Self-Study Geometric Algebra!

Transcript

so I've recently received a comment requesting a video discussing resources for geometric algebra self-study quick aside it's actually been quite a while real life grew a bit busier than I was expecting I know again so this video should have come out a while ago I even wrote the script over a month ago but it's here it's here now so hope it's helpful given this request and the requests I often hear from those new to the subject I decided to make a video on resources for this self-study this video will be divided into four main sections not including the intro and outro the best books for beginners books on geometric calculus some extra textbooks which are good reads and some papers which are good reads if you know of other books and can vouch for them I urge you to comment on the video I will only be showing writings that I've read and therefore only writings I can personally vouch for I will talk a little bit about each text to describe from which perspective it teaches and to give an idea of the prerequisite knowledge now if you enjoy learning by talking to others and also enjoy a good Community I recommend joining the bi Vector Discord server the link will be in the description I joined the server recently and I really like it the people there are kind and several of the authors from these upcoming books and papers are in the server so you can ask them questions directly schedule permitting and if it matters I can be found often in the physics and algebra channels within the server all three of these books are excellent for beginners but they approach the subject from very different perspectives linear and geometric algebra by Alan McDonald is a great textbook for someone who's mostly interested in the mathematics over the application it's also a great refresher on linear algebra I like the way the book is written but I'm not a huge fan of his visual formatting as I feel my eyes are a little overwhelmed by each page but it's still an excellent book especially for those new to the subject geometric algebra for physicists by Dorne and Lassen is by far my favorite textbook on geometric algebra while it assumes a physics background the writing logical flow and visual formatting are all extremely well done there's a reason I base my first YouTube lecture series off this book it's essentially the Bible of geometric algebra applications within undergraduate and entry graduate level physics geometric algebra for computer Graphics by John Vince is also a good introductory text especially for those in computer science I've not read the entirety of it but but it has good writing images and logical flow as an undergraduate student I was able to get my school library to purchase a copy of this book so that I could try to convince my professors that geometric algebra was actually useful for those interested in any Fields related to Quantum field Theory differential geometry Etc geometric calculus is a necessary subject to study it's more complicated in my opinion than geometric algebra so it requires the reader to have a decent understanding of geometric algebra already basically basically it's a generalization of calculus to work within the geometric algebra framework the essential textbook for anyone who wants to learn geometric calculus is geometric algebra to geometric calculus by hus and subject while the formatting makes this book seem daunting it's really understandable however I will say that some of the derivation skip steps that aren't super obvious so this book sometimes makes you work very hard to understand Alan McDonald also made a book titled vector and geometric calculus it's almost identical in format to his other aformentioned textbook so there's not much else to say I myself like to use this book as much as I do henus I also read through large portions of these two books and I recommend them to anyone who wants to have an extra dose of physics Insanity Matrix gateway to geometric algebra SpaceTime and Spinners is very well written and has great visualizations but the author is a demon and often skips many steps while demonstrating a proof or result the first half of the book is very introductory while the second half is very much not introductory but it's really good for understanding the fundamentals of geometric algebra and how they're constructed though I really only recommend the second half of the book for those who are really really dedicated or already have a background lesto Clifford algebras and Spinners is also an amazing read it's fairly Hefty but it covers the topic of spinners extremely well lesto has a very good intuition for Spinners and does an excellent job building up the physics and Mathematics for them and while he has some introductory chapters most of the book is non- introductory listed on the screen are five of my favorite papers on geometric algebra most of these are physics papers which use geometric algebra so they're likely only useful to those of you interested in physics so that's really it I hope these resources help you self-study geometric algebra with an undergraduate and entry gravel there's a reason I based my first YouTube lectured series off this VI F there's a reason I based my first YouTube lecture series off this book it's essentially the Bible of geometric algebra applications within undergraduate and gradu F there's a reason I based my first YouTube oh my gosh there's a reason I based my first YouTube lecture series off this book it's essentially the Bible of geometric algebra applications with an undergraduate and entry graduate level physics oh my gosh thank goodness