• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
Specialist
• Course subject Mathematics
• Areas of interest Mathematics
• Course convener
• Dr James Borger
• Mode of delivery In Person
• Co-taught Course
• Offered in First Semester 2020
Algebra 2: Field extensions and Galois Theory (MATH6215)

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: Graduate students attend joint classes with undergraduates but will be assessed separately.

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

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 contexts
2. 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:

• Assignment 1 (20%; LO 1-4)
• Assignment 2 (20%; LO 1-4)
• Assignment 3 (20%; LO 1-4)
• Final exam (40%; LO 1-4)

In response to COVID-19: Please note that Semester 2 Class Summary information (available under the classes tab) is as up to date as possible. Changes to Class Summaries not captured by this publication will be available to enrolled students via Wattle.

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

Three lectures per week, workshops by arrangement.

## Requisite and Incompatibility

You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.

## Fees

Tuition fees are for the academic year indicated at the top of the page.

If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Student Contribution Band:
2
Unit value:
6 units

If you are an undergraduate student and have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). You can find your student contribution amount for each course at Fees.  Where there is a unit range displayed for this course, not all unit options below may be available.

Units EFTSL
6.00 0.12500

## Course fees

Domestic fee paying students
Year Fee
2020 \$4050
International fee paying students
Year Fee
2020 \$5760
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

The list of offerings for future years is indicative only.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.

### First Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
3587 24 Feb 2020 02 Mar 2020 08 May 2020 05 Jun 2020 In Person View