@@PunmasterSTP Just general interest. There's something magical about abstract algebra that's very absorbing. But I often wonder if it isn't all just one big tautology (ala Wittgenstein).
Real numbers are dual to complex numbers! Real numbers are their own conjugates or self dual. "Always two there are" -- Yoda. SINE is dual to COSINE -- the word "co" means mutual and implies duality. SINH is dual to COSH -- hyperbolic functions. Positive curvature (convergence, syntropy) is dual to negative curvature (divergence, entropy) -- Gauss, Riemann geometry. Curvature or gravitation is dual -- potential energy is dual to kinetic energy. Injective is dual to surjective synthesizes bijective or isomorphism.
If there was no limit for clicking on the thumbs up icon, I would have click on it day and night continuously as long as I live. Thank you Dr. S
It be cool if RUclips had some kind of functionality like Cookie Clicker!
Brilliant video. You've clearly summarised in a few minutes what it's taken me weeks to get my head around. Thanks for sharing.
Out of curiosity, were you studying for a class, or just because you were interested in abstract algebra?
@@PunmasterSTP Just general interest. There's something magical about abstract algebra that's very absorbing. But I often wonder if it isn't all just one big tautology (ala Wittgenstein).
@@rubberubertuber I wasn't familiar with Wittgenstein's works, but that sounds fascinating!
I like your way of how to explain things
I am surprised how such beautiful videos about beauty of mathematics have so few likes and views.
Real numbers are dual to complex numbers!
Real numbers are their own conjugates or self dual.
"Always two there are" -- Yoda.
SINE is dual to COSINE -- the word "co" means mutual and implies duality.
SINH is dual to COSH -- hyperbolic functions.
Positive curvature (convergence, syntropy) is dual to negative curvature (divergence, entropy) -- Gauss, Riemann geometry.
Curvature or gravitation is dual -- potential energy is dual to kinetic energy.
Injective is dual to surjective synthesizes bijective or isomorphism.
Wonderful thank you sir 🙏🏻
3:14 Ah, so that's what Galois groups are!
Do u have pdf please send link sir
Hi,
I am an international studen, from Saudi arabia, and I would like to have a tutoring lessons with you by skybe, would you be available in May/2015
The entitlement is insane
Out of curiosity, did you end up getting tutoring, and how did your studies go?