A first course in the theory and analysis of functions of a real variable. Topics of study may include the real numbers, sequences and series, basic topology, limits, continuity, derivatives, and the Riemann integral. This course highlights the concept of rigor in the foundations of mathematics. The reading, writing, and evaluating of mathematical proofs is emphasized. The material covered and skills developed in this course will give students a deeper understanding of the general mathematical process, imperative for the future study and appropriate exposition of other mathematical concepts.