302.S13B: Fundamental Theorem of Algebra -- Proof

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Using three elementary properties of the real and complex fields, two Sylow-like results about subgroups of finite groups, and one heckuva lot of Galois correspondences, we prove the fundamental theorem of algebra.
  1. Matthew Salomone
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Комментарии
Автор

This is the clearest version of this proof that I've been able to find!

ai
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I don't quite understand everything, and I probably need to rewatch about 15 of these videos, but I just want to say that it's been a really fun ride. At this point it's cliché, but I really would like to thank you for making all of these wonderful videos and sharing them on YouTube!

PunmasterSTP
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Thanks so much for your lectures. Love them very much.

余淼-eb
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Just finished the whole playlist. Thank you professor Salomone.

essadababneh
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I truly enjoyed these videos. Modern Algebra is the course that convinced me to be a chemist (and not a mathematician). Regardless, Mathematics has always been my true love. So, thanks for finally bringing some light to what I found to be an almost impossible to understand topic.

shawnpheneghan
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I think your lessons are terrific. I have completed a number of them thus far and plan to continue.  Regarding your Table listing 3 key items of The Galois Correspondence, I believe the 2nd bullet should read degree of K over F = the Index of H in G.

kenflorek
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What guarantees that the extension E:R is finite?

raysaikat