Dr Ioannis Kouletsis

This course is compulsory on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics, BSc in Econometrics and Mathematical Economics, BSc in Economic History with Economics, BSc in Economics, BSc in Economics and Economic History, BSc in Economics with Economic History, BSc in Mathematics and Economics, BSc in Mathematics with Economics 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.

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

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.

22 hours of lectures, 10 hours of classes and 10 hours of workshops in the MT. 22 hours of lectures, 11 hours of classes and 10 hours of workshops in the LT.

Students will be expected to complete exercises assigned weekly in the lectures. Written answers to specified exercises are submitted to the appropriate class teacher for evaluation. Success in this paper depends on dealing with this written work as it is assigned, in a regular and systematic manner.

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

Exam (75%, duration: 3 hours) in the main exam period.
Exam (25%, duration: 1 hour) in the LT week 0.