Real Analysis

Boston College, Fall 2016

The aim of this course is to provide the basic methods and techniques of real analysis. We will start by going over the foundations of measure theory, which is necessary in order to properly study integration of real functions. We will then study elements of functional analysis such as L^p-spaces, Radon measures and their various applications.

Prerequisites

The course is intended for the first year graduate students; Interested undergraduate students are also welcome.

I will assume knowledge of a basic courses in analysis including the topology of metric spaces. Knowledge of linear algebra will also be assumed.

Bibliography

The main text book for the course is

• G.B Folland, Real Analysis: modern techniques and their applications.

You should also consult

• E. M. Stein and R. Shakarch, Real Analysis: Measure Theory, Integration, and Hilbert Spaces

you can also find the Course Syllabus in PDF here.

Schedule

MWF 11-11:50

Room:Gasson 208

Homework

There will be periodic homework assignments posted here.

1. Assignment 1, due date: Sep. 21, 2016.
2. Assignment 2, due date: Sep. 30, 2016.
3. Assignment 3, due date: Oct. 14, 2016.
4. Assignment 4, due date: Oct. 28, 2016.
5. Assignment 5, due date: Nov. 16, 2016.
6. Assignment 6, due date: Dec. 02, 2016.