MATH20310 Groups, Rings and Fields

Academic Year 2022/2023

This module is an introduction to group theory, ring theory and field theory. We will cover the following topics: definition and examples of groups, subgroups, cosets and Lagrange's Theorem, the order of an element of a group, normal subgroups and quotient groups, group homomorphisms and the homomorphism theorem, more isomorphism theorems, definitions of a commutative ring with unity, integral domains and fields, units, irreducibles and primes in a ring, ideals and quotient rings, prime and maximal ideals, ring homorphisms and the homomorphism theorem, polynomial rings, the division algorithm, gcd for polynomials, irreducible polynomials and field extensions. Time permitting, we may cover the Sylow theorems, solvable groups and further examples of groups.

[Disclaimer: module content and assessment strategies may be subject to minor changes during the trimester. These changes may not be reflected in this module descriptor at that time, but will be clearly communicated to all students via other means.]

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Curricular information is subject to change

Learning Outcomes:

On successful completion of this module the student should be able to explain what groups, rings, fields, their substructures, associated structures and associated maps are. The student should be able to give examples of these. The student should be able to explain the fundamental results concerning these structures, and solve routine as well as unseen problems.

Student Effort Hours: 
Student Effort Type Hours
Lectures

30
Tutorial

6
Specified Learning Activities

30
Autonomous Student Learning

50
Total

116
Approaches to Teaching and Learning:
The intention is to have all contact hours face-to-face.

Some of the lectures may be in blended or on-line format. 
Requirements, Exclusions and Recommendations
Learning Recommendations:

MATH 10270: Linear Algebra in the Mathematical Sciences


Module Requisites and Incompatibles
Incompatibles:
MST20010 - Algebraic Structures


 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Class Test: In-term test. Unspecified n/a Standard conversion grade scale 40% No

15
Examination: End of trimester exam. 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

85

Carry forward of passed components
No
 
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.