Linear algebra: introduction
Time: 18:30 - 20:00
This course will be delivered online. See the ‘What is the course about?’ section in course details for more information.
- Course Code: CLAM02
- Dates: 03/06/24 - 27/06/24
- Time: 18:30 - 20:00
- Taught: Mon+Thu, Evening
- Duration: 8 sessions (over 4 weeks)
- Location: Online
- Tutor: Rich Cochrane
Course Code: CLAM02
Duration: 8 sessions (over 4 weeks)
Please note: We offer a wide variety of financial support to make courses affordable. Just visit our online Help Center for more information on a range of topics including fees, online learning and FAQs.
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.
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.
Rich is a programmer, writer and educator with a particular interest in creative practice. In his previous career he worked as a software developer in the CIty, first at a dot-com startup and later at a top-tier investment bank where he worked mostly on trading floor systems and got to play with a wide range of languages and technologies. He now teaches coding and maths-related courses full time. Besides his work at City Lit he also teaches at Central Saint Martins, the Architecture Association and the Photographer's Gallery and is the author of two books about mathematics. His technical collaborations with artists have been shown at, among others, the Hayward gallery, the V&A, the ICA and Camden Arts Centre. He has a BSc in Mathematics from the Open University. He also has a BA in English Literature and a PhD in philosophy (both from Cardiff). He continues to teach a little philosophy and literature, especially as they intersect with his other interests, and as a partner in Minimum Labyrinth he has brought these ideas to wider audiences in collaboration with the Museum of London, the Barbican and various private sponsors.
Please note: We reserve the right to change our tutors from those advertised. This happens rarely, but if it does, we are unable to refund fees due to this. Our tutors may have different teaching styles; however we guarantee a consistent quality of teaching in all our courses.