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MA208 Half Unit

Optimisation Theory

**This information is for the 2018/19 session.**

**Teacher responsible**

Dr Julia Boettcher

**Availability**

This course is available on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics, BSc in Mathematics, Statistics, and Business and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

**Pre-requisites**

Mathematical Methods (MA100) and Introduction to Abstract Mathematics (MA103) are pre-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; shortest paths in directed graphs; algorithms and their running time. Classical results on continuous optimisation: Weierstrass's Theorem on continuous functions on compact set; optimisation of differentiable functions on open sets; Lagrange's Theorem on equality constrained optimisation; Kuhn and Tucker's Theorem on inequality constrained optimisation. Linear programming and duality theory.

**Teaching**

22 hours of lectures and 10 hours of classes in the LT.

**Formative coursework**

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 (100%, duration: 2 hours) in the summer exam period.

** Key facts **

Department: Mathematics

Total students 2017/18: 70

Average class size 2017/18: 15

Capped 2017/18: No

Lecture capture used 2017/18: Yes (LT)

Value: Half Unit

**PDAM skills**

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