Module manager: Onno Bokhove
Email: o.bokhove@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2025/26
| MATH1000 | Core Mathematics |
MATH2640 Introduction to Optimisation
This module is not approved as a discovery module
Optimisation, “the quest for the best”, plays a major role in financial and economic theory, such as maximising a company's profits or minimising its production costs. This course develops the theory and practice of maximising or minimising a function of many variables. It thus lays a solid foundation for progression onto more advanced topics, such as dynamic optimisation, which are central to the understanding of realistic economic and financial scenarios.
The module will provide learners with a collection of theoretical and algorithmic techniques for determining optimal extrema of arbitrary functions of several variables, either with or without constraints.
On successful completion of the module students will have demonstrated the following learning outcomes:
1. Determine the definiteness of quadratic forms;
2. Determine exactly extrema of functions of several variables, with or without constraints, using Lagrange multipliers;
3. Determine extrema of functions of several variables subject to inequality constraints, using both classical and Kuhn-Tucker approaches;
4. Apply the theory to a range of problems arising in Mathematical Economics.
Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills learning outcomes:
a. Problem solving in a real-world context.
b. Organisation and time management skills.
c. Mathematically contextualising information.
d. Cross-disciplinary thinking.
1. Review and extension of multi-variable calculus: the total derivative and Taylor series in many variables
2. Unconstrained optimisation: quadratic forms, extrema, and applications to economics
3. Constrained optimisation: Lagrange multipliers, the bordered Hessian, Kuhn-Tucker theory, and applications to finance
4. Additional topics that build on these may be covered as time allows. Further details of possible topics will be delivered closer to the time that the module runs.
Methods of assessment
The assessment details for this module will be provided at the start of the academic year
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 22 | 1 | 22 |
| Practical | 5 | 1 | 5 |
| Private study hours | 73 | ||
| Total Contact hours | 27 | ||
| Total hours (100hr per 10 credits) | 100 | ||
The reading list is available from the Library website
Last updated: 30/04/2025
Errors, omissions, failed links etc should be notified to the Catalogue Team