This is the first half of a one-year calculus sequence for first year students with a strong interest in mathematics with an emphasis on rigor and proofs. The course begins at the beginning but assumes the students have already studied the material from a more "mechanical" view. Students who complete both semesters will have completed the material Calc III and other topics that may let them move through the upper level math curriculum more quickly. Sets, functions, real numbers, and methods of proof. The Riemann-Darboux integral, limits and continuity, differentiation, and the fundamental theorems of calculus. Sequences and series of real numbers and of functions. Vector spaces and linear maps. Prerequisite: Score of 5 on the A.P Calculus Exam, BC version, or the equivalent.
Course Attributes: FA NSM; AR NSM; AS NSM; AS AN