GALOIS THEORY - 2017/8
Module code: MAT3011
FISHER D Dr (Maths)
Number of Credits
FHEQ Level 6
Module cap (Maximum number of students)
Overall student workload
Lecture Hours: 36
|Assessment type||Unit of assessment||Weighting|
|School-timetabled exam/test||IN-SEMESTER TEST||20%|
Prerequisites / Co-requisites
MAT2048 Groups and Rings
Galois Theory applies the principles of algebraic structure to questions about the solvability of polynomial equations. The feasibility of certain geometrical constructions is also considered.
review the theory of groups, rings, fields and polynomials.
develop and apply the theory of field extensions and Galois groups.
show the power of abstract algebra to produce practical and applicable results.
|Demonstrate a deeper appreciation of algebraic structures and of the power of linking different structures||KCT|
|Solve cubic and quartic equations, understanding the limitations of the methods||KC|
|Evaluate the degree of finite field extensions and apply this to algebraic and geometric examples||KC|
|Evaluate specific Galois groups and relate their structure to that of field extensions and to the solvability of polynomial equations .||KC|
|Construct simple proofs similar to those encountered in the module.||KCT|
C - Cognitive/analytical
K - Subject knowledge
T - Transferable skills
P - Professional/Practical skills
Indicative content includes:
Theory of polynomials. Criteria for irreducibility.
Solution of cubic and quartic equations.
Field extensions. The degree of an extension. The Tower law.
Field automorphisms and their properties.
The Galois correspondence and the fundamental theorem.
Solvable groups. Conditions for solvability of polynomials by radicals.
Methods of Teaching / Learning
The learning and teaching strategy is designed to provide:
An awareness of the applicability of abstract algebra to classical problems.
Knowledge of the historical context in which the subject material was developed.
Experience of the methods used to interpret, understand and solve problems in Galois theory.
The learning and teaching methods include:
Three 50-minute lectures per week for eleven weeks, some being used as tutorials, problem classes and in-semester tests.
Online notes supplemented by additional examples in lectures.
Two unassessed coursework assignments, marked and returned.
Personal assistance given to individuals and small groups in office hours.
The assessment strategy is designed to provide students with the opportunity to demonstrate their ability to
· construct and interpret mathematical arguments in the context of this module;
· display subject knowledge by recalling key definitions and results;
· apply the techniques learnt to both routine and unfamiliar problems.
Thus, the summative assessment for this module consists of:
· One two-hour examination at the end of Semester 1, worth 80% of the module mark.
· In-semester test, worth 20% of the module mark.
Formative assessment and feedback
Students receive written comments on their marked coursework assignments. Maple TA may be used in assignments to provide immediate is used for part of the assignments and provides instant grading and feedback.s to solve problemsials, complex numbers,grading and feedback. Verbal feedback is provided in lectures and office hours.
Reading list for GALOIS THEORY : http://aspire.surrey.ac.uk/modules/mat3011
Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.