TBD. A pragmatic guide to manifold wrangling, whatever your formalism.

Key words: Clifford algebra, differential forms…

See also information geometry.

TBD.

## Clifford Algebra formalism

Hestenes’ school.

- Cavendish laboratory’s introduction
- Hestene’s most famous bit of rhetoric
- Hestene’s most infamous bit of rhetoric
- stack exchange arguments.

Handy texts:

- Alan Bromborsky, An introduction to Geometric Algebra and Calculus

## 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

## Refs

- Amar01
- Amari, S. (2001) Information geometry on hierarchy of probability distributions.
*IEEE Transactions on Information Theory*, 47, 1701–1711. DOI. - Bach03
- Bachman, D. (2003) A Geometric Approach to Differential Forms.
- BrRi95
- Brody, D., & Rivier, N. (1995) Geometrical aspects of statistical mechanics.
*Phys. Rev. E*, 51(2), 1006–1011. DOI. - Chis12
- Chisolm, E. (2012) Geometric Algebra.
*arXiv:1205.5935 [Math-Ph]*. - DoLa15
- Doran, C., & Lasenby, A. (2015) Physical applications of geometric algebra.
- DoLa03
- Doran, C., & Lasenby, A. N.(2003) Geometric algebra for physicists. . Cambridge ; New York: Cambridge University Press
- DoFM10
- Dorst, L., Fontijne, D., & Mann, S. (2010) Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry. . Morgan Kaufmann
- Flan89
- Flanders, H. (1989) Differential Forms with Applications to the Physical Sciences. . Dover Publications
- Hest88
- Hestenes, D. (1988) Universal geometric algebra.
- Hest91
- Hestenes, D. (1991) The design of linear algebra and geometry.
*Acta Applicandae Mathematica*, 23(1), 65–93. DOI. - Hest03
- Hestenes, D. (2003) Spacetime physics with geometric algebra.
*American Journal of Physics*, 71(7), 691–714. DOI. - HeSo84
- Hestenes, D., & Sobczyk, G. (1984) Clifford Algebra to Geometric Calculus a Unified Language for Mathematics and Physics. . Dordrecht: Springer Netherlands
- Hest01
- Hestenes, P. D.(2001) Old Wine in New Bottles: A New Algebraic Framework for Computational Geometry. In D. E. B. Corrochano & P. G. Sobczyk (Eds.), Geometric Algebra with Applications in Science and Engineering (pp. 3–17). Birkhäuser Boston DOI.
- LaLD00
- Lasenby, J., Lasenby, A. N., & Doran, C. J. L.(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. - Laur87
- Lauritzen, S. L.(1987) Statistical manifolds. In Differential geometry in statistical inference (p. 164). JSTOR
- LPRS10
- Leibon, G., Pauls, S., Rockmore, D., & Savell, R. (2010) Statistical Learning for Complex Systems an Example-driven Introduction.
- Macd16
- Macdonald, A. (2016) A Survey of Geometric Algebra and Geometric Calculus.
*Advances in Applied Clifford Algebras*, 1–39. DOI. - Moor93
- Moore, C. (1993) Braids in classical dynamics.
*Physical Review Letters*, 70(24), 3675–3679. - WaAr96
- Warnick, K. F., & Arnold, D. V.(1996) Electromagnetic Green functions using differential forms.
*Journal of Electromagnetic Waves and Applications*, 10(3), 427–438. DOI. - WaAS96
- Warnick, K. F., Arnold, D. V., & Selfridge, R. H.(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.
- WaSA95
- Warnick, K. F., Selfridge, R. H., & Arnold, D. V.(1995) Electromagnetic boundary conditions and differential forms.
*IEE Proceedings-Microwaves, Antennas and Propagation*, 142(4), 326–332. DOI. - WaSA96
- Warnick, K. F., Selfridge, R. H., & Arnold, D. V.(1996) Electromagnetics made easy: differential forms as a teaching tool. In 2013 IEEE Frontiers in Education Conference (FIE) (Vol. 3, pp. 1508–1512). IEEE
- WaSA97
- Warnick, K. F., Selfridge, R. H., & Arnold, D. V.(1997) Teaching electromagnetic field theory using differential forms.
*IEEE Transactions on Education*, 40(1), 53–68. DOI.