What textbooks did you use for your abstract algebra course. Pic related

>>16700759
Was it a good book to learn from?

>>16700613 (OP)
Holy motherfucking filtered.

>>16700613 (OP)
Yeah I don't really get it. I really like PDEs, approximations, functional analysis, but I couldn't stomach abstract algebra courses. Like they're all about the integers? Who the fuck cares. More advanced courses sound more interesting, regarding algebra, but seems like a lot of tooling for problems I don't quite care about.

>>16700835
A lot of immediate applications in cryptography and number theory.

>>16700836
>A lot of immediate applications in cryptography and number theory.
>cryptography
This is a meme. And about number theory, it is too niche to justify taking the courses.
https://afiodorov.github.io/2015/09/17/number-theory/

>>16700613 (OP)
We used Herstein for both group and ring theory btw

>>16700843
Bit how was it anon, on a scale of 1 to 10 how was the experience with the book?

>>16700838
GF(256) is used in aes for instance å

>>16700835
>Like they're all about the integers?
No. For example the rational functions (polynomialis dividing other polynomials) form a field. You can study rational functions using abstract algebra without invoking any analysis. In fact, you'd likely obfuscate your results about rational functions if you intuit about them as analytic functions and not abstract algebraic objects.

So say your PDE results in polynomial solutions (Kepler problem for example). You can torture yourself with nasty integrals, coordinate transformations, and singularities. Or you can just think about the solution space as the space of algebraic varieties and use the tools of algebraic geometry.

>>16700850
It was kind of uninspiring, but it's a solid 8. A friend that is smarter than me liked Judson's when I let him borrow it from me (https://judsonbooks.org/aata/). It goes into the applications in coding theory in some chapters.

>>16700855
>No. For example the rational functions (polynomialis dividing other polynomials) form a field.
Yes, now I remember when you mention it, we saw that by the end of the course.

>Or you can just think about the solution space as the space of algebraic varieties and use the tools of algebraic geometry.
Well that sounds more of a motivation than "number theory" or "cryptography", but still quite niche IMO. "Introductory" PDE books like Evans won't go into it as a requirement, not even the 4 volume work on PDEs by Lars Hormander I remember going into anything related to abstract algebra. And PDEs is past the first year of graduate mathematics after you've taken the obligatory courses, there are a lot more courses that justify themselves immediately regarding this path.

That said Group and Ring theory are low hanging fruit of course it doesn't hurt to take the courses.

>>16700873
Group theory is much more appropriate for PDE. Check out Symmetry and Separation of Variables by Miller or Applications of Lie Groups to Differential Equations by Olver. Both requires some basic knowledge of group theory and Lie group theory in particular. But they demonstrate how abstract algebra isn’t just useless mumbo jumbo.

so it's official, only like 2 people on sci have ever taken a abstract algebra course

>>16700836
I think that's part of the problem for me. I don't give a shit about cryptography or number theory, at least beyond getting a basic understanding of what's possible (public/private keys etc).