Mathematics: Anyl in Several Real Vars I

Properties of the real numbers, basic topology of metric spaces, infinite sequences and series, continuity. Prerequisites: MATH 2468 or MATH 2551 or C- or better in MATH 2055; MATH 2248; MATH 2522 or MATH 2544.

Prereqs enforced by the system: (MATH 2055 or 2468 or 2551) and MATH 2248 and (MATH 2522 or 2544); Open to Degree and PACE students

This a proof heavy course, so you are required to have been take a proof class before this one. We will cover: - recap of basic properties of the real numbers and basic set theory - topology in Rd and general metric spaces - limits [of sequences and functions] and continuity [of functions]) - derivatives - infinite series.

Analysis is about reasoning with inequalities. Its fundamental definitions and results (about convergence, continuity, and limits) are expressed in terms of inequalities. This kind of reasoning can seem unnatural at first. You will begin to master it (real mastery will take several more years). At the end of the course you should know the fundamental definitions and theorems of mathematical analysis, and know how to use them to prove facts you took for granted in freshman calculus, as well as see where those facts fit in larger, more general contexts (e.g., in Rd and metric spaces). You should also know how to spot flaws in faulty proofs and, in many cases, provide and explain counterexamples to false conjectures

60% homework, 15% midterm, 25% final.