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 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 and BSc in Mathematics, Statistics and Business. 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.

This course is delivered through a combination of classes and lectures totalling a minimum of 60 hours across Michaelmas Term and 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.

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. Homework will be submitted weekly 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.

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

Exam (75%, duration: 3 hours) in the summer exam period.
Exam (25%, duration: 1 hour) in the January exam period.