| Module Code: |
H6DISMTHS |
|
Long Title
|
Discrete Mathematics
|
|
Title
|
Discrete Mathematics
|
| Module Level: |
LEVEL 6 |
| EQF Level: |
5 |
| EHEA Level: |
Short Cycle |
| Module Coordinator: |
MICHAEL BRADFORD |
| Module Author: |
MICHAEL BRADFORD |
| Departments: |
School of Computing
|
| Specifications of the qualifications and experience required of staff |
Master’s degree in mathematics, computing or cognate discipline. May have industry experience also.
|
| Learning Outcomes |
| On successful completion of this module the learner will be able to: |
| # |
Learning Outcome Description |
| LO1 |
Construct logical mathematical arguments and proofs. |
| LO2 |
Apply set algebra and logic operations to demonstrate problem solving and mathematical reasoning capabilities. |
| LO3 |
Associate the rules of sets and operations to the areas of Relations and Functions. |
| LO4 |
Construct and investigate a range of functions and describe their representations. |
| LO5 |
Apply set theoretical concepts and methods of counting to solve combinatorial problems. |
| LO6 |
Apply graph theory concepts to represent a set of finite objects and their inter-relationships. |
| Dependencies |
Module Recommendations
This is prior learning (or a practical skill) that is required before enrolment on this module. While the prior learning is expressed as named NCI module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).
|
| No recommendations listed |
Co-requisite Modules
|
| No Co-requisite modules listed |
| Entry requirements |
See section 4.2 Entry procedures and criteria for the programme including procedures recognition of prior learning
|
Module Content & Assessment
| Indicative Content |
|
Logic & Proof
Propositional Logic. Boolean Operators. Truth Tables. Boolean Expressions
|
|
Logic & Proof
Predicates and Quantifiers. Methods of Mathematical Proof
|
|
Set Theory
Naïve Set Theory. Finite and infinite sets. Set Operations
|
|
Set Theory
Partitions . Product Set and Power Set
|
|
Relations & Functions
Binary Relations. Properties of Relations. Equivalence Relations .
|
|
Relations & Functions
Partial Orders. Properties of Functions. Composition of Functions. Inverse Functions
|
|
Recurrence Relations & Generating Functions
Polynomials. Ordinary and Exponential Generating Functions
|
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Recurrence Relations & Generating Functions
Sequences and Recurrence Relations. Solution of Recurrence Relations. Linear Homogeneous Recurrence Relations. Linear Non-Homogeneous Recurrence Relations
|
|
Combinatorics
The Sum Rule and the Product Rule. The Pigeonhole Principle. The Inclusion-Exclusion Principle
|
|
Combinatorics
The Factorial Function. Permutations and Combinations
|
|
Graph Theory
Definition and Examples. Directed Graphs. Walks, Trails, Paths, Circuits, and Cycles
|
|
Graph Theory
Trees. Planar Graphs. Colouring and Matching Graphs.
|
| Assessment Breakdown | % |
|---|
| Coursework | 40.00% |
| End of Module Assessment | 60.00% |
AssessmentsFull Time
| Coursework |
| Assessment Type: |
Formative Assessment |
% of total: |
Non-Marked |
| Assessment Date: |
n/a |
Outcome addressed: |
1,2,3,4,5,6 |
| Non-Marked: |
Yes |
Assessment Description:
Ongoing independent and group class activities and feedback. |
|
| Assessment Type: |
Continuous Assessment |
% of total: |
40 |
| Assessment Date: |
n/a |
Outcome addressed: |
1,2,3,4,5 |
| Non-Marked: |
No |
Assessment Description:
A set of questions relating to Logic, Set Theory, Relations & Functions, and Recurrence Relations & Generating Functions, and Combinatorics. |
|
| End of Module Assessment |
| Assessment Type: |
Terminal Exam |
% of total: |
60 |
| Assessment Date: |
End-of-Semester |
Outcome addressed: |
1,2,3,4,5,6 |
| Non-Marked: |
No |
Assessment Description:
Written examination with questions from all module topic areas. |
|
| 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.
|
Reassessment Description
The repeat strategy for this module is an examination. All learning outcomes will be assessed in the repeat exam.
|
NCIRL reserves the right to alter the nature and timings of assessment
Module Workload
| Module Target Workload Hours 0 Hours |
| Workload: Full Time |
| Workload Type |
Workload Description |
Hours |
Frequency |
Average Weekly Learner Workload |
| Lecture |
Classroom & Demonstrations (hours) |
24 |
Per Semester |
2.00 |
| Tutorial |
Other hours (Practical/Tutorial) |
36 |
Per Semester |
3.00 |
| Independent Learning |
Independent learning (hours) |
65 |
Per Semester |
5.42 |
| Total Weekly Contact Hours |
5.00 |
| Workload: Part Time |
| Workload Type |
Workload Description |
Hours |
Frequency |
Average Weekly Learner Workload |
| Lecture |
No Description |
24 |
Every Week |
24.00 |
| Tutorial |
No Description |
36 |
Every Week |
36.00 |
| Independent Learning |
No Description |
65 |
Every Week |
65.00 |
| Total Weekly Contact Hours |
60.00 |
Module Resources
| Recommended Book Resources |
|---|
-
Ferland K.. (2017), Discrete Mathematics and Applications (2nd ed), Chapman and Hall/CRC.
-
Kenneth H. Rosen. (2018), Discrete Mathematics and Its Applications, 8th Edition. McGraw-Hill Education, [ISBN: 978-1260091991].
| | Supplementary Book Resources |
|---|
-
Oscar Levin. (2016), Discrete Mathematics, Createspace Independent Publishing Platform, p.342, [ISBN: 978-1534970748].
-
Jonathan L. Gross,Jay Yellen,Mark Anderson. (2018), Graph Theory and Its Applications, Chapman & Hall/CRC, p.577, [ISBN: 978-1482249484].
| | This module does not have any article/paper resources |
|---|
| This module does not have any other resources |
|---|
|
