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Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Optimisation
Module Code MS534
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Thomas Brady
Semester 2: Thomas Brady
Autumn: Thomas Brady
Module TeachersThomas Brady
NFQ level 9 Credit Rating 7.5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None

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.

Workload Full-time hours per semester
Type Hours Description
Independent Study170Independent learning
Directed learning3Final Exam
Total Workload: 221

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, trees, shortest path algorithms, greedy algorithm, matroids

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

matching problems, bipartite matching, weighted matching

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

Assessment Breakdown
Continuous Assessment20% Examination Weight80%
Course Work Breakdown
TypeDescription% of totalAssessment Date
In Class Test6 in-class tests15%Every Second Week
ParticipationWebwork homework5%As required
Reassessment Requirement Type
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
This module is category 3
Indicative Reading List

  • 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
Other Resources

Programme or List of Programmes
IFPFIMPre-Masters Intl. Foundation Programme
MFMMSc in Financial Mathematics

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