| Module Title |
Discrete Mathematics |
| Module Code |
MTH1095 (ITS: MTH1090, MS342) |
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Faculty |
Science & Health |
School |
Mathematical Sciences |
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NFQ level |
8 |
Credit Rating |
5 |
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Description
This module introduces students to some fundamental ideas and practices in the areas of Logic & Proof, Number Theory, Combinatorics and Graph Theory.
Students will be expected to work collaboratively to discuss and reflect on their learning.
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Learning Outcomes
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| Workload | Full time hours per semester | | Type | Hours | Description |
|---|
| Lecture | 24 | No Description | | Tutorial | 12 | No Description | | Assignment Completion | 3 | No Description | | Guided learning activities | 24 | Completion of problem sets | | Independent Study | 62 | No Description |
| Total Workload: 125 |
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| Section Breakdown | | CRN | 21467 | Part of Term | Semester 2 | | Coursework | 20% | Examination Weight | 80% | | Grade Scale | 40PASS | Pass Both Elements | N | | Resit Category | RC3 | Best Mark | Y | | Module Co-ordinator | Sinead Breen | Module Teacher | Niamh O'Sullivan |
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| Assessment Breakdown |
| Type | Description | % of total | Assessment Date |
|---|
| In Class Test | n/a | 10% | Week 7 | | Assignment | n/a | 10% | Week 11 | | Formal Examination | n/a | 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
Set Theory
revision of basic definitions and operations
Logic & Proof
simple & compound propositions, conditional connectives, truth tables, argument validation, quantifiers, methods of proof (direct, contraposition, contradiction, induction), counterexamples
Number Theory
divisibility of integers, properties of primes, modular arithmetic & linear congruences, applications in cryptography
Graph Theory
introduction to graphs & terminology, Euler circuits & trails, isomorphism, planarity, adjacency matrices
Combinatorics
addition & multiplication principles, permutations & combinations, arrangements and selections with repetitions, distributions, Pigeonhole Principle
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Indicative Reading List
Books:
- Tucker, A: 0, Applied Combinatorics, Wiley,
- Silverman, J.H: 0, A friendly introduction to Number Theory, Pearson,
- Chartrand, G., Polimeni, A.D. & P. Zhang, P: 0, Mathematical proofs: A transition to advanced mathematics, Pearson,
- Voloshin, V: 0, Introduction to Graph Theory, Nova Science,
Articles:
None |
Other Resources
None |
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