- Code MATH6215
- Unit Value 6 units
- Offered by Department of Mathematics
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics
- Academic career PGRD
- AsPr John Urbas
- Dr Jarod Alper
- Mode of delivery In Person
First Semester 2015
See Future Offerings
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.
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.
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)
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36 lectures, tutorials by arrangement
Requisite and Incompatibility
You will need to contact the Department of Mathematics to request a permission code to enrol in this course.
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:
- 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.
Offerings, Dates and Class Summary Links
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
|Class number||Class start date||Last day to enrol||Census date||Class end date||Mode Of Delivery||Class Summary|
|2172||16 Feb 2015||06 Mar 2015||31 Mar 2015||29 May 2015||In Person||N/A|