Module: Introduction to Abstract Algebra

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Introduction to Abstract Algebra
Module Code	MTH1053 (ITS: MS321)
Faculty	Science & Health	School	Mathematical Sciences
NFQ level	8	Credit Rating	5

Description

This module provides an introduction to modern abstract algebra. In this module students will develop knowledge and skills in the basic algebraic structure of groups. The participants are expected to have a good knowledge of linear algebra and experience with the abstract approach to mathematics. Students are expected to attend lectures, participate in tutorials and take in-class tests.

Learning Outcomes

1. 1D878E2E-38D5-0001-C25C-C5E0FE10117F
2. Do basic computations in groups.
3.
4. 7,6,8,11
5. 1
6. 1D878E2E-44BC-0001-7F20-8D80108CF4B0
7. Compute structures of factor groups
8.
9. 7,6,8,11,9
10. 2
11. 1D878E2E-5386-0001-A7D7-3B202D591E7D
12. Compute structures of abelian groups
13.
14. 7,6,8,11,9
15. 3
16. 1D878E2E-5C62-0001-D240-C7812F00E660
17. Construct proofs of simple propositions
18.
19. 7,6,8,11,9,10
20. 4

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	Lecture
Tutorial	11	tutorial
Independent Study	90	No Description
Total Workload: 125

Section Breakdown
CRN	11219	Part of Term	Semester 1
Coursework	20%	Examination Weight	80%
Grade Scale	40PASS	Pass Both Elements	N
Resit Category	RC3	Best Mark	Y
Module Co-ordinator	Niamh O'Sullivan	Module Teacher	Thomas Brady

Type	Description	% of total	Assessment Date
Assessment Breakdown
Short Answer Questions	n/a	20%	As required
Formal Examination	End-of-Semester Final Examination	80%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Groups
Definition, examples, basic properties

Subgroups
Definition, examples, classification of subgroups of cyclic groups

Factor groups
Cosets, Lagrange's Theorem, normal subgroups, homomorphisms, factor groups

Finite abelian groups
Direct products, structure of finite abelian groups

Indicative Reading List

Books:

Jonathan K. Hodge,Steven Schlicker,Ted Sundstrom: 2013, Abstract Algebra, CRC Press, 595, 9781466567061
John B. Fraleigh;: 2003, A first course in abstract algebra, Addison-Wesley, Boston, 9780201763904
David S. Dummit,Richard M. Foote: 2004, Abstract Algebra, John Wiley & Sons, 932, 9780471433347
Joseph J. Rotman: 1996, A first course in abstract algebra, Prentice Hall, Upper Saddle River, N.J., 0133113744
Joseph A. Gallian: 2020, Contemporary Abstract Algebra, CRC Press, 624, 9780367651787

Articles:
None

Other Resources

None