MA208 Half Unit
Optimisation Theory
This information is for the 2020/21 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 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. This year, some or all of this teaching will be delivered through a combination of virtual classes and lectures delivered as online videos.
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 (90%, duration: 2 hours) in the summer exam period.
Continuous assessment (10%).
Important information in response to COVID-19
Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.
Key facts
Department: Mathematics
Total students 2019/20: 57
Average class size 2019/20: 30
Capped 2019/20: No
Value: Half Unit
Personal development skills
- Self-management
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills
