TBD. A pragmatic guide to manifold wrangling, whatever your formalism.
Key words: Clifford algebra, differential forms…
See also information geometry.
Clifford Algebra formalism
- Cavendish laboratory's introduction
- Hestene's most famous bit of rhetoric
- Hestene's most infamous bit of rhetoric
- stack exchange arguments.
Alan Bromborsky, An introduction to Geometric Algebra and Calculus
Alan Macdonald, Geometric Algebra:
Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas, including linear algebra, multivariable calculus, real analysis, complex analysis, and euclidean, noneuclidean, and projective geometry. They provide a unified mathematical language for physics (classical and quantum mechanics, electrodynamics, relativity), the geometrical aspects of computer science (e.g., graphics, robotics, computer vision), and engineering.
Differential forms formalism
- Flanders, Differential forms
- Frankel, the geometry of physics
- Bachman's book (Bach03) seems popular and is free.
- John Baez's high speed introduction
How is tensor?
Baby steps to picking up all the vector space multilinear weirdness I never got around to.
The intersection point of differential geometry and geometric algebra and linear algebra.
Basic tensor handling
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- BoWa06: (2006) Introduction to vectors and tensors, Vol 2: vector and tensor analysis
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- LPRS10: (2010) Statistical Learning for Complex Systems an Example-driven Introduction.
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