Real Analysis I

3 credits · Undergraduate

(3 hrs Lecture) This course lays the theoretical foundation of single-variable calculus by providing a careful introduction to several fundamental concepts of analysis on the real line, and it provides a gateway to more advanced studies in analysis, topology and set theory. Topics covered include: functions acting on sets; countable and uncountable sets; suprema and infima; properties of the real numbers including completeness, the Archimedean property and density of the rational numbers in the real numbers; sequence convergence, monotone sequences, subsequences, the Bolzano-Weierstrass theorem and Cauchy sequences; limits of functions; continuous functions including proofs of the extreme and intermediate value theorems. Requisite Courses: Minimum grade of C in both MATH-1104 and MATH-1401 [prerequisite(s)].