What are the pros and cons for students of taking introductory real analysis before or after introductory abstract algebra, assuming they are going to take both?
I recognize that the overlap between the two courses is minimal, and therefore they are largely independent of one another. (A debatable minor exception could be discussing fields when introducing the real numbers axiomatically, when the notion of a field is discussed in more detail in an abstract algebra course.) That said, students might cope better with real analysis than abstract algebra because it initially covers familiar ground (calculus). On the other hand, they might find the challenges of epsilontics, including working with double quantifiers and inequalities particularly difficult in contrast to the early proofs in abstract algebra.
(By introductory real analysis, I mean primarily a course covering the theory of single variable calculus and possibly also introducing metric spaces; a typical textbook could be Abbott's Understanding Analysis; by introductory abstract algebra, I mean a first course on groups, rings and fields; a typical textbook might be Fraleigh's A First Course in Abstract Algebra or Gallian's Contemporary Abstract Algebra.)