MATH3345 Algebra 2 Honours: Field extensions and Galois Theory
Later Year Course
| Offered By | Department of Mathematics |
|---|---|
| Academic Career | Undergraduate |
| Course Subject | Mathematics |
| Offered in | First Semester, 2011 and First Semester, 2012 |
| Unit Value | 6 units |
| Course Description |
Just as there is a formula for solving a quadratic equation, there are similar formulae for solving the general cubic and quartic. Galois theory provides a solution to the corresponding problem for quintics --- there is no such formula in this case! Galois theory also enables us to prove (despite regular claims to the contrary) that there is no ruler and compass construction for trisecting an angle. Topics to be covered include: Galois Theory – fields, field extensions, normal extensions, separable extensions. Revision of group theory, abelian and soluble groups. Galois’ Theorem. Solubility of equations by radicals. Finite fields. Cyclotomic fields. Note: This is an HPC. It emphasises mathematical rigour and proof and continues the development of modern analysis from an abstract viewpoint. |
| Learning Outcomes |
On satisfying the requirements of this course, students will have the knowledge and skills to: 1. Explain the fundamental concepts of field extensions and Galois theory and their role in modern mathematics and applied contexts2. Demonstrate accurate and efficient use of field extensions and Galois theory 3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from field extensions and Galois theory 4. Apply problem-solving using field extensions and Galois theory applied to diverse situations in physics, engineering and other mathematical contexts. |
| Indicative Assessment |
Assessment will be based on:
|
| Workload |
36 lectures, tutorials by arrangement |
| Areas of Interest | Mathematics |
| Requisite Statement | A mark of 60 or more in MATH2322. |
| Consent Required | Departmental consent is required to enrol in this course. |
| Science Group | C |
| Academic Contact | Dr Jim Borger |
The information published on the Study at ANU 2011 website applies to the 2011 academic year only. All information provided on this website replaces the information contained in the Study at ANU 2010 website.
