Mathematical Studies Analysis I

12 units · Undergraduate

Fall: 12 units A component of the honors program, 21-235 is a more demanding version of 21-355 of greater scope. Topics to be covered typically include: metric spaces, normed spaces, and inner product spaces; further properties of metric spaces such as completions, density, compactness, and connectedness; limits and continuity of maps between metric spaces, homeomorphisms, extension theorems, contraction mappings, extreme and intermediate value theorems; convergence of sequences and series of functions; metric spaces of functions, sequences, and metric subsets; Stone-Weierstrass and Arzela-Ascoli theorems; Baire category and applications; infinite series in normed spaces, convergence tests, and power series; differential calculus of maps between normed spaces, inverse and implicit function theorems in Banach spaces; existence results in ordinary differential equations. The prerequisite sequence 21-128 , 21-242 , 21-269 is particularly recommended. (Three 50 minute lectures, one 50 minute recitation) Prerequisites: 21-268 or 21-256 or 21-269 or 21-259 Course Website: https://www.cmu.edu/math/undergrad/math-course-information.html