### 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: Symmetric Functions

**Description:** The theory of symmetric functions is one of the richest and most beautiful topics in enumerative combinatorics, with deep connections to group theory, Lie algebras, and algebraic geometry. To work out examples in representation theory, one often needs to do computations in the ring of symmetric functions; there are well-developed software packages freely available to handle larger computations. This class will focus on the basic combinatorial properties of symmetric functions, briefly indicating applications to other branches of math.

**Prerequisites:** MATH 5210 (Abstract Algebra I) or consent of instructor.

**Offered:** Spring

**Credits:** 3

### MATH 5020 - Section 2: Intorduction to p-adic Numbers

**Description:** In addition to completing the rational numbers to form the real numbers, the rationals can be completed in infinitely many other ways, one completion for each prime number p. The resulting completions are called the p-adic numbers. Many concepts from classical analysis can be developed over these fields, with properties that are sometimes similar and sometimes quite different from the classical case. The p-adic numbers were originally studied just within number theory and were viewed as somewhat exotic, but over time they became more mainstream through applications in other areas of mathematics, such as representation theory, commutative algebra, algebraic geometry, and model theory. This course should be of interest to students in algebra as well as students in analysis who want a broader sense of the scope in which analytic concepts can be developed over fields other than the real or complex numbers.
If anyone has a question about this course, please send an email to liang.xiao@uconn.edu

**Prerequisites:** MATH 5211 (Abstract Algebra II), and one of Math 5110 (Introduction to Modern Analysis) or Math 5310 (Introduction to Geometry and Topology I).

**Offered:** Spring

**Credits:** 3

**Sections: **Spring 2015 on Storrs Campus

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

07648 | 5020 | 001 | Lecture | TuTh 2:00:00 PM-3:15:00 PM | MSB411 | Roby, Thomas |

11129 | 5020 | 002 | Lecture | TuTh 9:30:00 AM-10:45:00 AM | MSB203 | Xiao, Liang |