Introduction to Galois Theory

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Below are the top discussions from Reddit that mention this online Coursera course from HSE University.

Offered by HSE University. A very beautiful classical theory on field extensions of a certain type (Galois extensions) initiated by Galois ... Enroll for free.

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Taught by
Ekaterina Amerik
Professor
and 10 more instructors

Offered by
HSE University

Reddit Posts and Comments

1 posts • 7 mentions • top 5 shown below

r/math • post
61 points • octatoan
Galois theory course on Coursera!
r/math • comment
1 points • suzieqandchuckondown

Sure: https://www.coursera.org/learn/galois

r/math • comment
1 points • chebushka

You can see the syllabus on the page https://www.coursera.org/learn/galois#syllabus. I don't think the course overall was an information dump since many (not all) of the topics in it look standard. Galois theory is a pretty challenging course since so many new concepts arise and interact.

The parts of that syllabus I'd say could have been removed for an undergraduate level course are an in-depth discussion of inseparable extensions in week 3, the commutative algebra digression in week 4, properties of separable extensions via tensor products in week 5, and the proofs of the approach to computing Galois groups over Q using prime ideals and decomposition groups at the end. I can see from the syllabus why tensor products were introduced: they allow for slick and efficient proofs of some properties of separable extensions. Those properties have more elementary proofs, but such proofs can look a bit tedious by comparison. As for the computation of Galois groups using reduction mod p, the instructor evidently wanted to have a logically self-contained treatment justifying the method used, and that necessitates all the technical material on integral extensions and prime ideals in rings of integers of a number field. It is a lot to absorb, and at an undergraduate level I'd probably just state the result and show how it can be used, leaving the justification to a later course on algebraic number theory.

You wrote in you first commen that you first saw Kummer extensions in a course on local class field theory. That seems late to me. I heard about them in my first undergraduate Galois theory course (or at least they were in the textbook, which I read very closely). I think Kummer extensions are an appropriate topic for an undergraduate course if time allows, since they are closely related to the whole apparatus around solvability. I don't mean arbitrary Kummer extensions, but just the cyclic case.

r/math • comment
2 points • onetwosex

Trust the Russians

https://www.coursera.org/learn/general-relativity

https://www.coursera.org/learn/galois

https://www.coursera.org/learn/modular-forms-jacobi

Disclaimer: I haven't taken any of the aforementioned courses, but they look very advanced to me.

r/mathematics • comment
1 points • minishrink

Do you mean to take for credit, or to do in your own time? I don't know about getting university credits, but here are some I found online which are free, provided by universities, and include assignments. Unfortunately they don't all align with your list, but maybe you'll be interested in some of these, if you haven't already taken some of them?

Intro to Complex Analysis (Wesleyan university)
Complex Analysis (MITx, touches on Riemann surfaces)
Intro to Galois Theory
Initiation à la théorie des distributions

Not really sure about this, it's a mix of analysis and computer science, but
Intro to Numerical Analysis

And from Stanford:
PDEs in Applied Mathematics