Math 131C: General Course Outline
131C. Topics in Analysis. (4) Lecture, three hours; discussion, one hour. Requisites: courses 131A, 131B. Advanced topics in analysis, such as Lebesgue integral, integration on manifolds, harmonic analysis. Content varies from year to year. May be repeated for credit by petition.
Math 131AB is the core undergraduate course sequence in mathematical analysis. The aim of the course is to cover the basics of calculus, rigorously. Along with Math 115A, this is the main course in which students learn to write logically clear and correct arguments.
There is an honors sequence Math 131AH-131BH running parallel to 131A-131B in fall and winter. 131AH: Rigorous treatment of the foundations of real analysis, including construction of the rationals and reals; metric space topology, including compactness and its consequences; numerical sequences and series; continuity, including connections with compactness; rigorous treatment of the main theorems of differential calculus. 131BH: The Riemann integral; sequences and series of functions; power series, and functions defined by them; differential calculus of several variables, including the implicit and inverse function theorems.
Math 131C is a special topics analysis course offered in the spring that is designed for students completing the honors sequence as well as the regular 131AB sequence. It traditionally covers Lebesgue measure and integration. Math 131A is offered each term, while 131B is offered only Winter and Spring.