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
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?
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.
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 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?
Subgroups are dual to subfields -- the Galois correspondence.
"Always two there are" -- Yoda.
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
Dr. Salamone has recommended Dummit and Foote, Abstract Algebra in another video. Links to it can be found online.
@@rdubeau Awesome; thanks!
1:28 I don't see anything to click on screen 😥
But in any case, thanks for another outstanding video!
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?
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.
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.
Don't be fooled, I'm a disorganized mess IRL too... but at least my exams are more reasonable 😋
@@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?
@@qwertyuiop1tiop590 This was from ages ago, but you're welcome to check it out: www.dropbox.com/s/5zdp82n9ln05bvq/302final.pdf?dl=1
@@MatthewSalomone Whoa, thanks for sharing one of your finals; I'm going to take a look at that as well!
Out of curiosity, what university did you/do you go to?