This year I am giving a new course on Geometric Algebra as part of the Masters Course in Scientific Computing at Cambridge University. This course is run by the Doctoral Training Centre in Scientific Computing, in the Physics Department at Cambridge.
The lecture course runs from October 9 to October 26 and will consist of 8 lectures introducing various aspects of GA.
The course provided an opportunity to update the material presented in the “Physical Applications of Geometric Algebra” course from 2000. Since that course Anthony Lasenby and I finished our textbook and, looking back at that older material, I decided I needed to make room for:
- Alternative geometric pictures: projective and conformal geometry. In particular, conformal geometry has now become a core topic of research, which was not the case back in 1998 when the first course was give.
- Algebraic fundamentals. While it is useful to introduce algebraic concepts alongside applications, I felt a section on the fundamentals alone would be helpful.
- Computational aspects. This course is part of the Masters in Scientific Computing, so this was a good opportunity to include more material about coding issues with GA.
- A new set of slides in PowerPoint to replace the old overheads ‘designed’ in LaTeX.
With only 8 lectures, and new material to include, some of the physical applications had to be dropped. In particular, this course does not get to:
- Modelling quantum systems and the geometric origins of spinors.
- Gauge theory and gravity.
Hopefully we can cover these topics in future years.
Each lecture will be posted as a separate blog page to enable comments and discussion. The pages are listed below.
Lectures
- Lecture 1: Geometric Algebra in 2 Dimensions
- Lecture 2: Geometric Algebra in 3 Dimensions
- Lecture 3: Applications to 3D dynamics
- Lecture 4: Algebraic Foundations and 4D
- Lecture 5: Spacetime Algebra
- Lecture 6: Geometric Calculus
- Lecture 7: Conformal Geometric Algebra
- Lecture 8: Unification and Implementation