Mathematics is an important component of Computer Science. This module offers a first introduction to some of the principles that computer scientists will use and apply to solving everyday tasks and introduces students to sets, relations, combinatorial graphs and functions.
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1
Manipulate a wide variety of algebraic expressions and equations.
LO2
Work with the abstract concepts of set and relation.
LO3
Model and solve problems using combinatorial graphs.
LO4
Evaluate real-valued functions and interpret the relationship between real-valued functions and their graphical representations.
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).
No recommendations listed
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
Co-requisites
No Co Requisites listed
Module Content & Assessment
Indicative Content
Algebra
Simplification and factorisation of expressions. Manipulation and solving of equations. Exponents: definition and properties. Logarithms: definition and properties.
Sets and Relations
Set notation and Venn diagrams. Set operations and the laws of set theory. The cardinality of sets. Generating subsets lexicographically with binary numbers. Cartesian products. Relations: definition, notation and graphical representation. Equivalence relations and equivalence classes.
Combinatorial Graphs
Edges, nodes, graphs, connectedness and valency. Trees, paths and cycles. Eulerian paths and Fleury's algorithm. Hamiltonian paths and Dirac's theorem.
Functions
Functions described as relations. Dependent and independent variables. The graph of a function. Composition and inverses. Examples of linear, quadratic, exponential and logarithmic functions.
Assessment Breakdown
%
Course Work
30.00%
End of Module Formal Examination
70.00%
Course Work
Assessment Type
Assessment Description
Outcome addressed
% of total
Assessment Date
Short Answer Questions
In class test.
1
15.0
Week 5
Short Answer Questions
In-class test.
2,3
15.0
Week 9
End of Module Formal Examination
Assessment Type
Assessment Description
Outcome addressed
% of total
Assessment Date
Formal Exam
End of Semester Formal 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
Lecture underpinning learning outcomes
3.0
Every Week
3.00
Tutorial
Tutorial supporting content given in lecture
1.0
Every Week
1.00
Independent Learning
Independent study
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
Lecture underpinning learning outcomes
3.0
Every Week
3.00
Tutorial
Tutorial supporting content given in class
1.0
Every Week
1.00
Independent Learning
Independent study
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
Taylor, J. and Garnier, R. 2010, Discrete Mathematics, Proofs, Structures, and Applications, 3 Ed., CRC Press [ISBN: 978143981280]
Stroud, K.A. and Booth, Dexter J. 2009, Foundation Mathematics, Palgrave MacMillan England [ISBN: 9780230579071]
Supplementary Book Resources
Grossman, P. 2009, Discrete Mathematics for Computing, 3 Ed., Palgrave Macmillan [ISBN: 9780230216112]
This module does not have any article/paper resources