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I don't know this channel, maybe it was useful to its viewers, but to me, it didn't give anything. The presenter spent half the time waiting for answers which never came or caused even more delays, then "constructed" something without showing it, and at the end ran out of time before getting to the actual stuff, such as how you multiply 2δ*δ, what is exp(δ) and so on.

This video does a kinda bad job at communicating why geometric algebra should be teached. Showing the effectiveness of a certain method requires the following two steps: 1. Explain how the existing methods deal with a problem that you can solve with your method. 2. If your method is doing the same thing as an existing method, explain why your method still gives a more complete and general view of the solution, and how it impacts generalisations. For example, if you want to explain why umbral calculus (look it up, it is pretty cool) should be teached, you should show how it solves linear differential equations and linear recurrence relations in the same way as the laplacian and the generating series, but it unifies these two concepts in an algebraically rigorous way, and actually gives deeper insight in these solutions. The worst way to do this is to say "oh look at how nice we can write this", without actually showing how they would work, or just implying that it simplifies some of the proofs (like with the determinant). You wouldn't tell people how food tasted if you have samples of that food, right? This isn't any different. At least you didn't just gave definitions of Clifford algebra, that would be like giving out empty plates :)

23:38 numerical solutions of polynomial

4:15 3264

1:26 how many conic sections are in tangent

0:59 euclidean

This app has been horrible for my center. So much work to download photos onto the app when in reality it could be easier just to WhatsApp parents instead..why is this such a outdated and confusing format?!

this is such an incredibly helpful presentation, tysm

Interesting use of Bloom's Taxonomy of Educational Objectives. I've not seen this before.

Saved to Watch Later!

Best simplest straight-to-the-point explanation I could find all over the Internet, sincerely thankful Parker 🙏🏻

This is amazing!

Great video. Thanks for sharing

2:13 the leftmost pair of P's are at an awry angle.

Very interesting stuff

nice explanation

Irrespective of curriculum, where on the internet is there a course that teaches geometric algebra from beginning to end? I can't find anything and I can't find any schools teaching it locally (Sydney, Oz). I need a standard uni-like program with exams and course work.

[Solved] I'm lost at 9:32, is "u wedge v" a real number (as it can be added to u dot v, the number given by the dot product)? In that case isn't the uv (the left hand side) just a number as well? OR should the + sign understood purely as a simple rather than the usual addition between real numbers? [Edit] I figured it out (after watching Alan Macdonald's playlist, cited in the latter part of this video): the plus sign in the definition of geometric product uv = u dot v + u wedge v is understood purely symbolically, instead of the the usual addition in R. That is, uv is an ordered pair (u dot v, u wedge v), not a real number. The plus sign is merely a suggestive notation to facilitate computation in a more natural manner. Just like with complex numbers a+bi, we can still do complex arithmetic without the symbols + and i but they make things easier to memorize. Thanks for the presentation. It is really eye opening!

A lot of errors In "Drawing with ideal points" you use R (3,0,1) but define the point as a trivector. Which occurs in R*(3,0,1)

ive been trying to remember this version for forever, thank you so much! one of my favorite string tricks!

Thank you for that lovely introduction.

Hi! May you send me the email of one of the authors? I'm using your research for a paper and could use some more information :)

It's amazing and genius , thank you very much❤

I wish Logan would continue the geometric algebra series lectures!

Good lecture, a question; with everything matrix it's easy to make a computer do numerical calculations, how can geometric algebra can be used to do the same calculations?

Thanks for the lesson mr.dema!

Convergence (syntropy) is dual to divergence (entropy) -- the 4th law of thermodynamics! "Always two there are" -- Yoda.

Perpendicularity in hyperbolic geometry is measured in terms of duality! "Always two there are" -- Yoda.

I think Im going to start a youtube channel in english to start geometry from scratch.

18:25 so, i is a bivector (confusing, because I is the unit n-vector). what does it mean to raise a scalar to the power of a blade? You know what - I'll ask chatgpt.

2:57 - "And importantly, the subspaces must be (mumble)". Damn. I bet this is going to be a problem in a minute.

WRONG VIDEO... HELLO?? 📣

This has totally failed to explain for why.

Great job 👏

very good video

ABSOLUTELY AGREE, as a recent compsci grad who took many courses in LA, i agree, and would have muched preferred this, i thought my classes were stale, and I think geometric algebra is a really good framework and context for solving some of the most pressing problems across multiple fields in science.

How the hell can i see

Isn't the definition of compactness given here missing the word "open"?

Really inspiring work ! I think there is a typo at 30:29, f(y_n) should be "1/y^2 - x", instead of "1/y^2 + x" (even though it does not affect the derivative, it should mess with your signs, but you fixed it at 30:36) Very cool anyway !

Is this part of any playlist?

Great mathematics

Very cool!

"Geometric algebra" is just a goofy way of saying "some relatively elementary geometric aspects of Clifford algebras". It hardly deserves the name of "theory". It's stuff like the determinant trick to compute curl in vector calculus.

I *could not* agree with you more. I think geometric algebra brings a unity and clarity to things that we just don't get from the standard way all this stuff is taught. I think teaching us cross products instead of bivectors is... well, it's offensive. It's like saying "All you ever need to know is the stuff you can do with this hack." The cross product *only works* in 3D. Even when we use it in 2D we're really "cheating" - those 2D cross products fall outside of our "space at hand." We're expected to just hum and overlook this fact.

Thank you very much for the detailed explanation

I feel like I just keep going further down the rabbit hole with this stuff. I'm glad I didn't go to school for this. I might go insane trying to understand it. cos(arctan(i*v/c))=cosh(arctanh(v/c))=γ=1/sqrt(1-(v/c)^2)=c/sqrt(c^2-v^2) sin(arctan(i*v/c))=i*sinh(arctanh(v/c))=i*(v/c)*γ=i(v/c)/sqrt(1-(v/c)^2)=i*(v/c)*c/sqrt(c^2-v^2)=i*v/sqrt(c^2-v^2) This works for vector addition, but you have to include the 'i' or you do regular vector addition. (i*tanh(θ)+i*tanh(φ))/(1-i^2*tanh(θ)*tanh(φ))=i*tanh(θ+φ) It seems to me like sinh and cosh were invented because of 'i' getting passed into pythagorean theorem. I could also put 'i' in the denominator of 'v,' which would change very litte, just the sign and imply a real time in 'c' and an imaginary time in 'v.' The real axis would be the frame of reference frozen in time. The imaginary axis would be the time sticking out perpendicularly. There is a parabola associated with it. I think '-c/(2a)' in a*x^2+b*^x+c (not speed of light) represents the mass. It becomes sqrt([M]/[T]). I feel like it has meaning in the context of the reference frame I just mentioned, but I'm drawing up a blank.

Let suppose s is the supremum of near standards s. There are two alternatives: 1) s is near standard and 2) s is not near standard. If 1, s+1 is near standard so s cannot be the supremum. If 2 s-1 should be near standard but it is not possible. Booth case s lead to a false consequence, so there is not a supremum of the set of near standard.

The set of infinitesimal ha not a supremum

THIS IS THE WRONG VIDEO HOW COULD YOU DO THIS TO US

Great teaching 😊