Module description
Syllabus:
Complex numbers. Vector spaces: row and column vectors (real and complex), linear combinations, abstract vector spaces, bases and dimension of vector spaces. Linear maps: definitions and examples, matrix of a linear map, composition, invertibility and isomorphisms. Solving systems of linear equations using linear algebra. Determinants: definition and properties. Eigenvectors and eigenvalues: definitions, diagonalisation of matrices, canonical forms of 2x2 matrices.
Assessment details
Written examination and class tests or alternative assessment. Details to be confirmed.
Exercises or quizzes will be set each week to be handed in the following week. These problems will be discussed in the tutorials and solutions will be available.
Educational aims & objectives
Linear algebra provides basic ideas and tools for much of the work we do in mathematics, particularly the aspects which concern geometry in 3D Euclidean space. The module introduces the general notion of linearity, a principle which illuminates wide areas of Mathematics. In pursuit of this, we cover a range of topics and provide a unifying framework for them.
Learning outcomes
Understand and be able to apply basic concepts of linear algebra: especially vector spaces, bases, linear maps and matrices. Apply these concepts to solving systems of linear equations. Be able to compute the determinant of a matrix and understand its relation to volume and invertibility. Understand the definitions of eigenvalues and eigenvectors of linear maps or matrices and be able to compute simple examples.
Teaching pattern
Three hours of lectures and one hour of tutorial per week throughout the term
Suggested reading list
Indicative reading list - link to Leganto system where you can search with module code for lists