Abstract Mathematics II

MATH 124 is where you stop taking the number system for granted and start building it: you construct the naturals from ZF axioms, the reals from Cauchy sequences, and meet your first serious algebraic structures (groups, rings, quotients) along the way. Expect weekly problem sets and quizzes that lean hard on writing clean proofs, by the end you should be comfortable stating Lagrange's Theorem, proving completeness of R, and arguing why the Bolzano-Weierstrass Theorem holds. It's the spring half of the proof-writing sequence that follows MATH 123, and it's the bedrock for everything later: real analysis, abstract algebra, and topology all assume you internalized this material.