MATH40710 Galois Theory

Academic Year 2023/2024

This is a standard course on field and Galois theory, a cornerstone of advanced algebra. It is the culmination of undergraduate mathematics in algebra, using the theory of groups, rings, modules, and fields in a beautiful way to solve central problems of both ancient and modern mathematics.

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Curricular information is subject to change

Learning Outcomes:

Upon completion of this module, a successful student should:
1. have a good working knowledge of several constructions of fields;
2. be able to compute the Galois group of the splitting field of a polynomial;
3. have a good understanding of the Galois correspondence theorem;
4. be able to use the Galois correspondence to obtain the subfield lattice of a Galois extension from the subgroup lattice of the Galois group of that extension and vice versa;
5. be able to use the discriminant of a polynomial as a tool in the classification of its Galois group;
6. be able to compute the fixed fields of subgroups of the Galois group of a field extension;
7. be able to identity normal field extensions;
8. be familiar with a further topic in algebra that relies on Galois theory

Student Effort Hours: 
Student Effort Type Hours
Lectures

30
Tutorial

6
Autonomous Student Learning

84
Total

120
Approaches to Teaching and Learning:
We use state-of-the-art teaching methods in advanced algebra, whiteboards as well as blackboards. 
Requirements, Exclusions and Recommendations

Not applicable to this module.


Module Requisites and Incompatibles
Not applicable to this module.
 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Class Test: midterm class test Week 7 n/a Standard conversion grade scale 40% No

25
Examination: end of trimester exam 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

75

Carry forward of passed components
Yes
 
Resit In Terminal Exam
Autumn Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
 
Spring
      
Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Fri 09:00 - 09:50
Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Thurs 12:00 - 12:50
Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Thurs 15:00 - 15:50
Spring