Math 316: Differential Equations taught by Chuck Cadman*.
- Math 351: Principles of Analysis taught by Jason Bell.
- Math 389: Explorations in Mathematical Research taught by Tatiana Chmutova.* This course was designed by Michael Artin while visiting from MIT. It’s goal is to engage students in discovery inquiry-based learning projects on research topics. (IBL).
- Math 412: Introduction to Modern Algebra taught by Tomasso DeFernex, Nick Ramsey, and Tatiana Howard.*
- Math 416: Introduction to Algorithms taught by Loren Spice.
- Math 417: Matrix Algebra taught by Tatiana Chmutova,* Nathan Reading,* Russell Goward, Eshmatov.
- Math 419: Linear Spaces and Matrix Theory taught by Radu Laza, Ben Howard,* Russell Goward.
- Math 425: Introduction to Probability taught by Ivan Petrakiev*, Chris Hall, Julianna Tymozcko, Radu Laza, Carl Miller.*
- Math 433: Introduction to Differential Geometry taught by Renzo Cavalieri.
- Math 451: Advanced Calculus taught by Tatiana Howard* and Paul Horja.
- Math 475: Elementary Number Theory taught by Nick Ramsey
- Math 490: Introduction to Topology taught by Renzo Cavalieri and Tomasso DeFernex.

**Courses for Education Students.**

- Math 385: Math for Elementary School Teachers taught by Loren Spice
- Math 431: Geometry for High School Teachers taught by Loren Spice
- Math 486: Concepts Basic to Secondary School Mathematics taught by Loren Spice.

**Courses for Honors Math Majors and (usually non-pure-math) Graduate Students.**

- Math 512: Algebraic Structures taught by Tatiana Chmutova.*
- Math 513: Introduction to Linear Algebra taught by Howard Thompson,* Amanda Knecht,* and Tom Nevins.
- Math 555: Introduction to Complex Variables taught by Radu Laza. This is more concrete than the standard “pure math” introduction to complex variables, though many PhD students in applied math take this course.
- Math 590: Introduction to Topology taught by Tomasso DeFernex.

**Courses for Math PhD Students.**

- Math 565: Combinatorics and Graph Theory taught by Pavlo Pylyvavskyy and Nathan Reading.*
- Math 566: Combinatorial Theory taught by Pavlo Pylyvavskyy.
- Math 594: Algebra II taught by Loren Spice. All regular math PhD students must take (or test out of) this course.
- Math 614: Commutative Algebra taught by Neil Epstein.
- Math 632: Introduction to Scheme Theory by Karl Schwede.*
- Math 669: Matroid theory designed and taught by David Speyer.
- Math 679: Arithmetic of Elliptic Curves taught by Nick Ramsey.
- Math 715: p-adic representation theory taught by Loren Spice.
- Math 731: Moduli Spaces of Curves and Gromov Witten Theory designed and taught by Renzo Cavalieri.