P&S: Gibbs? Clifford!

Abstract

The category of "Laboratory Courses, Projects, Seminars" includes courses and laboratories in various formats designed to impart practical knowledge and skills. Moreover, these classes encourage independent experimentation and design, allow for explorative learning and teach the methodology of project work.

Objective

Python, an interpreted, high-level programming language, has arguably become the de facto standard for exploratory, interactive, and computation-driven scientific research. Free and universally available, Python comes prepackaged with a wealth of general-purpose libraries, popularizing the notion that it comes with “batteries included.” Geometric Algebra, based on the algebra of multivectors introduced by Clifford in1878 and applied to the mathematical description of physics by Hestenes a century later, is a revelation, like the sun making its way through the fog: the Gibb’s cross product in R3 with its troubling sides is merged into the more general vector product (inner and outer product) so that e.g. the electromagnetic field in the Maxwell equations as well as the imaginary unit in quantum mechanics suddenly acquire another (and hopefully more limpid) meaning. Objective of this practical course is to introduce the students to the power of Python by making them discover geometric algebra. Each of the seven sessions begins with an introduction about a geometric algebra aspect (first 2 h) followed by corresponding exercises in Python (second 2 h). Students are thus expected to bring their own laptop for the activity with Python! Attendance is compulsory for at least five out of the seven afternoons (QR code scanning at the entrance). Students divided in subgroups will be required to submit two homeworks (~15 h each), mandatory to earn the two credit points! Dates: Wed 26.2, 5.3, 12.3, 19.3, 26.3, 9.4, 16.4 (14:15-18:00)

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