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I am a physics student. I recently watched some videos on geometric algebra. I found it very intuitive and interesting. I want to do some rigorous study on this topic. Could someone suggest to me some good books on geometric algebra?

I have the following Mathematical background:

  1. Real analysis (Bartle & Sherbert)
  2. Metric Spaces ( G.F. Simmons )
  3. Calculus of several variables ( Rudin )
  4. Topology ( Munkres )
  5. Differential forms ( Morita $^*$ )

I have good experience with linear algebra, but I have not done any mathematical course on this topic.

My thought

I think that the art of products in geometric algebra is related to differential form. So if some book is relating these concepts will be great.

* S. Morita, Geometry of differential forms. Providence, R.I: American Mathematical Society, 2001.

Shriman Keshri
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2 Answers2

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Books

  1. New Foundations for Classical Mechanics by David Hestenes

It does all of highschool classical mechanics and beyond in the formalism of GA. I found it hard to read at some points and some definitions non intuitive but if you stick on, it'll help you reach your goal of seeing how GA can be used practically.

  1. Leo Dorst, Daniel Fontijne, Stephen Mann - Geometric Algebra for Computer Science An Object-Oriented Approach to Geometry

Do not let the title fool you to thinking it's a computer science book, the above is mostly a mathematics book. It requires some knowledge of linear algebra to fully grasp but it is much more depth and views GA from many angles.

  1. Alan MacDonald's Geometric Algebra book

It is a book written for undergraduate, it begins with linear algebra and then smooths itself into geometric algebra. The linear algebra is not very rigorous but it is enough to 'understand' the main ideas.

Lecture introductions

Have a look at the GAME lectures on how Dual quarternions can be written in geometric algebra. It has some coding fluff, but I guarantee it's mostly on GA only. There are other game lectures on the other sub branches/ prespectives on GA that you can view on the channel.

Other mentions include sudgylacmoe, Mathoma as lectures but they do not go into as much depth as the game lectures above.

Video games(?)

You may be interested in this geometric algebra video game as well

tryst with freedom
  • 11,538
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Additional to literature hints already given, the following books might be useful:

  • "Geometric Algebra Applications" by Eduardo Bayro-Corrochano (there are two volumes and the first volume already deals also with Machine Learning), see Google Books
  • "Geometric Algebra for Physicists" by Chris Doran (it maintains the background of Physics, which can be useful in your particular case). Doran's slides are publicly available here
  • "Geometric Algebra Computing" by Eduardo Bayro-Corrochano and Gerik Scheuermann, see Google Books
  • "Geometric Algebra with Applications in Engineering" by Christian Perwass, see ResearchGate
  • A taste of Alan Macdonald's "Linear and Geometric Algebra" you can get here
  • The complete book "Geometric Algebra for Computer Graphics" by John Vince is linked from Google Scholar and can be directly viewed here
  • My absolute favorite literature source is "MAA" and you find there useful sources from journal articles until whole books, see for example the PDF file "Geometric Approaches to Quadratic Equations from Other Times and Places" on MAA site here