Currently a 5th year PhD student, and I've been fighting tooth and nail to teach one of our junior-year honors sections in undergraduate algebra next fall (desperately hopeful we'll be able to return to normal in-person lectures at that point). Looks like it may come to fruition. Some questions on texts.
When I took undergraduate algebra, it was taught out of Herstein's classic Topics in Algebra for a two-semester honors sequence. The reception was somewhat lukewarm from the students. I definitely recall a point towards the end of the second semester (Galois theory) when about half the class was more-or-less completely lost, and from what I remember I was a bit lost myself but still managed to do well in the course. I liked the book at the time, but I remember feeling like it was times a bit slick, bit generally a good read overall and I learned a ton.
Recently, I've been made aware of another text by Dan Saracino titled Abstract Algebra: An Introduction, and apparently it's well-regarded by some people I respect. I've ordered a copy, but in the meantime I'm curious what others' opinions are on a comparison between the two, and experience with students' performance using both? In previous years, the course has used Herstein (and I believe at one point Artin, another great option but with a very different style).
The course is aimed at some pretty bright students, many of whom will pursue PhDs themselves, so I'm tempted to use Herstein (the problems are great, albeit at times very challenging, and it's one of the standards for this purpose). At the same time, I'm always of the opinion that students learn best when the exposition is clear and well-motivated, and it sounds like Saracino is a good candidate for that.
Any advice or anecdotes for people who have used both texts? I'm very passionate about teaching and I'd like to put the students in a good position for future graduate work. At the same time, I want the material to actually stick. I guess everyone has their own style, but I prefer courses that follow a text pretty closely rather than relying only on lecture notes.
For context, most students will be coming from a history of similar honors-type courses (including a recent course in Linear Algebra from Axler's excellent book, and an analysis course from baby Rudin, so they're well-versed in proof-writing and have a bit of maturity). It sounds like about half of students are expected to have taken a general intro to abstract algebra course (basic group theory, rings, and vector spaces) and half will be seeing it for the first time.
