| Unit name | Algebraic Number Theory 4 |
|---|---|
| Unit code | MATHM6205 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Dr. Pila |
| Open unit status | Not open |
| Pre-requisites |
Number Theory & Group Theory (MATH 11511, Level 4), Algebra 2 (MATH 21800, Level 5) C0-requisite Number Theory (MATH 30200, Level 6) is recommended but not necessary. Note: Students may not take this unit if they have taken the corresponding Level 6 unit Algebraic Number Theory 3, or if they have previously taken Algebraic Number Theory (MATH 31110, Level 6). |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Algebraic Number Theory is a major branch of Number Theory (alongside Analytic Number Theory) which studies the algebraic properties of algebraic numbers $� in particular the factorization of algebraic integers and ideals $� in a setting in which familiar features of the (usual) integers, such as unique factorization, need not hold. The unit will provide an introduction to algebraic number theory, focussing on algebraic number fields and their rings of integers, ideals and factorization, units and the ideal class group, and will explore some applications to Diophantine equations. In addition, students will have the opportunity to develop an awareness of a broader literature and gain an appreciation of how the basic ideas may be further developed through an individual project.
