Syllabus for "Applied Algebra" (Graduate Course)   (Fall 2018)

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Professor: Yoonjin Lee

Prerequisite: Linear Algebra I and II, Elementary Number Theory, Abstract Algebra I and II

Course Description:

It is desirable that students have some basic background on Graduate Algebra I and II and Graduate Algebraic Number Theory I (preferably II). We study current research developments on Function Field Arithmetic, Drinfeld modules, Algebraic Geometric Codes, Self-dual codes, Formally Self-dual codes, Cyclic codes and etc. Furthermore, we investigate some concrete research problems on the following topics:

-  Drinfeld modules
-  Class Groups of Function Fields
-  Isogeny Theorems of Elliptic curves
-  Algebraic Geometric Codes
-  Self-dual codes, Formally Self-dual codes, and Invariant theory
-  Cyclic codes and Quasi-cyclic codes

Grading Scheme:
-  Presentation: 50%
-  Research project: 50%

*  A research project consists of one expository paper (typed 8-10 pages) and a class presentation. More details will be announced in class.

Grades and policy:
*  You will be evaluated throughout the whole semester by means of presentations and a research project.