Linear and Geometric Algebra

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1. thechaoApr 2024
   I recently bootstrapped myself from your level to algebraic geometry — enough to read an annotated version of Einstein's paper. If I had to do it again, I'd just skip to the parts that worked: (1) hit up Michael Penn on YT, but work all the problems he works; and, (2) learn GA, I like MacDonald's "Linear and Geometric Algebra". I'm going to be honest: unless you do the homework, you can't learn the math.

   I learned Penn because it's "real" (mainstream) math & lets you read in the same language; I learned GA because it's designed to proselytize to other mathematicians & deliberately presents serous ideas in very approachable ways.

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2. _ktndMar 2024
   My unworthy opinion:

   Herbert Gross' “Calculus Revisited” three-part series.

   https://ocw.mit.edu/courses/res-18-006-calculus-revisited-si...

   https://ocw.mit.edu/courses/res-18-007-calculus-revisited-mu...

   https://mitocw.ups.edu.ec/resources/res-18-008-calculus-revi...

   The above is more or less “engineering math”.

   The below is “normal college” math:

   Edward Frenkel's Multivariable Calculus lectures:

   https://www.youtube.com/playlist?list=PLaLOVNqqD-2GcoO8CLvCb...

   Dr. Valerie Hower's Linear Algebra lectures:

   https://youtube.com/playlist?list=PLpcwHaLYiaEXW5fLNOlItPH4A...

   Interactive Linear Algebra (online “college level” textbook):

   https://textbooks.math.gatech.edu/ila/

   Tutorial-like Linear Algebra (interactive online textbook):

   https://immersivemath.com/ila/index.html

   Sheldon Axler's Linear Algebra Done Right book:

   https://linear.axler.net/

   Sergei Treil's Linear Algebra Done Wrong book:

   https://www.math.brown.edu/streil/papers/LADW/LADW-2014-09.p...

   Linear algebra and vector calculus revamped:

   — Linear and Geometric Algebra by Alan Macdonald: http://www.faculty.luther.edu/~macdonal/laga/index.html

   — Vector and Geometric Calculus: http://www.faculty.luther.edu/~macdonal/vagc/index.html

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3. _ktndJan 2024
   Below is a list of resources that I personally like, because most of them emphasize derivations/motivations (e.g., deriving the cross product out of 3 assumptions/axioms) over (mechanical) memorization (e.g., just showing the mechanics of matrix multiplication/determinants without derivations/motivations):

      - Bari A., Algorithms, YouTube (playlist),
     https://www.youtube.com/playlist?list=PLDN4rrl48XKpZkf03iYFl-O29szjTrs_O
   
     - Frenkel E., UC Berkeley: MATH 53 - Multivariable Calculus with Edward Frenkel, YouTube (playlist) https://www.youtube.com/playlist?list=PLaLOVNqqD-2GcoO8CLvCbprz2J0_1uaoZ
   
     - Hower V., Linear Algebra Full Course, YouTube (playlist), https://www.youtube.com/playlist?list=PLpcwHaLYiaEXW5fLNOlItPH4ATorKjBuc
   
     - Lockhart P., Measurement
   
     - Axler S., Linear Algebra, Springer, 2024, https://link.springer.com/content/pdf/10.1007/978-3-031-41026-0.pdf
   
     - Ström et al., Immersive Linear Algebra, https://immersivemath.com/ila/index.html (online book)
   
     - Margalit et al., Interactive Linear Algebra, https://textbooks.math.gatech.edu/ila/ (online textbook)
   
     - Macdonald A., Linear and Geometric Algebra
   
     - Macdonald A., Vector and Geometric Calculus
   
     - Ramirez et al., From Vectors to Geometric Algebra, 2018, https://doi.org/10.48550/arXiv.1802.08153
   
     - Hertzmann et al., Computer Graphics Lecture Notes, Computer Science Department - University Toronto, 2005, https://www.dgp.toronto.edu/~hertzman/418notes.pdf
   

   Further, see Sergey Trail's "Linear Algebra Done Wrong" and watch Grant Sanderson, Easy Theory (theoretical CS), Jacob Sorber (operating systems), Graphics in 5 Minutes, Sam Buss (computer graphics), Dr. Daniel Page (theory of computation, data structures and algorithms), First Principles of Computer Vision on YouTube.

   Mr. Hertzmann has some more resources (that I haven't checked out yet):

   https://www.dgp.toronto.edu/~hertzman/research.html

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4. SAI_PeregrinusOct 2023
   Have you seen Macdonald's "Linear and Geometric Algebra"? I found it a much nicer introduction to the subject.
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5. neodypsisAug 2023
   Indeed, I have a copy of "Linear and Geometric Algebra" and its exposition is very friendly for self-learners!
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6. neodypsisAug 2023
   Thanks for the detailed answer. I have previously studied a bit from "Linear and Geometric Algebra" by Alan Macdonald (nice book) but I don't have any Physics background. I'm interested in learning more, however!
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