Modules

95
Further Mathematics for Economists

Prerequisite – 05a Mathematics 1 and 05b Mathematics 2.

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 stability). 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 R^m. Limits and continuity of functions. Open subsets and closed subsets of R^m. Compact subsets of R^m. 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: Candidates will be expected to work with formal definitions and be able to prove results as well as apply techniques and methods.