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?
- Bach03: (2003) A Geometric Approach to Differential Forms
- Macd16: (2016) A Survey of Geometric Algebra and Geometric Calculus. Advances in Applied Clifford Algebras, 1–39. DOI
- LaLD00: (2000) A unified mathematical language for physics and engineering in the 21st century. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 358(1765), 21–39. DOI
- Moor93: (1993) Braids in classical dynamics. Physical Review Letters, 70(24), 3675–3679.
- HeSo84: (1984) Clifford Algebra to Geometric Calculus a Unified Language for Mathematics and Physics. Dordrecht: Springer Netherlands
- Port95: (1995) Clifford algebras and the classical groups. Cambridge ; New York: Cambridge University Press
- WaAS96: (1996) Differential forms in electromagnetic field theory. In Antennas and Propagation Society International Symposium, 1996. AP-S. Digest (Vol. 2, pp. 1474–1477 vol.2). DOI
- Flan89: (1989) Differential Forms with Applications to the Physical Sciences. Dover Publications
- WaSA95: (1995) Electromagnetic boundary conditions and differential forms. IEE Proceedings-Microwaves, Antennas and Propagation, 142(4), 326–332. DOI
- WaAr96: (1996) Electromagnetic Green functions using differential forms. Journal of Electromagnetic Waves and Applications, 10(3), 427–438. DOI
- WaSA96: (1996) Electromagnetics made easy: differential forms as a teaching tool. In 2013 IEEE Frontiers in Education Conference (FIE) (Vol. 3, pp. 1508–1512). IEEE
- Chis12: (2012) Geometric Algebra. ArXiv:1205.5935 [Math-Ph].
- DoFM10: (2010) Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry. Morgan Kaufmann
- DoLa03: (2003) Geometric algebra for physicists. Cambridge ; New York: Cambridge University Press
- BrRi95: (1995) Geometrical aspects of statistical mechanics. Phys. Rev. E, 51(2), 1006–1011. DOI
- Amar01: (2001) Information geometry on hierarchy of probability distributions. IEEE Transactions on Information Theory, 47, 1701–1711. DOI
- BoWa76: (1976) Introduction to vectors and tensors, Vol 1: linear and multilinear algebra. Plenum Press
- BoWa06: (2006) Introduction to vectors and tensors, Vol 2: vector and tensor analysis
- Hest01: (2001) Old Wine in New Bottles: A New Algebraic Framework for Computational Geometry. In Geometric Algebra with Applications in Science and Engineering (pp. 3–17). Birkhäuser Boston DOI
- Hest03: (2003) Spacetime physics with geometric algebra. American Journal of Physics, 71(7), 691–714. DOI
- LPRS10: (2010) Statistical Learning for Complex Systems an Example-driven Introduction.
- Laur87: (1987) Statistical manifolds. In Differential geometry in statistical inference (p. 164). JSTOR
- WaSA97: (1997) Teaching electromagnetic field theory using differential forms. IEEE Transactions on Education, 40(1), 53–68. DOI
- Hest91: (1991) The design of linear algebra and geometry. Acta Applicandae Mathematica, 23(1), 65–93. DOI
- Hest88: (1988) Universal geometric algebra.