MATH8009 - Maths Methods and Modelling

Module Details

Module Code: MATH8009
Title: Maths Methods and Modelling
Long Title: Maths Methods and Modelling
NFQ Level: Advanced
Valid From: Semester 1 - 2018/19 ( September 2018 )
Duration: 1 Semester
Credits: 5
Field of Study: 4610 - Mathematics
Module Delivered in: 2 programme(s)
Module Description: This module will explore various mathematical techniques and will focus on mathematical models of real world processes, their formulation and methods of solution - both numerical and analytical. Central to the module will be practical problems that arise in industry and commerce.
 
Learning Outcomes
On successful completion of this module the learner will be able to:
# Learning Outcome Description
LO1 Formulate and analyse well posed linear, exponential, Markov chain and statistical models.
LO2 Examine linear systems, matrix operations and Gaussian elimination.
LO3 Select and develop numerical methods/algorithms to solve statistical models.
LO4 Write computer programs which yield sensible answers to linear, exponential and statistical models.
LO5 Develop programs to implement numerical algorithms to solve formulated models.
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
Introduction to modelling
Highlight the pattern in the modelling process. Examine linear and exponential functions – with models.
Linear Algebra
Introduce linear systems, matrices and Gaussian elimination, in addition to covering topics such as matrix operations and inverse of a matrix and linear independence.
Markov chains
Introduce and explore properties of discrete time Markov chains. Demonstrate how effective Markov chains are at modelling practical situations.
Statistical modelling
Derive and model situations using statistical distribution functions, including normal, binomial and Poisson distributions. Explore real world statistical models.
Linear regression analysis
Describe the relationship between two quantitative measurements (scatter plots); the strength of the relationship (correlation coefficient); and model the relationship (simple linear regression).
Software
R, Excel, VBA.
Module Content & Assessment
Assessment Breakdown%
Coursework50.00%
End of Module Formal Examination50.00%

Assessments

Coursework
Assessment Type Practical/Skills Evaluation % of Total Mark 25
Timing Week 6 Learning Outcomes 1,2,4,5
Assessment Description
Mathematical Analysis and Linear Algebra
Assessment Type Practical/Skills Evaluation % of Total Mark 25
Timing Week 12 Learning Outcomes 1,3,4,5
Assessment Description
Numerical Methods
End of Module Formal Examination
Assessment Type Formal Exam % of Total Mark 50
Timing End-of-Semester Learning Outcomes 1,2,3
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 Module Content delivery Every Week 2.00 2
Lab Contact Software packages Every Week 2.00 2
Independent & Directed Learning (Non-contact) Non Contact Review of lecture notes and solving problems from worksheets 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 Module Content delivery Every Week 1.50 1.5
Lab Contact Software packages Every Week 1.50 1.5
Lecturer-Supervised Learning (Contact) Contact Solving problems from worksheets Every Week 1.00 1
Independent & Directed Learning (Non-contact) Non Contact Review of lecture notes and solving problems from worksheets 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
  • Gilbert Strang. (2016), Introduction to Linear Algebra, 5th. Wellesley-Cambridge Press, [ISBN: 9780980232776].
  • Milton Abramowitz, Irene Stegun. (2014), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, [ISBN: 9781614276173].
  • Nicolas Privault. (2013), Understanding Markov Chains: Examples and Applications, Springer, [ISBN: 9814451509].
  • Daniel P. Maki, Maynard Thompson. (2006), Mathematical modeling and computer simulation, Thomson Brooks/Cole, Belmont, CA, [ISBN: 0534384781].
Supplementary Book Resources
  • Gary N. Felder. (2015), Mathematical methods for physics and engineering, John Wiley & Sons, Cambridge, [ISBN: 1118449606].
  • Bennett, J and Briggs, W.. (2014), Using and understanding mathematics: A quantitative reasoning approach, 6th. Pearson, [ISBN: 1292062304].
  • D. W. Jordan and P. Smith. (2008), Mathematical techniques, 4th. OUP Oxford, [ISBN: 0199282013].
  • Frank R. Giordano, Maurice Weir. (1997), First Course in Mathematical Modeling, 2nd. Brooks/Cole, [ISBN: 0534222482].
This module does not have any article/paper resources
Other Resources
 
Module Delivered in
Programme Code Programme Semester Delivery
CR_SDAAN_8 Higher Diploma in Science in Data Science & Analytics 1 Mandatory
CR_SDAAN_9 Master of Science in Data Science & Analytics 1 Mandatory