Prof Giacomo Zambelli COL.2.06

This course is compulsory on the BSc in Mathematics with Data Science. This course is available on the BSc in Actuarial Science, 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.

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.

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.

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

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.

Exam (90%, duration: 2 hours) in the spring exam period.
Continuous assessment (10%).