Geometric Algebra 2016


(Lecture 9 slides are included for interest only.)


This year will see the second running of 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 11 to November 3rd and will consist of 8 lectures introducing various aspects of GA. Lectures take place in the new Maxwell Centre in West Cambridge.

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.

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.

The new course was given for the first time in 2015, and the overall feedback was very positive. The one consistent negative comment was that students would like to have seen more material on hands-on implementation. For 2016 there will be a new lecture covering implementation details given towards the end of the course (probably lecture 7). This will cover:

  • Implementation of geometric algebra in a symbolic algebra environment, with a demo using Maple.
  • How to write GA code, with examples and a live demonstration built in Haskell.
  • A tour of other GA libraries to get started.

If you have any questions or feedback on the contents of these lectures please enter them in the comments section below.

2015 Course

The contents of the 2015 Lecture Course are also still available.


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