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/sci/ - Science & Math

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11214602 No.11214602 [Reply] [Original]

Any Good Resources for Galois Theory? I'm reading Milne now and finding it dry. It also has too few examples and problems for me to really understand the concepts.

>> No.11214752
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11214752

>> No.11214768

>>11214602
https://www.math.ens.fr/~debarre/Algebre2.pdf
God tier and treats Galois theory in under 40 pages

>> No.11214849

>>11214768
c'est en français ça gros ^^

>> No.11214852

>>11214602
hey friend, just read the late robert ash's notes.
https://faculty.math.illinois.edu/~r-ash/Algebra.html

chapter 6 is what ur looking for.

ignore the frenchman, those notes are shite

>> No.11214882
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11214882

Always read the original first, and ignore textbooks. Textbooks are usually written by ignorant people. It is always best to read authors that know the subject, so original papers are best unless they are so old they start speaking latin.
https://anonfile.com/Nci8BcE9nf/
https://anonfile.com/Haj5B9E5n5/
https://anonfile.com/Z6j9B9Ecna/
https://anonfile.com/1fj9BcE7nd/
This should be enough to get you going. After this you should follow the /sci/ wiki. Remember: math is fun. Don't forget to have fun.

>> No.11214905
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11214905

>>11214602

>> No.11214908

>>11214602
If you're already familiar with fields, then the first part of Kaplansky's Fields and Rings is really good.
Morandi's Fields and Galois Theory is really slow and easy so it can be boring if you're not interested in the material, but it has a lot of problems so it might be what you want.

>> No.11214925

>>11214852
>ignore the frenchman, those notes are shite
LOL, how can one man be so wrong ?

>>11214882
>Always read the original first, and ignore textbooks.
Terrible idea. The original is usually not normalized, with antiquated language that might not even be in use anymore, and suboptimal treatment.
In fact, the original presentation is almost never the place to learn something, especially something that is more than 100 years old.
In most cases, conceptual simplifications occur after the fact that make the theory clearer and better articulate its connections with other subjects.
This is not to say that there is no value in reading old texts, of course. There is a lot to be gained by doing that, especially Galois' texts, but not as a first approach of the subject.
In fact, if you are not familiar with Galois theory as it is taught today, you probably will not understand anything Galois wrote. I mean, if the best mathematicians of his century had to wait half a century to decipher his manuscripts, then in all likelihood, you are probably not going to be the one to do it, no offence.

>> No.11214944

>>11214602
I actually just started reading Stewart's book and I find it very well written so far, I think it's a great and very friendly intro. I also have Cox's book downloaded and just skimming over the contents and a little bit at the beginning seems to suggest it's also of good quality

>> No.11214947

>>11214882
>Always read the original first, and ignore textbooks
This is true in some cases and very wrong in others. You could for example read Gauss' Disquisitiones and get a kick out of it, but I wouldn't recommend reading Galois theory in its original form, from what I've read of the history of the subject it has gone through significant reforming and its modern presentation in terms of field extensions is vastly different to Galois' own work.

>> No.11214954

>>11214905

Galois died a virgin, he was a supreme gentleman alright

>> No.11215043

>>11214925
>>11214947
you missed the joke, guys

>> No.11215102

>>11215043
idk, there is so much edginess and so many pseuds on this board that I would not be surprised if someone were seriously recommending this.
I want OP to get some serious recs

>> No.11215162

>>11215043
we did? mb then, but i'm absolutely sure there'll be idiots on this board who will in all seriousness recommend something like this. and going back to the sources isn't necessarily a bad thing, just most of the times it's better to have some footing in the subject first, although there are exceptions, like the writings of Gauss, Hermite, Klein and Dedekind (ones I know of)

>> No.11215274

OP here, thanks for the suggestions, everybody. I'll definitely check them out.

>> No.11215931
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11215931

>>11214882
>Always read the original first
I disagree. The only possible motivation would be to grasp the motivation behind the modern definitions but in most cases, a good textbook will provide the motivation anyway. Otherwise, you'd be wasting your time and mind, and people who aren't namefagging schizos often like to economize both.

>> No.11215951

>>11215931
see >>11215043

>> No.11217034

>>11214602
Just wikipedia desu.

>> No.11217225

>>11214602
[eqn]\mathbb{SUPREME\ GENTLEMAN}[/eqn]