Ioannis Kouletsis

This course is compulsory on the BSc in Finance. This course is available on the BSc in Accounting and Finance, BSc in Econometrics and Mathematical Economics, BSc in Economics, BSc in Philosophy and Economics, BSc in Philosophy, Politics and Economics and BSc in Philosophy, Politics and Economics (with a Year Abroad). This course is not available as an outside option. This course is available to General Course students.

This is an introductory level course for those who wish to use mathematics seriously in finance or economics. 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: One-variable calculus including inverse functions, local inverses, critical points, optimisation, integration and differential equations, Functions of several variables including derivatives, gradients, tangent hyperplanes, directional derivatives, classification of critical points, convexity, concavity, unconstrained optimisation and Lagrange's method, Matrices including determinants, reduced row echelon form and rank, Systems of linear equations including Gaussian elimination and analysis of solution sets, Vector spaces including subspaces, linear independence, linear span, basis and dimension, Linear transformations including diagonalisation. Some applications of the above topics.

20 hours of lectures, 10 hours of classes and 10 hours of workshops in the AT.

This course is delivered through a combination of lectures, example sessions (workshops), and classes, totalling a minimum of 40 hours across Autumn Term.

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, Home Assignments with Exam-Style 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 (100%, duration: 2 hours, reading time: 15 minutes) in the January exam period.