| Title: | Discrete Maths |
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| Long Title: | Discrete Maths |
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| Field of Study: |
Mathematics
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| Valid From: |
Semester 1 - 2019/20 ( September 2019 ) |
| Module Coordinator: |
Sean McSweeney |
| Module Author: |
MICHAEL BRENNAN |
| Module Description: |
Discrete mathematics encompasses a range of topics in mathematics.This module focuses in particular on the study of logic, linear algebra and recursion. |
| Learning Outcomes |
| On successful completion of this module the learner will be able to: |
| LO1 |
Model and solve problems using recurrence relations. |
| LO2 |
Explain and use the language, notation, and methods of symbolic logic. |
| LO3 |
Develop and apply mathematical reasoning in constructing valid arguments. |
| LO4 |
Find an inverse of a matrix and use it to solve a system of equations. |
| Pre-requisite learning |
Module Recommendations
This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named CIT module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s). |
|
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list. |
| No incompatible modules listed |
Co-requisite Modules
|
| No Co-requisite modules listed |
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.
|
| No requirements listed |
Module Content & Assessment
| Indicative Content |
|
Recurrence Relations
Recursively defined sequences. Arithmetic and geometric sequences. Modelling using recursively defined sequences.
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Logic
Propositions, logical connectives, truth tables. Compound propositions, logical equivalence, laws of logic including De Morgan’s Laws. Introduction to rules of inference (Modus Ponens/Modus Tollens). Valid arguments.
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Linear Algebra
Matrices and matrix operations, Gaussian elimination, algebra of matrices, matrix inversion. Applications: solving systems of linear equations, networks, geometry of linear transformations (computer graphics).
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Practical Content
Introduction to appropriate mathematical software. Application of mathematical software to enhance student teaching and learning.
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| Assessment Breakdown | % |
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| Course Work | 30.00% |
| End of Module Formal Examination | 70.00% |
| Course Work |
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| Assessment Type |
Assessment Description |
Outcome addressed |
% of total |
Assessment Date |
| Other |
One hour in-class exam on recurrence relations and mathematical logic. |
1,2,3 |
20.0 |
Week 7 |
| Practical/Skills Evaluation |
Short in-class quizzes. |
1,2,3,4 |
10.0 |
Every Second Week |
| End of Module Formal Examination |
|---|
| Assessment Type |
Assessment Description |
Outcome addressed |
% of total |
Assessment Date |
| Formal Exam |
End-of-Semester Final Examination |
1,2,3,4 |
70.0 |
End-of-Semester |
| Reassessment Requirement |
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.
|
The institute reserves the right to alter the nature and timings of assessment
Module Workload
| Workload: Full Time |
| Workload Type |
Workload Description |
Hours |
Frequency |
Average Weekly Learner Workload |
| Lecture |
Formal lecture. |
3.0 |
Every Week |
3.00 |
| Lab |
Work on assignment sheets aided by mathematical software. |
1.0 |
Every Week |
1.00 |
| Independent & Directed Learning (Non-contact) |
Review of lecture notes and engage in assigned activities. |
3.0 |
Every Week |
3.00 |
| Total Hours |
7.00 |
| Total Weekly Learner Workload |
7.00 |
| Total Weekly Contact Hours |
4.00 |
| Workload: Part Time |
| Workload Type |
Workload Description |
Hours |
Frequency |
Average Weekly Learner Workload |
| Lecture |
Formal lecture |
3.0 |
Every Week |
3.00 |
| Lab |
Work on assignment sheets aided by mathematical software. |
1.0 |
Every Week |
1.00 |
| Independent & Directed Learning (Non-contact) |
Review of lecture notes and engage in assigned activities |
3.0 |
Every Week |
3.00 |
| Total Hours |
7.00 |
| Total Weekly Learner Workload |
7.00 |
| Total Weekly Contact Hours |
4.00 |
Module Resources
| Recommended Book Resources |
|---|
- Peter Grossman 2009, Discrete Mathematics for Computing, Third Ed., Palgrave Macmillan [ISBN: 9780230216112]
- Howard Anton 2015, Elementary linear algebra with supplemental applications, Eleventh Ed., Wiley [ISBN: 9781118677308]
| | Supplementary Book Resources |
|---|
- Rowan Garnier & John Taylor 2010, Discrete Mathematics, Proofs, Structures, and Applications, Third Ed., CRC Press [ISBN: 9781439812808]
| | This module does not have any article/paper resources |
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| Other Resources |
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- Website: Maple Website
- Website: Wolfram's Mathworld
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Module Delivered in
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