MATH5706 is a Honours and Postgraduate Coursework Mathematics course. See the course overview below.

**Units of credit:** 6

**Exclusions: **MATH3711 (MATH3711 jointly taught with MATH5706)

**Cycle of offering:** Term 1

**Graduate attributes: **The course will enhance your research, inquiry and analytical thinking abilities.

**More information: **This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains information about the course.

If you are currently enrolled in MATH5706, you can log into UNSW Moodle for this course.

#### Course Overview

This course introduces the basic language and ideas of modern algebra, the two main concepts being that of a group and that of a ring. Groups are the vehicle through which mathematicians study symmetry. The data used to define them involves one algebraic operation, group multiplication. Rings on the other hand have two algebraic operations, addition and multiplication, much as you find with ordinary numbers. Historically, solving polynomial equations was a major driving force for the development of group theory, while number theory was the major driving force for ring theory. In particular, we will look at the role rings played in attempts to prove Fermat's last theorem in the 19th century, and to study groups through representation theory in the early 20th century.