Foundations of Algebra: An Introduction to Advanced Mathematics

This text is used at Lawrence University for a sophomore level course introducing advanced mathematics. Topics include basic logic and set theory, the integer axioms, elementary number theory, group theory to Sylow's existence theorem, rings, and polynomials. Proof techniques and mathematical notation are carefully introduced and reinforced. The student is expected to read actively and carefully, working both theoretical and computational exercises along the way. Problems given at the end of each chapter exhibit problem-types rather than to give a comprehensive set of exercises.