MT3095 Further mathematics for economists
Students may bring into the examination hall their own hand held electronic calculator. If calculators are used they must satisfy the requirements listed in Section 4, Assessment for the programme, of the Detailed Regulations.
Graph paper will be provided.
May not be taken with MT2116 Abstract mathematics or MT2176 Further calculus (half course) or MT2175 Further linear algebra (half course).
Prerequisites (applies to degree students only)
Eitherboth MT105A Mathematics 1 and MT105B Mathematics 2 or MT1174 Calculus.
Linear algebra: Vector spaces, linear independence and dependence, bases and dimension, rank and nullity of a matrix. Linear mappings, their rank and nullity, their matrix representation, and change of basis. Eigenvalues and eigenvectors. Diagonalisation of matrices, with applications to systems of difference and differential equations (including stabililty). Quadratic forms and orthogonal diagonalisation. Inner product spaces, norms, orthogonality and orthonormalisation.
Functions and mathematical analysis: Sets and functions. Supremum and infinum of bounded sets. Limits of sequences in R and Rm. Limits and continuity of functions. Open subsets and closed subsets of Rm. Compact subsets of Rm. Convex sets, convex and concave funstions. Gradients and directional derivatives. The Jacobian derivative. The Edgeworth Box and contract curves.
Optimisation: Inconstrained optimisation and the second-order conditions. Constrained optimisation and the Kuhn-Tucker theorem. Envelope Theorems. Theory of linear programming
(computational methods will not be included). Duality, with applications. Basic Game Theory.
Note: Students will be expected to work with formal definitions and be able to prove results as well as apply techniques and methods.