What is the course about?
Vectors were originally invented to describe positions and movement in space and time. This also makes them indispensable in the fields of 2D and 3D design, animation and computer games. Because of the way vectors are defined, though, they allow us to very easily express position and motion in high-dimensional space we can’t otherwise picture. They also offer an attractive gateway into more advanced mathematics.
Vectors are simple gadgets that can only do a limited number of things. They are not at all difficult to understand and work with if we begin with visual intuition and build up from there. We will do a lot more drawing than algebra! However, optional exercises involving calculations will be provided – doing these can also help your general understanding and help you spot gaps or misconceptions.
The first half of the course introduces vectors and builds up a very concrete sense of what they are and how they behave. Almost everything we do will begin with a sketch; only when our ideas are clear will we add symbolic shorthand notation (“algebra”) to simplify our work, and even then we often return to drawing.
Alongside individual vectors, two concepts have proven to be extremely useful. The first is that of a “linear transformation”, represented by a matrix and describing a single change such as a rotation, scaling or shearing effect. The other is the “vector field”, which can represent the interplay of forces or flows in a real or virtual space. The second half of the course is dedicated to an intuitive understanding of these simple but expressive ideas.
As well as abstract visual pictures (lines and arrows and the like) we will also emphasise different real-world applications of these ideas in a variety of different fields. Your own interests and experience will be invaluable in this area as you are almost certainly working with vectors already without necessarily knowing it.
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?
• Basic ideas of vector algebra such as addition, scaling and length
• Vector concepts from physics including velocity, acceleration and forces
• Vectors in 2D and 3D computer graphics
• Applications of high-dimensional spaces in fields such as robotics, finance and machine learning
• Matrix transformations such as rotations, shears and scaling, and affine transformations
• Iteration of matrices, including convolution kernels used in image processing
• Vector fields and their applications in physics and computer simulations
• An intuitive treatment of vector calculus concepts in 3D, including divergence and curl.
What will I achieve?
By the end of this course you should be able to...
• Perform the most important calculations in vector algebra by hand
• Recognise the visual and spatial meaning of vectors and matrices
• Transform space using matrices
• Sketch a vector field and describe it in qualitative terms
• Use some of the language of 3D calculus (we will not be performing any actual calculations in this area).
What level is the course and do I need any particular skills?
This course is intended for complete beginners – its purpose is to give you a solid grasp of the basics and an overview of more intermediate parts of the subject. No previous maths skills are needed.
How will I be taught, and will there be any work outside the class?
The class is taught online through a mixture of tutor presentation and discussion. You will be in a small group with plenty of time for questions, exploratory conversations and discussions of how to apply the ideas to your own areas of interest. Exercises will be provided for practice outside class but these are completely optional.
Are there any other costs? Is there anything I need to bring?
There are no other costs.
When I've finished, what course can I do next?
Linear Algebra and Optimization for Machine Learning develops vectors and matrices in a more abstract way and covers some different elements of the calculus.
Students are free to ask the tutor for advice on related courses.
General information and advice on courses at City Lit is available from the Information and Advice Shop, open Monday to Friday 12:00 – 19:00 during term time, and Monday to Friday 12:00 – 17:00 out of term time. Website for term dates and further details.