Module: Introduction to Abstract Algebra

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Introduction to Abstract Algebra
Module Code	MS321 (ITS) / MTH1053 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Niamh O'Sullivan
Module Teachers	Thomas Brady
NFQ level	8	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat examination

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. Do basic computations in groups.
2. Compute structures of factor groups
3. Compute structures of abelian groups
4. Construct proofs of simple propositions

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

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

Assessment Breakdown
Continuous Assessment	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Short Answer Questions	n/a	20%	As required

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 3

Indicative Reading List

Jonathan K. Hodge,Steven Schlicker,Ted Sundstrom: 2013, Abstract Algebra, CRC Press, 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, 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, 9780367651787

Other Resources

None