Description (from Math Department)
Background and Goals
This is a course in analysis for students who know how to write rigorous mathematical arguments and possess a firm understanding of the standard concepts of linear algebra. It is specifically designed for students who excelled in Math 217, love mathematics, and wish to transition into the Honors Analysis Sequence.
Content
This is a course in real analysis for students possessing both a firm understanding of how to read and write rigorous mathematical arguments and a solid understanding of the standard concepts of linear algebra at the level of Math 217. Topics covered include: axioms of the real numbers; complete-ness, compactness, and connectedness for finite dimensional inner product spaces; sequences, series, and limits in inner product spaces; continuity and uniform continuity for functions of finite dimensional inner product spaces; the extreme and intermediate value theorems, differentiation, integration, the fundamental theorem of calculus, and Taylor’s theorem with remainder for functions of one real variable. The emphasis is on concepts, problem solving, and the underlying theory and proofs. It provides an excellent background for advanced courses in mathematics.