Title:  Discrete Maths 
Long Title:  Discrete Maths 
Field of Study: 
Mathematics

Valid From: 
Semester 1  2018/19 ( September 2018 ) 
Module Coordinator: 
David Goulding 
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 recursive thinking. 
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. 
LO5 
Use a Computer Algebra System (e.g. Maple) to explore logic and linear algebra. 
Prerequisite 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 
Corequisite Modules

No Corequisite 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 
Corequisites

No Co Requisites listed 
Module Content & Assessment
Indicative Content 
Recurrence Relations
Recursively defined sequences. Arithmetic and geometric sequences. Modelling using recursively defined sequences.

Logic
Propositions, logical connectives, truth tables. Compound propositions, logical equivalence, laws of logic including De Morganâ€™s Laws. Introduction to rules of inference (Modus Ponens/Modus Tollens). Valid arguments.

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).

Maple
Introduction to a computer algebra system(CAS) such as Maple or an equivalent. The following is an indicative list of practicals that may be attempted in this course:
1. The CAS environment, command syntax, creating worksheets to include text,
calculations, graphics and analysis.
2. Assignment of variables, expressions, lists, sets, operations on lists
including the map command, solving equations, sequences, limits.
3. Simplify logical expressions using CAS commands. Construct truth tables. Analyse arguments.
4. Algebra of matrices. Determining matrix inverses. Solving linear systems. Use of a CAS to visualise a linear system's solution space.

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 
Other 
One hour inclass exam on recurrence relations and mathematical logic. 
1,2,3 
20.0 
Week 7 
Practical/Skills Evaluation 
Short quizzes and CAS/Maple lab work. 
1,2,3,4,5 
10.0 
Every Second Week 
End of Module Formal Examination 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Formal Exam 
EndofSemester Final Examination 
1,2,3,4 
70.0 
EndofSemester 
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 
Tutorial 
Work on assignment sheets. 
0.5 
Every Week 
0.50 
Lab 
CAS/Maple Lab. 
0.5 
Every Week 
0.50 
Independent & Directed Learning (Noncontact) 
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 
Tutorial 
Work on assignment sheets. 
0.5 
Every Week 
0.50 
Lab 
CAS/Maple lab. 
0.5 
Every Week 
0.50 
Independent & Directed Learning (Noncontact) 
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 

Other Resources 

 Website: Maple Website
 Website: Wolfram's Mathworld

Module Delivered in
