This webpage is for the *Fall 2020 course* at the University of Pittsburgh. The main page can be found in canvas.

**The classes will be in-person as much as possible. You have the right to attend digitally, classes will be recorded and available to students.**

**Homework is to be submitted digitally. Office hours only via zoom or similar**

# Syllabus

The lecture is based on the following book by P. Hajlasz

I will post lecture notes here: lecture notes

For the full syllabus see canvas.

## Recomended books:

Berkeley Problems in Mathemtics, Third Edition, by P. N. De Souza and J.-N. Silva

This is an excellent collection of problems for the course. Problems have full solutions. Chapters 1,2,4 cover much of the material needed for the Preliminary Exam in Analysis. Other chapters contain excelelnt problems for other graduate courses like Linear Algebra, Algebra, Analysis II and Ordinary Differential Equations. This book is a must for any Ph.D. student.

Elementary Classical Analysis , Second Edition, by J. E. Marsden and M. J. Hoffman

Principles of Mathematical Analysis, by W. Rudin

Mathematical Analysis, Second Edition, by T. M. Apostol

Real Mathematical Analysis by Ch. Ch. Pugh.

## Course content

Set theory. Axiom and construction of real numbers. Supremum, infimum, limits and seties, upper and lower limits. Continuity and differentiability of functions. Riemann integral. Metric spaces, contraction principle with applications, Arzela Ascoli theorem, Stone-Weierstrass theorem.

## Office hours

Office hours available upon request by email: armin@pitt.edu

## Teaching Assistant

Teaching Assistant: Tyler Gaona