- Code MATH3345
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics
- Academic career UGRD
- AsPr James Borger
- Mode of delivery In Person
- Co-taught Course
First Semester 2022
See Future Offerings
See https://www.anu.edu.au/covid-19-advice. In Sem 1 2022, this course is delivered on campus with adjustments for remote participants.
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. More broadly, the purpose of Galois theory is to study polynomials at a deep level by using symmetries between the roots. This is a pervasive theme in modern mathematics, and Galois theory is traditionally where one first encounters it.
Topics to be covered include:
Galois Theory - fields, field extensions, normal extensions, separable extensions. Revision of group theory, abelian and soluble groups.The main theorem of Galois theory.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.
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 AssessmentAssessment will be based on:
- Assignments 50%
- Mid semester 20%
- Final exam 30%
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WorkloadThree lectures per week, workshops by arrangement.
Requisite and Incompatibility
Tuition fees are for the academic year indicated at the top of the page.
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- Student Contribution Band:
- Unit value:
- 6 units
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Offerings, Dates and Class Summary Links
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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|
|3048||21 Feb 2022||28 Feb 2022||31 Mar 2022||27 May 2022||In Person||View|