Introduction to Linear Algebra

Why should you learn Linear Algebra?

Linear Algebra underlies almost all of modern science and technology. While it is a beautiful and accessible field of mathematics in its own right, it has far-reaching and powerful applications. Whether you want to work in the data driven world – Machine Learning, Artificial Intelligence, Big Data – or embark on further study in other areas of science and mathematics, Linear Algebra is a great enabler for your future success. 

This Introduction to Linear Algebra course will be accessible to all. It assumes only basic high-school level mathematics and will quickly equip you with the mathematical foundations to ‘up-skill’ and thereby open up new opportunities. This course is particularly welcoming for people wanting to re-energise their skills and capacities for their future careers. 

What will you learn? 

In this course, you will learn the basic rudiments of vectors and matrices. How to compute with them and how to apply them to real-life problems. Specifically, after this course, you will be able to: 

1. Compute with geometric and algebraic vectors.

2. To understand and compute dot products and cross products of vectors and their applications.

3. Compute equations of lines and planes in three-dimensional Euclidean space.

4. Manipulate the augmented matrix for a system of linear equations via Gaussian Elimination.

5. Compute with matrices of various dimensions and use these computations to solve linear equations.

6. Find eigenvectors and eigenvalues for a square matrix and use these in applications such as Markov chains and modelling population 

How will you be taught? 

This course will be entirely taught online. The course will run for 6 weeks, where each will comprise a: 

  • 2-hour live-streamed interactive lecture with the participants. This lecture will also be recorded so participants can revise in their own time. 
  • 1-hour tutorial session where students will work through and be invited to ask questions to the tutor on the week’s materials based on the lecture tutorial exercises. 

On top of the lecture and tutorial, students will be given week-by-week exercise sheets, with accompanying solutions, that have been carefully designed to maximise their learning. There will also be online ‘progress quizzes’ with immediate feedback to students can gauge how they are progressing through the material. 

What you will need? 

As this is an introductory course, you will only need a computer/laptop/tablet/smart phone to screen the live-streamed lecture and a pen and notebook to take notes and to do the weekly exercises. The online quizzes can be done on any device. 

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