- 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 Rm
- Limits and continuity of functions
- Open subsets and closed subsets of Rm
- Compact subsets of Rm
- Convex sets, convex and concave functions
- Gradients and directional derivatives
- The Jacobian derivative
- The Edgeworth Box and contract curves.
- 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.
If you complete the course successfully, you should be able to:
- Use the concepts, terminology, methods and conventions covered in the unit to solve mathematical problems in this subject.
- Demonstrate an understanding of the underlying principles of the subject.
- Solve unseen mathematical problems involving understanding of these concepts and application of these methods.
- Prove statements and to formulate precise mathematical arguments.
Unseen written exam (3 hrs).
- Simon, C.P. and L. Blume Mathematics for Economists. New York and London: W.W. Norton and Company.
- Anton, Howard A. Elementary Linear Algebra. Wiley Text Books.
- Ostaszewski, A. Advanced Mathematical Methods. Cambridge: Cambridge University Press.
Course information sheets
Download the course information sheets from the LSE website.