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: NoCourse selection videos
Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.
Personal development skills
- Self-management
- Problem solving
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- Application of numeracy skills
- Specialist skills