302.S7b: Field Automorphisms and Galois Groups

Motivated by symmety groups of polygons, we define automorphisms of a field extension, their fixed fields, and the Galois group. The real-to-complex number field extension provides a basic but fully-worked example.

[ali]

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

[rubberubertuber]

Brilliant video. You've clearly summarised in a few minutes what it's taken me weeks to get my head around. Thanks for sharing.

[anodamer]

I like your way of how to explain things

[yashmakwana]

I am surprised how such beautiful videos about beauty of mathematics have so few likes and views.

[hyperduality]

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.

[PunmasterSTP]

3:14 Ah, so that's what Galois groups are!

[anodamer]

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