### MATH 5020: Topics in Algebra

**Description:** Advanced topics chosen from group theory, ring theory, number theory, Lie theory, combinatorics, commutative algebra, algebraic geometry, homological algebra, and representation theory. With change of content, this course may be repeated to a maximum of twelve credits.

**Prerequisites:** MATH 5211.

**Credits:** 3

### MATH 5020 - Section 1: Enumerative Combinatorics

**Description:** The course will give an introduction to enumerative combinatorics at the graduate level. Topics will include: basic enumeration, multiset permutations and statistics, generating functions, bijective proofs, q-analogues, sieve methods, exponential formula, and Lagrange inversion.

**Text:** Enumerative Combinatorics 1 (2nd edition) and 2, by Richard Stanley (selections from chapters 1,2,4,5, and 6).

**Instructor:** Tom Roby

**Prerequisites:** MATH 5210

**Offered:** Spring

**Credits:** 3

### MATH 5020 - Section 2: Introduction to Modular Forms

**Description:** While modular forms are at the heart of number theory, they also appear in representation theory, geometry and mathematical physics. This course will introduce the basic theory of modular forms and provide an overview of more advanced topics. The prerequisite is Math 5210 (Abstract Algebra I), and other basic materials will be explained according to students' backgrounds.

**Instructor:** Kyu-Hwan Lee

**Prerequisites:** MATH 5210

**Offered:** Spring

**Credits:** 3

**Sections: **Spring 2017 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

16050 | 5020 | 001 | Lecture | TuTh 02:00:00 PM-03:15:00 PM | MONT 313 | Roby, Tom |

24843 | 5020 | 002 | Lecture | TuTh 12:30:00 PM-01:45:00 PM | MONT 314 | Lee, Kyu-Hwan |