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302.S9A: Galois Groups and "Stubborn" Polynomials 

Matthew Salomone
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In what sense does the Galois group of a polynomial measure how "stubborn" it is to splitting? We look at two examples of cubics, one of which is maximally stubborn -- has largest possible Galois group -- and the other of which is more easygoing.

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14 окт 2024

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Комментарии : 13   
@hyperduality2838
@hyperduality2838 Месяц назад
Subgroups are dual to subfields -- the Galois correspondence. "Always two there are" -- Yoda.
@alunroberts3694
@alunroberts3694 9 лет назад
As I have said before, these videos are really, really good! I'm getting to understand the whole theory, but will need to do more work to master it. Could you recommend any suitable text and/or excercises which would aid my understanding? Thanks
@rdubeau
@rdubeau 5 лет назад
Dr. Salamone has recommended Dummit and Foote, Abstract Algebra in another video. Links to it can be found online.
@PunmasterSTP
@PunmasterSTP 2 месяца назад
@@rdubeau Awesome; thanks!
@PunmasterSTP
@PunmasterSTP 2 месяца назад
1:28 I don't see anything to click on screen 😥 But in any case, thanks for another outstanding video!
@christiansmakingmusic777
@christiansmakingmusic777 3 года назад
This is where galois theory always loses me. The roots have to be complex numbers, and aren't there numerical algorithms for finding the actual values?
@PunmasterSTP
@PunmasterSTP 2 месяца назад
Yeah this stuff is pretty dense. I think there are numerical algorithms for *approximating* values, but as far as finding exact answers, I think you have to make use of roots and field theory.
@qwertyuiop1tiop590
@qwertyuiop1tiop590 2 года назад
I would kill to study under you, my Galois teacher doesn't publish videos online for study and his notes are very dense and 90% difficult to follow proofs. His tests are ridiculously difficult with an average grade of 41 and he frequently makes mistakes when lecturing.
@MatthewSalomone
@MatthewSalomone 2 года назад
Don't be fooled, I'm a disorganized mess IRL too... but at least my exams are more reasonable 😋
@qwertyuiop1tiop590
@qwertyuiop1tiop590 2 года назад
@@MatthewSalomone And you respond very swiftly 🙂 Of course, I do respect my teacher, he always responds to my queries very swiftly, I just wish his final exam was easier, where can I find final exams from your course?
@MatthewSalomone
@MatthewSalomone 2 года назад
@@qwertyuiop1tiop590 This was from ages ago, but you're welcome to check it out: www.dropbox.com/s/5zdp82n9ln05bvq/302final.pdf?dl=1
@PunmasterSTP
@PunmasterSTP 2 месяца назад
@@MatthewSalomone Whoa, thanks for sharing one of your finals; I'm going to take a look at that as well!
@PunmasterSTP
@PunmasterSTP 2 месяца назад
Out of curiosity, what university did you/do you go to?