## MA208Half UnitOptimisation Theory

This information is for the 2022/23 session.

Teacher responsible

Prof Julia Boettcher

Availability

This course is available on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics, BSc in Data Science, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. 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 concerning continuous functions on compact sets; optimisation of differentiable functions on open sets; Lagrange's Theorem on equality constrained optimisation; Karush, Kuhn, and Tucker's Theorem on inequality constrained optimisation. Linear programming and duality theory.

Teaching

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Lent Term.

Formative coursework

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

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: 2 hours) in the summer exam period.
Continuous assessment (10%).

Key facts

Department: Mathematics

Total students 2021/22: 65

Average class size 2021/22: 13

Capped 2021/22: No

Lecture capture used 2021/22: Yes (LT)

Value: Half Unit

Guidelines for interpreting course guide information

Course 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
• Application of information skills
• Communication
• Application of numeracy skills
• Specialist skills