MATH5645 Algebraic Number Theory

MATH5645 is a Honours and Postgraduate coursework Mathematics course. See the course overview below.

Units of credit: 6

Pre-requisite: MATH2501 or MATH2601 and at least two out of MATH3521, MATH3711 or MATH5706, with an average mark of at least 70

Exclusions:  MATH3570, MATH3611, MATH5705

Cycle of offering: Term 3 

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

More information: 

The recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus. 

The Online Handbook entry contains information about the course. (The timetable is only up-to-date if the course is being offered this year.) 

If you are currently enrolled in MATH5645, you can log into UNSW Moodle for this course.

Course Overview

The theory of finite fields is one of the most elegant areas of mathematics with links to many other areas such as algebra, number theory, combinatotics and graph theory. It also appears in a wide range of applied disciplines such as theoretical computer science, coding theory and cryptography.  

In this course, we start by discussing some fundamental notions of the theory of finite fields such as polynomials, bases, primitive elements and several others. After this, we will move to more advanced topics such as characters and character sums and additive combinatorics which are at the forefront of current developments.