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Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Introduction to Abstract Algebra
Module Code MS321
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Niamh O'Sullivan
Semester 2: Niamh O'Sullivan
Autumn: Niamh O'Sullivan
Module TeachersNiamh O'Sullivan
NFQ level 8 Credit Rating 5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None
Repeat examination

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

Workload Full-time hours per semester
Type Hours Description
Independent Study90No 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

Definition, examples, basic properties

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 Assessment20% Examination Weight80%
Course Work Breakdown
TypeDescription% of totalAssessment Date
Short Answer Questionsn/a20%As required
Reassessment Requirement Type
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
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

Programme or List of Programmes
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PEMBSc in Physical Education with Maths.
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SMPSCSingle Module Prof. Science and Health
Date of Last Revision26-JAN-12

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