Module: Optimisation

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Optimisation
Module Code	MTH1073 (ITS: MS534)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	9	Credit Rating	7.5

Description

This module provides an introduction to combinatorial optimisation. In this module students will develop knowledge and skills in the basic combinatorial algorithms applied to optimisation and the mathematics behind these algorithms. They will also interpret the algorithm outputs and translate this into knowledge about the geometry of the original problem and its solution. The participants are expected to have a good knowledge of linear algebra and experience with the abstract approach to mathematics. This module provides the first steps in the discipline known as operations research. Students are expected to attend lectures, participate in tutorials, take in-class tests and do online homework.

Learning Outcomes

1. Apply algorithms in optimisation problems
2. Demonstrate a knowledge of the mathematics underlying algorithms
3. Interpret algorithm output
4. Construct proofs of simple propositions
5. Determine geometry of optimisation problems from linear algebra computations.

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	36	Lecture
Tutorial	12	Tutorial
Independent Study	170	Independent learning
Directed learning	3	Final Exam
Total Workload: 221

Section Breakdown
CRN	20800	Part of Term	Semester 2
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC3	Best Mark	Y
Module Co-ordinator	Marco Viola	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	6 in-class tests	15%	Every Second Week
Participation	Webwork homework	5%	As required
Formal Examination	End-of-Semester Final Examination	80%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Graphs
Graphs, trees, shortest path algorithms, greedy algorithm, matroids

Polytopes
Polytopes, Farkas' Lemma, linear programming, the geometry of linear inequalities

Matchings
matching problems, bipartite matching, weighted matching

Network flow
max-flow via simplex method, and via graph search

Indicative Reading List

Books:

Eugene Lawler: 2001, Combinatorial optimization, Dover Publications, Mineola, N.Y., 0486414531
Hamdy A. Taha,: 0, Operations Research: An Introduction, 9780132555937
David G. Luenberger, Yinyu Ye (Contributor): 0, Linear and Nonlinear Programming, 978-1441945044

Articles:
None

Other Resources

None