Module Details

Module Code: MATH6004
Title: Discrete Maths
Long Title: Discrete Maths
NFQ Level: Fundamental
Valid From: Semester 1 - 2019/20 ( September 2019 )
Duration: 1 Semester
Credits: 5
Field of Study: 4610 - Mathematics
Module Delivered in: 7 programme(s)
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:
# Learning Outcome Description
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.
Dependencies
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 MTU 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
 
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 Morgan’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).
Practical Content
Introduction to appropriate mathematical software. Application of mathematical software to enhance student teaching and learning.
Module Content & Assessment
Assessment Breakdown%
Coursework30.00%
End of Module Formal Examination70.00%

Assessments

Coursework
Assessment Type Other % of Total Mark 20
Timing Week 7 Learning Outcomes 1,2,3
Assessment Description
One hour in-class exam on recurrence relations and mathematical logic.
Assessment Type Practical/Skills Evaluation % of Total Mark 10
Timing Every Second Week Learning Outcomes 1,2,3,4
Assessment Description
Short in-class quizzes.
End of Module Formal Examination
Assessment Type Formal Exam % of Total Mark 70
Timing End-of-Semester Learning Outcomes 1,2,3,4
Assessment Description
End-of-Semester Final Examination
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 University reserves the right to alter the nature and timings of assessment

 

Module Workload

Workload: Full Time
Workload Type Contact Type Workload Description Frequency Average Weekly Learner Workload Hours
Lecture Contact Formal lecture. Every Week 3.00 3
Lab Contact Work on assignment sheets aided by mathematical software. Every Week 1.00 1
Independent & Directed Learning (Non-contact) Non Contact Review of lecture notes and engage in assigned activities. Every Week 3.00 3
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
Workload: Part Time
Workload Type Contact Type Workload Description Frequency Average Weekly Learner Workload Hours
Lecture Contact Formal lecture Every Week 3.00 3
Lab Contact Work on assignment sheets aided by mathematical software. Every Week 1.00 1
Independent & Directed Learning (Non-contact) Non Contact Review of lecture notes and engage in assigned activities Every Week 3.00 3
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. Palgrave Macmillan, [ISBN: 9780230216112].
  • Howard Anton. (2015), Elementary linear algebra with supplemental applications, Eleventh. Wiley, [ISBN: 9781118677308].
Supplementary Book Resources
  • Rowan Garnier & John Taylor. (2010), Discrete Mathematics, Proofs, Structures, and Applications, Third. CRC Press, [ISBN: 9781439812808].
This module does not have any article/paper resources
Other Resources
 
Module Delivered in
Programme Code Programme Semester Delivery
CR_KSDEV_8 Bachelor of Science (Honours) in Software Development 2 Mandatory
CR_KDNET_8 Bachelor of Science (Honours) in Computer Systems 2 Mandatory
CR_KITMN_8 Bachelor of Science (Honours) in IT Management and Cybersecurity 2 Mandatory
CR_KWEBD_8 Bachelor of Science (Honours) in Web Development 2 Mandatory
CR_KITSP_7 Bachelor of Science in Information Technology and Cybersecurity 2 Mandatory
CR_KCOMP_7 Bachelor of Science in Software Development 2 Mandatory
CR_KCOME_6 Higher Certificate in Science in Software Development 2 Mandatory