MA204-5-SP-CO:
Abstract Algebra

The details
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Undergraduate: Level 5
Current
Monday 13 January 2025
Friday 21 March 2025
15
10 May 2024

 

Requisites for this module
(none)
(none)
MA201
(none)

 

MA301, MA316

Key module for

BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
MMATG198 Mathematics,
BSC G1G4 Mathematics with Computing (Including Year Abroad),
BSC G1G8 Mathematics with Computing (Including Foundation Year),
BSC G1GK Mathematics with Computing,
BSC G1IK Mathematics with Computing (Including Placement Year),
MSCIG199 Mathematics and Data Science

Module description

This module introduces the key abstract algebraic objects of groups, rings and fields and develops their fundamental theory. The theory will be illustrated and made concrete through numerous examples in settings that students will already have encountered.

Module aims

The aim of this module is:



  • To introduce basic principles of abstract algebraic structures and to teach how an extensive and important theory can be developed by logical deductions from a small number of axioms.

Module learning outcomes

By the end of this module, students will be expected to be able to:



  1. Know and understand the formal definitions for Groups, Rings, and Fields.

  2. Produce simple proofs based on the algebraic axioms.

  3. Be familiar with standard examples of these algebras, including the Symmetric Group, Modular Arithmetic, finite abelian groups, Polynomial and Matrix Rings, and examples of finite fields.

  4. Be familiar with the notions of subalgebras as they apply to Groups, Rings, and Fields.

  5. Understand the notion of isomorphism and homomorphism of these algebra types.

Module information

Syllabus



  • Groups: Binary operations, groups, subgroups, cyclic groups, direct products, groups of permutations, cosets, Lagrange's theorem.

  • Isomorphisms and homomorphisms of groups.

  • Rings, Fields, zero divisors and integral domains, subrings, ideals.

  • Direct products, homomorphisms, Isomorphisms.

  • The Ring of integers modulo n, polynomial rings.

Learning and teaching methods

Teaching in the School will be delivered using a range of face-to-face lectures, classes, and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.

Bibliography

This module does not appear to have a published bibliography for this year.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   Assignment  18/02/2025   
Exam  Main exam: In-Person, Closed Book, 120 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Closed Book, 120 minutes during September (Reassessment Period) 

Exam format definitions

  • Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
  • In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
  • In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
  • In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Overall assessment

Coursework Exam
10% 90%

Reassessment

Coursework Exam
10% 90%
Module supervisor and teaching staff
Prof Gerald Williams, email: gerald.williams@essex.ac.uk.
Prof. Gerald Williams
maths@essex.ac.uk

 

Availability
Yes
No
No

External examiner

Prof Stephen Langdon
Brunel University London
Professor
Dr Rachel Quinlan
National University of Ireland, Galway
Senior Lecturer in Mathematics
Resources
Available via Moodle
Of 33 hours, 33 (100%) hours available to students:
0 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s), module, or event type.

 

Further information
Mathematics, Statistics and Actuarial Science (School of)

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