Linear algebra: introduction
Time: 15:00 - 17:10
This course is FREE if a) you live in London and your job is at risk of redundancy or b) you are either on Jobseekers' Allowance (JSA) or Employment & Support Allowance(ESA) or c) you receive other state benefits (including Universal Credit). For more information click here
This course will be delivered online. See the ‘What is the course about?’ section in course details for more information.
Course Code: CLAM01
Duration: 6 sessions (over 6 weeks)
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. This makes it an ideal partner for our course Machine Learning with Python but it’s also designed to stand alone.
Rather than focusing on practical methods and techniques, here 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. We will emphasis concepts rather than calculation: the computer can do that for us when we need it, but first we must understand what to ask it to calculate and why!
We will therefore work with pen and paper and no coding is required. However, those who want to apply this material to their programming will certainly be able to do so, whatever language they may be using. Beyond machine learning, these ideas are highly relevant to other coding topics such as computer graphics and vision, VR, games, data mining and algorithms. Furthermore, they are useful outside programming in physics, engineering, finance and countless other disciplines.
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
• Constructions including direct sum, tensor product and exterior product
• Homomorphisms and, in particular, a detailed study of linear operators.
What will I achieve?
By the end of this course you should be able to...
• Express appropriate ideas in the language of linear algebra
• Solve algebraic problems involving vectors, scalars and matrices
• Describe some elements of the theory of linear algebra
• Understand and confidently use the jargon of modern linear algebra
• Explore more deeply into linear algebra or vector calculus 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 (5-10 pages) to study in advance. The session are student-led discussions of the material that you can 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?
Introduction to Python, introduction to machine learning, algorithms in Python.
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.