Linear algebra is the mathematics that underlies most computing languages and is also prevalent in many scientific disciplines. It was essentially born out of the study of finding solutions to systems of linear equations. It has a far reaching number of applications from describing quantum mechanical systems to predicting stock market growth. It is an essential component to any student planning on pursuing a career in finance, big data or the sciences. This course will be an introduction to linear algebra. The topics covered will be the following: - Propositional and First Order Logic - Set Theory and Mathematical Proofs - Complex Numbers - Properties of Vectors in R^n - Cross products, dot products, projections and equations of lines and planes. - Matrices - Solving Systems of Linear Equations - Determinants - Vector Spaces - Eigenvalues and Eigenvectors - Diagonalisation - Basis Representations and Linear Transformations - Inner Product Spaces