Module Title  Group Theory and Galois Theory 
School  Mathematics 
Department  Mathematics 
Module Code  06 22500 
Module Lead  S Shpectorov 
Level  Honours Level 
Credits  20 
Semester  Full Term 
Prerequisites 
LI Linear Algebra & Linear Programming  (06 25765)
LH Algebra & Combinatorics 2  (06 27142)
Linear Algebra  (06 15552)
LI Algebra & Combinatorics 2  (06 25665)

Corequisites 

Restrictions  None 
Contact Hours 
Lecture46 hours
Seminar0 hours
Tutorial10 hours
Project supervision0 hours
Demonstration0 hours
Practical Classes and workshops0 hours
Supervised time in studio/workshop0 hours
Fieldwork0 hours
External Visits0 hours
Work based learning0 hours
Guided independent study0 hours
Placement0 hours
Year Abroad0 hours

Exclusions  
Description  Group theory is the mathematical study of symmetry. In this course groups and their actions on sets, and geometric structures will be studied. A highlight of this course is Sylow's Theorem, which is probably the most fundamental results about the structure of finite groups. Finite simple groups are the building blocks from which all finite groups are built (the JordanHolder theorem makes this statement precise) and these will be studied. The alternating groups and linear groups will be introduced as first examples of nonabelian simple groups.
Later in the course field automorphisms may be considered so that an overview of Galois Theory can be given.
is related to the structure of the field extension via the Fundamental Theorem of Galois Theory 
Learning Outcomes  By the end of the module the student will be able to: Understand and apply the theory of groups and group actions and calculate in examples;
 Understand the concepts of homomorphism, isomorphisms and quotient groups;
 Analyse the structure of groups using Sylow’s theorem and other results from the course, for example, the JordanHolder theorem.

Assessment 
2250001 : Raw Module Mark : Coursework (0%)
2250003 : Final Module Mark : Coursework (100%)

Assessment Methods & Exceptions  Assessments: 2250001: Exam : Exam (CT)  Written Unseen (90%)
2250002 : Continuous Assessment : Coursework or class Tests (10%)

Other  None 
Reading List 
