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From Zero to Geo Introduction (Geometric Algebra Series)

This video is the introduction to my series on geometric algebra, From Zero to Geo. In this series, we will build geometric algebra from the ground up, starting from just high school algebra. My hope is that this series can be used by motivated high schoolers (or anybody above that level) to learn geometric algebra. And yes, I do know that a few of the things I presented aren't quite correct (such as when I reflected a shape across a line or when I divided by a bivector). The point of this video is just to be an introduction to the series, not to teach anything. Also, I can't make videos this fast! I actually had almost finished this one before deciding to make the calculus one for SoME1. Full playlist here:    • From Zero to Geo   Next video here:    • Why do we care about vectors?  From Z...   Discord:   / discord   Patreon:   / sudgylacmoe   "But sudgy," I hear you say, "you haven't finished the series yet! I want to learn geometric algebra now!" If you want to, you can try learning through the materials that I learned from. I learned mainly from some of David Hestenes' work such as his Oersted medal paper (http://geocalc.clas.asu.edu/pdf/Oerst...) and his book "New Foundations for Classical Mechanics". Another very helpful resource for me was Doran and Lasenby's "Geometric Algebra for Physicists". Other books that I've heard great things about but didn't use while learning are MacDonald's "Linear and Geometric Algebra" (which is the most beginner-friendly book of the bunch) and Dorst et al's "Geometric Algebra for Computer Science". However, many of the things I've learned about geometric algebra I learned through random papers and discussions with others. Some of the things I've learned I figured out for myself, too. Table of Contents: Chapter 1: Vectors - Section 1 (Introduction):    • Why do we care about vectors?  From Z...   - Section 2 (Length and Scalar Multiplication):    • The length of a vector and how to cha...   - Section 3 (Adding Vectors):    • How to Add Vectors - From Zero to Geo...   - Section 4 (Algebra of Vectors):    • The Algebra of Vectors - From Zero to...   - Section 5 (Spaces/Subspaces):    • What is (a) Space? From Zero to Geo 1.5   - Section 6 (Linear Combinations/Span):    • Describing Many Vectors With a Few - ...   - Section 7 (Linear Dependence/Bases):    • Superior Spanning Sets - From Zero to...   - Section 8 (Components):    • Vectors Are Not Lists of Numbers (Par...   - Section 9 (Linear Spaces):    • Vectors Are Not Lists of Numbers (Par...   - Section 10 (Dimension):    • Dimension is Multi-Dimensional - From...   - Section 11 (Direct Sums):    • You can add scalars and vectors!  Fro...   More to come! Special thanks to wooden cube for doing the captions. Sections: 00:00 What is Geometric Algebra? 01:28 History of Geometric Algebra 02:57 Why isn't Geometric Algebra used more? 03:40 From Zero to Geo 04:16 Why a video series? 05:04 Flavors of Geometric Algebra 06:18 Exercises 08:31 Outline of Series