Course overview
Mathematical Foundations of Management II develops students’ understanding of the concepts of linear algebra and provides experience with its methods and applications.
The module covers fundamental algebraic tools involving matrices and vectors to study systems of linear equations and Gaussian elimination, linear transformations, orthogonal projection, least squares, determinants, and eigenvalues and eigenvectors. The module includes examples that illustrate the concepts and their practical application in management.
The aim is to develop a rigorous understanding of key mathematical concepts that underpin the practice of management and develop strong quantitative thinking skills. The concepts and tools covered in the module will be applied in later modules to support the analysis of complex management problems and the development of associated mathematical models. Important concepts in other areas (e.g. economics, finance, data analytics) can be explored in more depth if students have a strong background in the underlying mathematics.
Learning outcomes
Upon successful completion of the module, students will be able to:

Perform the operations of addition, multiplication and find the inverse and transposes of vectors and matrices.

Solve systems of linear equations using Gaussian elimination.

Define and identify linear dependence and independence of a collection of vectors.

Calculate determinants using row operations, column operations, and expansion down any column or across any row.

Calculate eigenvalues, eigenvectors and eigenspaces.

Determine if a matrix is diagonalisable, and if it is, diagonalise it.

Solve systems of dynamic linear equations using eigenvalues
Topics covered

Systems of linear equations

Linear transformations and inverses

Matrices and operations

Subspaces and their dimensions

Orthogonality and least squares

Determinants

Eigenvalues and eigenvectors

Discrete and continuous linear dynamic systems

Singular value decomposition

Applications of linear algebra
Assessment summary
20% is awarded for individual coursework, comprising four problem sets. 80% is awarded for a 3hour written examination.
Current students should refer to Moodle for specific details of the current year’s assessment.
Essential reading
Linear Algebra with Applications (5th Edition), Otto Bretscher, Pearson (ISBN10: 0321890582, ISBN13: 9780321890580)