**First semester, 2018-2019**

**Module summary**

The module covers a variety of topics in linear algebra and discrete mathematics, with an emphasis on their application to financial problems.

**
Objectives**

On completion of this module students should be able to:

(a) use Gaussian elimination to solve systems of linear equations;

(b) work with the basic concepts of linear algebra: linear independence, bases, dimension, linear independence;

(c) compute the product of matrices;

(d) compute the inverse of a specified invertible matrix; calculate the determinant of a square matrix, with numerical and algebraic entries;

(e) compute the eigenvalues and eigenvectors of a specified matrix; determine whether a specified matrix can be diagonalized;

(f) model and solve problems in linear programming;

(g) use stochastic matrices to determine the limiting behaviour of simple Markov processes.

**Syllabus**

- Linear equations: manipulation of inequalities, matrices, Gaussian elimination, linear independence, bases, dimension, linear transformations, matrix algebra, inverse matrices, determinants, eigenvalues and eigenvectors, diagonalisation.

- Linear programming: feasible sets, slack resources, the simplex method, marginal analysis.

- Theory of games: games and strategies, mixed strategies, determining optimal mixed strategies.

- Markov processes: transition matrices, stochastic matrices, regular and absorbing stochastic matrices, convergence to stable states.

**Recommended book**

L. Goldstein, D. Schneider and M. Siegel, *Finite Mathematics and its Applications*, Prentice Hall, 1998.

Information from module catalogue

Last updated 3rd July 2018