May not be taken with MT105A Mathematics 1.
May not be taken with MT105B Mathematics 2.
This course develops basic mathematical methods and concepts of algebra and will include their applications to problems in economics, management and related areas.
Matrices, vectors and their geometry:
Vectors and matrices, the algebra of vectors and matrices; Cartesian and vector equations of a straight line; normal vectors and planes; the Cartesian and vector equations of a plane; extension to higher dimension.
Systems of linear equations:
Systems of linear equations and their expression in matrix form; Solving systems of linear equations using row operations; consistent and inconsistent systems; systems with free variables; range and rank of a matrix; general solution of linear systems.
Matrix inversion and determinants:
Finding inverses using row operations; determinants; matrix inversion using cofactors; Cramer's rule; input-output analysis.
Sequences, series and difference equations:
Arithmetic and Geometric Progressions; sums of numbers, squares and cubes; solving first-order difference equations; application of first-order difference equations to financial problems; The cobweb model; Second-order difference equations;
Vector spaces and related concepts:
Vector spaces; subspaces, including those associated with matrices; linear span; linear independence and dependence; bases and dimension; coordinates; linear transformations.
Diagonalisation of matrices:
Eigenvalues and eigenvectors; diagonalisation of a matrix and its connection with eigenvectors; finding powers of matrices using diagonalisation;
Applications of diagonalisation:
Markov chains; using diagonalisation to solve systems of differential equations; using diagonalisation to solve systems of difference equations