MA208      Half Unit
Optimisation Theory

This information is for the 2025/26 session.

Course Convenor

Prof Giacomo Zambelli

Availability

This course is compulsory on the BSc in Mathematics with Data Science. This course is available on the BSc in Data Science, BSc in Mathematics and Economics, BSc in Mathematics with Economics, BSc in Mathematics, Statistics and Business, Erasmus Reciprocal Programme of Study and Exchange Programme for Students from University of California, Berkeley. This course is freely available as an outside option to students on other programmes where regulations permit. It does not require permission. This course is available with permission to General Course students.

Requisites

Pre-requisites:

Students must have completed MA100 and MA103 before taking this course.

Additional requisites:

Real Analysis (MA203) is desirable, and students who have not done MA203 should contact the teacher responsible.

Course content

Based on the relevant mathematical theory, the course describes various techniques of optimisation and shows how they can be applied. More precisely, the topics covered are: Introduction and review of mathematical background. Introduction to combinatorial optimisation; maximum matchings in bipartite graphs; algorithms and their running time. Classical results on continuous optimisation: Weierstrass's Theorem concerning continuous functions on compact sets; optimisation of differentiable functions on open sets; convex functions and convex sets, Lagrangian duality, Lagrange's Theorem on equality constrained optimisation; Karush, Kuhn, and Tucker's Theorem on inequality constrained optimisation. Linear programming and duality theory.

Teaching

20 hours of lectures and 10 hours of classes in the Winter Term.

Formative assessment

Written answers to set problems will be expected on a weekly basis.

 

Indicative reading

Good sources of literature are R K Sundaram, A First Course in Optimisation Theory; N L Biggs, Discrete Mathematics (2nd edition). Additional notes will be made available throughout the course.

Assessment

Exam (90%), duration: 120 Minutes in the Spring exam period

Continuous assessment (10%)


Key facts

Department: Mathematics

Course Study Period: Winter Term

Unit value: Half unit

FHEQ Level: Level 5

CEFR Level: Null

Total students 2024/25: 82

Average class size 2024/25: 16

Capped 2024/25: No
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Personal development skills

  • Self-management
  • Problem solving
  • Application of information skills
  • Communication
  • Application of numeracy skills
  • Specialist skills