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Semester 2
Galois Theory (MATH10080)
Subject
Mathematics
College
SCE
Credits
10
Normal Year Taken
4
Delivery Session Year
2023/2024
Pre-requisites
Course Summary
This is a course in abstract algebra, although connections with other fields will be stressed as often as possible. It will cover some of the jewels in the crown of undergraduate mathematics, drawing together groups, rings and fields to solve problems that resisted the efforts of mathematicians for many centuries. The powerful central ideas of this course are now crucial to many modern problems in algebra, differential equations, geometry, number theory and topology.
Course Description
- Fields: examples, constructions and extensions- Separability, normality & splitting fields- Field automorphisms & Galois groups- The fundamental theorem of Galois Theory- Solvable groups and the insolubility of the general quintic- Ruler and Compass constructions- Calculation of Galois groups
Assessment Information
Written Exam 80%, Coursework 20%, Practical Exam 0%
Additional Assessment Information
Coursework 20%, Examination 80%
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