I'm working on a M.S. in stats and have a very similar background to yours. I am not a fan of Dummit and Foote - the first chapter I found a nightmare to read through myself and I could not get past how dense and terse it was. I've also read Pinter's text and it's good for summarization, but it's not something that really engages me with the subject.
Ultimately, of all of the abstract algebra books I've read, I would have to recommend Abstract Algebra: Theory and Applications by Judson, which the author has made available for free online. Here's an excerpt from an MAA review for this text by Thron:
For many students, abstract algebra is the most daunting of math
classes. Many students (particularly those who do not have a strong
theoretical bent) see abstract algebra as symbol-twiddling with no
apparent rhyme or reason. To them, group theory proofs are just so
many rabbits pulled from hats.
The book’s presentation should be interspersed with numerous,
easily-worked examples. The exercises should be progressive, with a
generous number of relatively easy problems for student practice.
Practical applications of abstract algebra should figure prominently.
Of all the prospective texts I looked at from the standpoint of these
requirements, Thomas Judson’s Abstract Algebra: Theory and
Applications (AATA) was the best. (The fact that it was free was an
added bonus.) The level was non-threatening, and the order and
presentation of topics seemed perfect for what I was looking for. The
“Preliminaries” chapter begins with several pointers on reading and
writing proofs — vital background knowledge that most a abstract
algebra books take for granted. Next, the book covers sets and
equivalence relations in a way that bridges from familiar material to
a more abstract setting. In the chapters dealing with groups, there
are entire sections devoted to the integers mod n, symmetries, and
If you don't like Judson, I would try Fraleigh's text: A First Course in Abstract Algebra, 7th Edition.