Algebra I

Group theory is the spine of modern algebra, and this course is where you learn to think structurally — recognizing when two seemingly different objects (symmetries of a polygon, permutations, modular arithmetic) are really the same group in disguise. You'll spend the semester proving things: chasing cosets through Lagrange, decoding group actions via the class equation, and using the Sylow theorems to classify groups of small order. It's the prerequisite spine for MATH 324 (rings and fields), Galois theory, and essentially any algebraic structure you'll meet later, so the proof fluency you build here pays off well beyond this one course.