Mathematical Methods

**This information is for the 2019/20 session.**

**Teacher responsible**

Dr Ioannis Kouletsis

**Availability**

This course is compulsory on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics, BSc in Econometrics and Mathematical Economics, BSc in Economics, BSc in Economics with Economic History, BSc in Finance, BSc in Financial 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 on the BSc in Accounting and Finance, BSc in Philosophy and Economics, BSc in Philosophy, Politics and Economics and MSc in Economics (2 Year Programme). This course is available as an outside option to students on other programmes where regulations permit and to General Course students.

**Pre-requisites**

This course assumes knowledge of the elementary techniques of mathematics including calculus, as evidenced for example by a good grade in A Level Mathematics.

**Course content**

This is an introductory level course for those who wish to use mathematics seriously in social science, or in any other context. A range of basic mathematical concepts and methods in calculus of one and several variables and in linear algebra are covered and some applications illustrated. It is an essential pre-requisite for any mathematically orientated economics options and for many further mathematics courses. Topics covered: Matrices, reduced row echelon form, rank. Systems of linear equations, Gaussian elimination. Determinants. Vector spaces, linear independence, basis, dimension. Linear transformations, similarity. Eigenvalues. Diagonalization. Orthogonal diagonalization. Complex numbers. Vectors. Functions of several variables, derivatives, gradients, tangent hyperplanes. Optimisation including Lagrange's method. Vector-valued functions, derivatives and their manipulation. Inverse functions, local inverses and critical points, use in transformations. Integration, differential and difference equations. Some applications of the above topics.

**Teaching**

20 hours of lectures, 20 hours of classes and 10 hours of workshops in the MT. 20 hours of lectures, 20 hours of classes and 10 hours of workshops in the LT. 2 hours of lectures in the ST.

**Formative coursework**

Students will be expected to attempt a number of weekly self-study exercises (and check their answers using solutions provided) in preparation for their classes. In-class open book practice sessions will be conducted weekly in class and be submitted to the appropriate class teacher for marking and feedback. In addition, Mock Exam questions will be submitted for marking and feedback at regular intervals throughout the year. Success in this paper depends on dealing with the written work as it is assigned, in a regular and systematic manner.

**Indicative reading**

Ken Binmore & Joan Davies, Calculus, Concepts and Methods; Martin Anthony & Michele Harvey, Linear Algebra, Concepts and Methods.

**Assessment**

Exam (75%, duration: 3 hours) in the summer exam period.

Exam (25%, duration: 1 hour) in the January exam period.

**
Key facts
**

Department: Mathematics

Total students 2018/19: 720

Average class size 2018/19: 29

Capped 2018/19: No

Value: One Unit

**Personal development skills**

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