MATH 5110, Fall 2021

course home page: 5110 Introduction to Modern Analysis

Course description as a pdf file

The purpose of this course is to give students preparation in point-set (general) topology of metric spaces and analysis of functions of one real variable. Topics will include construction of the real numbers, basic topology of metric spaces, compactness and connectedness of sets in the Euclidean space, convergence of sequences and series (e.g. Bolzano-Weierstrass and Heine-Borel theorems), limits and continuity of real-valued functions, differentiation and Riemann integration of functions on the real line and the Fundamental Theorem of Calculus, the Arzela-Ascoli Theorem, and the Stone-Weierstrass Theorem. We expect to cover chapters 1-7 of the textbook along with some additional material.

A large part of the homework and exams will involve mathematical writing. It will be helpful to write your homework using LaTeX.

More information can be found at the Campuswire course webpage.

Masha Gordina (maria.gordina at