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MATH6004 - Discrete Maths

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Title:Discrete Maths
Long Title:Discrete Maths
Module Code:MATH6004
 
Credits: 5
NFQ Level:Fundamental
Field of Study: Mathematics
Valid From: Semester 1 - 2019/20 ( September 2019 )
Module Delivered in 6 programme(s)
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 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).
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
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.
Assessment Breakdown%
Course Work30.00%
End of Module Formal Examination70.00%
Course Work
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
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 2 Mandatory
CR_KITSP_7 Bachelor of Science in Information Technology 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

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Email: help@cit.edu.ie