Compatibility of Physics and Abstract Algebra

[TRB8985]

One of the last classes I'm taking before finishing my degrees as an undergraduate is abstract algebra. My professor uses the textbook 'Contemporary Abstract Algebra' by Joseph Gallian. The book isn't written terribly nor is the teacher a poor one, but I just find this subject so uncharacteristically challenging compared to all other math experiences I've had up until this point.

I've shared my experience with a couple professors from my physics department, whose specialties lie in heavy-ion physics, lasers, and mathematical physics, and they all seemed to share a common trait of also having difficulty in this subject at an undergraduate level.

This had me curious - do most undergraduate physics majors also have difficulty with this course?

It feels like there's just something uniquely difficult about this subject compared to, say, multivariable calculus or a PDE course. The content is so monumentally boring and so far-removed from anything familiar that even mustering up the energy to do the homework is like pulling teeth, which is funny, because I really do enjoy physics and mathematics.

Has anyone else had this experience? Do you have any suggestions? Thank you for your input.

 

[fresh_42]

The way of thinking is a different one. Whereas you seem to be accustomed to think in terms of functions, the thinking here is along structures. And as always a change of habit is a difficulty per se. I had a look at the content of the book and to me, these are all simple basics, like Newton's mechanics would be for physicists. It apparently doesn't contain any advanced things as Galois theory, spectral theory or any other more interesting subjects. However, if it happens that you will be interested in QFT or cosmolgy or crystallography someday, those fundamentals are the basic language for Lie theory (QFT), algebraic varieties and topological invariants (cosmology), and symmetry groups (cristallography).

 

[PeroK]

Abstract algebra is a very different beast. My only advice is to try to arm yourself with good examples of all the key concepts to try to anchor the abstraction in concrete examples.

Even though I studied pure maths, I was generally much happier with analysis and linear algebra. Group theory never caught my imagination.