Learn Linear Algebra at the University of Oxford with this 10-week online course led by Tom. Full information below.

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 Linear Algebra: Introduction course would be ample preparation.

The overall structure of the course follows the Undergraduate Mathematics Syllabus at the University of Oxford. Courses on the Weekly Oxford Worldwide programme consist of weekly live webinars with a tutor and weekly pre-recorded lectures.

Programme details

Course Begins: 23 Jan 2025

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: Vector Spaces and Subspaces
Week 5: Basis, Spanning and Linear Independence
Week 6: Dimension Formula and Direct Sum
Week 7: Linear Transformations
Week 8: Rank Nullity Theorem
Week 9: Inner Product Spaces and the Gram-Schmidt Procedure
Week 10: Spectral Theorem     

All students who pass their final assignment, whether registered for credit or not, will be eligible for a digital Certificate of Completion. Upon successful completion, you will receive a link to download a University of Oxford digital certificate. Information on how to access this digital certificate will be emailed to you after the end of the course. The certificate will show your name, the course title and the dates of the course you attended. You will be able to download your certificate or share it on social media if you choose to do so. 

Please note that assignments are not graded but are marked either pass or fail. 

Course aims

Develop a deeper knowledge of Linear Algebra with rigorous mathematical proofs. This follows on from the Linear Algebra: Introduction course.

Course Objectives

• Introduce abstract concepts through the vehicle of Linear Algebra;
• Extend student’s knowledge beyond the basics of computation, to an understanding of theory and proof;
• Develop the high-level analytical skills required of a Mathematician.

Teaching methods

The course will consist of the following:
– A weekly lecture video (averaging 50-60 minutes over the 10 weeks) to cover the core concepts of each topic
– Guided reading of lecture notes, textbooks, sample exercises
– A weekly problem set
– A 1-hour weekly group tutorial to cover the solutions to the problem set and answer any questions about the content

Learning outcomes

By the end of the course students will be expected to:
– Utilise the tools of matrix algebra such as inverses, determinants, eigenvalues and eigenvectors to solve a variety of problems;
– Demonstrate an understanding of the structure of a Vector Space, the properties that follow, and their relationship to Linear Transformations.
– Explain the Spectral and Rank-Nullity Theorems and describe the key steps in their proofs.

Assessment methods

Weekly problem sets which will be used to determine the content of the tutorials. A ‘mock’ exam in week 5 as a formative assessment and practice for the final exam at the end of the course. The final exam will be untimed, open-book and will cover all topics in the course. It will determine the final grade.

Coursework is an integral part of all weekly classes and everyone enrolled will be expected to do coursework in order to benefit fully from the course. Only those who have registered for credit will be awarded CATS points for completing work the required standard.