TITLE: Is it possible to learn abstract algebra no precalculus or calculus?
QUESTION [6 upvotes]: See above. I am trying to re-teach myself mathematics in a different manner than is formally taught (i.e., set theory, number theory, mathematical logic, abstract algebra, discrete math and then precalculus (college algebra and analytical geometry). These are the pillars to upper level mathematics correct?

REPLY [7 votes]: You can certainly learn abstract algebra before you learn calculus (I did this myself), but you (almost certainly) won't be able to learn it if you aren't comfortable with high school algebra (which, I guess, is a sizable component of what is called pre-calculus).   A basic facility with factorization, algebraic manipulations (like modifying two sides of an equation by applying the same process to both sides),
exponential notation, and complex numbers (among various algebra topics of this
sort) is more-or-less essential to successfully learning abstract algebra.