Strongly recommended for future math majors, this course covers calculus more thoroughly and more theoretically, giving an introduction to important mathematical techniques and results that give a foundation for further work in analysis. It serves as an introduction to the rigorous proofs and formal mathematical arguments needed in all upper division math courses.

Equal emphasis is given to learning new mathematics and to learning how to construct and write down a correct mathematical argument by dividing the question into logical steps where each step is explained and justified carefully, giving references if necessary. For most students this will be a completely new and very challenging way of doing mathematics, very far removed from the process of memorizing algorithms and working through concrete calculations typical of high school math.