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Can I ask you (and keldaris) what precisely you mean by geometric algebra, and how you would propose to teach it? I'm a math professor. To me "geometric algebr
by impendia 8y ago
Can I ask you (and keldaris) what precisely you mean by geometric algebra, and how you would propose to teach it?
I'm a math professor. To me "geometric algebra" refers to any use of geometry in mathematics to illuminate algebraic principles. There are very very many of these -- this article illustrates one good example. I try to incorporate intuition from geometry into my teaching whenever possible.
It seems that the two of you are referring to some particular unifying framework, and/or set of definitions and notation. Could I ask you to elaborate on what you mean?
Thanks.
- cartep 8y agoI'm not any of the two you asked, but given that @eigenspace is a physicist, what you are looking for (notations used, etc) is possibly here: http://geocalc.clas.asu.edu/html/Evolution.html#References http://geocalc.clas.asu.edu/html/Evolution.html#References under "Recent Books". Notably "Clifford Algebra to Geometric Calculus" and "New Foundations for Classical Mechanics" by Hestenes. PD: if you ever attempt to read any of those two, I'd advise to go to the latest (corrected) reprint.
- nanofortnight 8y agohttps://en.wikipedia.org/wiki/Geometric_algebra https://en.wikipedia.org/wiki/Geometric_algebra Less ambiguously called "Clifford algebras", though Clifford himself prefered the term geometric algebra.
- deleted 8y ago[deleted]
- dahart 8y agoGeometric algebra has a definition that is more specific than any use of geometry to teach Elementary Algebra on real numbers. https://en.m.wikipedia.org/wiki/Geometric_algebra https://en.m.wikipedia.org/wiki/Geometric_algebra https://en.m.wikipedia.org/wiki/Clifford_algebra https://en.m.wikipedia.org/wiki/Clifford_algebra For teaching geometric algebra, there are curricula and textbooks available... http://geometry.mrao.cam.ac.uk/home/introduction-to-ga/ http://geometry.mrao.cam.ac.uk/home/introduction-to-ga/ https://arxiv.org/abs/1205.5935v1 https://arxiv.org/abs/1205.5935v1 http://www.faculty.luther.edu/~macdonal/GA&GC.pdf http://www.faculty.luther.edu/~macdonal/GA&GC.pdf http://assets.cambridge.org/052148/0221/sample/0521480221WS.pdf http://assets.cambridge.org/052148/0221/sample/0521480221WS.... http://geometricalgebra.org/downloads/ga4cs_toc.pdf http://geometricalgebra.org/downloads/ga4cs_toc.pdf https://www.amazon.com/dp/0792355148/ https://www.amazon.com/dp/0792355148/
- impendia 8y agoThanks, I'll have a look! This looks a bit too high-level to inform my undergraduate teaching, but certainly I could learn something from this.