Linear algebra: introduction

What is the course about?

Vectors are the basic building-blocks of most science and technology. They “package up” data in a way that has very useful structural features. The theory of vectors – known as “linear algebra” – is one of the most elegant and complete in all of mathematics and has extremely wide-ranging applications.

This course looks at the theory of vector spaces in some detail, with a particular emphasis on those areas that underpin machine learning. We emphasise understanding of fundamental principles. This leads us a little way into pure mathematics, but in the spirit of this course everything will be developed “from the ground up” and we assume no particular mathematical knowledge or skill beyond a (perhaps fuzzy) recall of some high-school algebra. This course doubles as a very efficient introduction to “real” mathematics for the non-mathematician.

We emphasise concepts rather than calculations: the computer can do those for us when we need it, but first we must understand what to ask it to calculate and why. Beyond machine learning, these ideas are underpin many other areas of technology such as computer graphics and vision, VR, games, data mining, algorithms and robotics. Furthermore, they are fundamental to physics, engineering, finance and countless other disciplines.

Participants who will attend the full course will receive a City Lit certificate of attendance electronically for their CV or CPD records. The certificate will show your name, course title and dates of the course you have attended.

This is a live online course. You will need:
- Internet connection. The classes work best with Chrome.
- A computer with microphone and camera.
- Earphones/headphones/speakers.
We will contact you with joining instructions before your course starts.

What will we cover?

• Scalars, vectors and basic vector algebra.
• Abstract vector spaces and the dual space.
• Inner products and geometric constructions with vectors.
• The exterior product and the determinant of a linear operator.
• Homomorphisms and their relationship to the tensor product.
• The notions of dimension, basis and the direct sums of vector spaces.

What will I achieve?
By the end of this course you should be able to...

• Express appropriate ideas in the language of linear algebra.
• Perform calculations involving vectors, scalars and matrices.
• Carry out constructions using the tensor product.
• Describe some elements of the abstract theory of linear algebra.
• Understand and confidently use the jargon of modern linear algebra.
• Explore more deeply into linear algebra through independent study.

What level is the course and do I need any particular skills?

This course uses lots of algebra. Although we develop everything from scratch, some facility with school algebra will be very helpful. For example,
• If 3x + 2 = 14, what is the value of x?
• Can you “multiply out the brackets” of (2x + 3)(1 – x)?

You do not need to know anything at all about machine learning or programming. If your algebra is rusty, you may like to take the City Lit course Precalculus first.

How will I be taught, and will there be any work outside the class?

You will be given weekly readings to study in advance. These are short (5-10 pages) but can be challenging and often take some time to digest. The sessions are student-led discussions of the material that we use to clarify your understanding, work through explicit calculations, visualize geometric ideas and so on.

Are there any other costs? Is there anything I need to bring?

There is no other costs.

When I've finished, what course can I do next?

Please click here to view our Programming and Maths courses.