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Elementary topological and analytic properties of real numbers, especially the completeness axiom, limit, convergence, and the basic theory underlying differential and integral calculus.

This course is an introduction to analysis, designed for undergraduate STEM majors who have already studied calculus. The focus is on rigor and foundational concepts. The material begins with logical systems and set theory notations, then progresses to the basics of analysis, including natural numbers, axioms of real numbers, limits, series, continuity, differentiation, and integration. It also covers Taylor and power series. The course thoroughly explores real numbers, including concepts such as open and closed sets, and compactness, with a strong emphasis on understanding and constructing mathematical proofs. The goal is to help students think clearly and write logically. This course serves not only as the first step in theoretical mathematics, but also for a solid foundation for applications in STEM fields. 

This course is taught by a faculty member and complemented by a weekly discussion section with a TA to help students understand the course materials and homework.