An intermediate course in the theory of metric spaces and the continuous functions that act on them: metric spaces and normed vector spaces; complete metric spaces and the Baire category theorem; continuous functions on compact metric spaces and uniform convergence; the contraction mapping principle and applications; theorems of Stone-Weierstrass and Arzelà-Ascoli; differentiability on Euclidean spaces and the implicit function theorem.
This course may not be repeated for credit.
Prerequisite(s)
- Mathematics 367 or 377; and 3 units from Mathematics 311, 313, 361 or 411; and Mathematics 335 or 355.
Antirequisite(s)
- Credit for Mathematics 445 and 447 will not be allowed.
Sections
This course will be offered next in
Winter 2022.