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

Key words: Clifford algebra, differential forms… Bollu’s Handy list of differential geometry definitions.

See information geometry.

🏗

## Differential forms formalism

- Flanders, Differential forms (Flanders 1989) is a wildly popular classic available for cheap used
- Frankel, the geometry of physics (Frankel 2011) attempts to update Flanders, trading slightly improved pedagogy for slightly more physics focus.
- Bachman’s book (Bachman 2003) seems popular and is free.
- John Baez’s high speed introduction

## 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

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.

## References

*Optimization Algorithms on Matrix Manifolds*. Princeton, N.J.; Woodstock: Princeton University Press.

*Differential-Geometrical Methods in Statistics*. Springer.

*IEEE Transactions on Information Theory*47: 1701–11. https://doi.org/10.1109/18.930911.

*A Geometric Approach to Differential Forms*. http://arxiv.org/abs/math/0306194.

*Introduction to Vectors and Tensors, Vol 1: Linear and Multilinear Algebra*. Plenum Press. http://oaktrust.library.tamu.edu/handle/1969.1/2502.

*Introduction to Vectors and Tensors, Vol 2: Vector and Tensor Analysis*. http://oaktrust.library.tamu.edu/handle/1969.1/3609.

*Phys. Rev. E*51 (2): 1006–11. https://doi.org/10.1103/PhysRevE.51.1006.

*Riemannian Geometry*. Birkhauser.

*American Journal of Physics*73 (10): 938–45. https://doi.org/10.1119/1.2034523.

*Geometric Algebra for Physicists*. Cambridge ; New York: Cambridge University Press.

*Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry*. Morgan Kaufmann. http://books.google.com?id=Sg_uR57ZktoC.

*Introduction to Tensor Calculus*.

*Advanced Calculus: A Differential Forms Approach*. Birkhauser.

*Differential Forms with Applications to the Physical Sciences*. Dover Publications.

*The Geometry of Physics: An Introduction*. 3 edition. Cambridge ; New York: Cambridge University Press.

*Acta Applicandae Mathematica*23 (1): 65–93. https://doi.org/10.1007/BF00046920.

*American Journal of Physics*71 (7): 691–714. https://doi.org/10.1119/1.1571836.

*Clifford Algebra to Geometric Calculus a Unified Language for Mathematics and Physics*. Dordrecht: Springer Netherlands.

*Geometric Algebra with Applications in Science and Engineering*, edited by Dr Eduardo Bayro Corrochano and Prof Garret Sobczyk, 3–17. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-0159-5_1.

*Modern Differential Geometry for Physicists*. Allied Publishers.

*Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences*358 (1765): 21–39. https://doi.org/10.1098/rsta.2000.0517.

*Differential Geometry in Statistical Inference*, 164. JSTOR.

*Differential and Physical Geometry*.

*Advances in Applied Clifford Algebras*, April, 1–39. https://doi.org/10.1007/s00006-016-0665-y.

*Physical Review Letters*70 (24): 3675–79.

*Clifford Algebras and the Classical Groups*. Cambridge Studies in Advanced Mathematics 50. Cambridge ; New York: Cambridge University Press.

*Journal of Electromagnetic Waves and Applications*10 (3): 427–38. https://doi.org/10.1163/156939396X00504.

*Antennas and Propagation Society International Symposium, 1996. AP-S. Digest*, 2:1474–1477 vol.2. https://doi.org/10.1109/APS.1996.549876.

*IEEE Transactions on Education*40 (1): 53–68. https://doi.org/10.1109/13.554670.

*IEE Proceedings-Microwaves, Antennas and Propagation*142 (4): 326–32. https://doi.org/10.1049/ip-map:19952003.

*2013 IEEE Frontiers in Education Conference (FIE)*, 3:1508–12. IEEE. https://em.groups.et.byu.net/pdfs/publications/fie.pdf.

*Differential Forms, Second Edition: Theory and Practice*. Academic Press.