| Module Title |
Introduction to Abstract Algebra |
| Module Code |
MTH1053 (ITS: MS321) |
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Faculty |
Mathematical Sciences |
School |
Science & Health |
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NFQ level |
8 |
Credit Rating |
5 |
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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.
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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
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| Workload | Full time hours per semester | | Type | Hours | Description |
|---|
| Lecture | 24 | Lecture | | Tutorial | 11 | tutorial | | Independent Study | 90 | No Description |
| Total Workload: 125 |
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| Section Breakdown | | CRN | 11219 | Part of Term | Semester 1 | | Coursework | 0% | Examination Weight | 0% | | Grade Scale | 40PASS | Pass Both Elements | Y | | Resit Category | RC3 | Best Mark | Y | | Module Co-ordinator | Niamh O'Sullivan | Module Teacher | Thomas Brady |
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| Assessment Breakdown |
| Type | Description | % of total | Assessment Date |
|---|
| 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
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Pre-requisite |
None
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Co-requisite |
None |
| Compatibles |
None |
| Incompatibles |
None |
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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
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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
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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 |
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