MAT357H1: Foundations of Real Analysis

Hours: 
36L

Function spaces; Arzela-Ascoli theorem, Weierstrass approximation theorem, Fourier series. Introduction to Banach and Hilbert spaces; contraction mapping principle, fundamental existence and uniqueness theorem for ordinary differential equations. Lebesgue integral; convergence theorems, comparison with Riemann integral, L^p spaces. Applications to probability.

Prerequisite: 

MAT257Y1/​(MAT327H1 and permission of instructor)

Exclusion: 
Distribution Requirements: 
Science
Breadth Requirements: 
The Physical and Mathematical Universes (5)