Linear Algebra is one of the most fundamental areas of Mathematics with applications in Geometry, Statistics, Applied Mathematics, Algebra, Analysis and indeed most topics within Mathematics. This course begins with the familiar example of solving linear equations, and gradually progresses into the abstract. You will be introduced to the central concept of a vector space, and the linear maps between them which ensure their structure is preserved. You will see proofs of two of the most famous results in Linear Algebra – the Spectral Theorem and Rank-Nullity Theorem, as well as an introduction to the idea of an Inner Product which is commonplace in Quantum Physics.

This is an ‘intermediate’ FHEQ level 4 course and therefore in order to get the most out of the teaching you should have some familiarity with Linear Algebra as a pre-requisite. Taking the ‘Beginning Linear Algebra’ course would be ample preparation.

Course Begins 25 April 2024 and last for 10 weeks. The detailed breakdown is as follows:

Week 1: Solving a Linear System and Finding a Matrix Inverse via Elementary Row Operations
Week 2: The Determinant Function
Week 3: Eigenvalues and Eigenvectors
Week 4: The Spectral Theorem
Week 5: Vector Spaces and Subspaces
Week 6: Basis, Spanning and Linear Independence
Week 7: Dimension Formula and Direct Sum
Week 8: Linear Transformations
Week 9: Rank Nullity Theorem
Week 10: Inner Product Spaces and the Gram-Schmidt Procedure     

Tutor: Dr Tom Crawford

Tom is the Public Engagement Lead at the Department and is also a Fellow by Special Election at St Edmund Hall where he teaches mathematics to the first and second year undergraduate students.

Alongside his teaching commitments, Tom runs an award-winning outreach programme through his website ’Tom Rocks Maths’ which hosts videos, podcasts, puzzles and articles that aim to make maths entertaining and understandable to all. Tom works with several partners including the BBC and the Numberphile YouTube channel – the largest maths channel on the platform with over pi-million subscribers. With over 20 million YouTube views, 2 TEDx talks, and guest lectures at the Royal Institution and New Scientist Live, Tom is well on his way to his goal of bringing maths to the masses.

Full information can be found at the Oxford University Department for Continuing Education website.