This course constitutes a bridge between calculus and theoretical, proof-based courses such as real analysis, abstract algebra and set theory. The emphasis is on understanding and mastering increased levels of rigor, dealing with mathematical notation, and learning how to write, present and analyze proofs. Course content includes axiomatic systems, the principle of mathematical induction, proof by contradiction, existence principles, mathematical logic, elementary set theory, countable and uncountable sets, bijections between sets, combinatorics, and abstract structures and isomorphism.