Institute for Mathematical Science

Stony Brook University

office: Math Tower 4-103

phone: (631) 632-8266

e-mail: remus.radu@stonybrook.edu

MAT 324: Real Analysis

Fall 2016

Course Information

Fall 2016

Course Information

In this course we will discuss Lebesgue measure, Lebesgue integration, metric spaces (including compactness, connectedness, completeness, and continuity), aspects of Fourier series, function spaces, Hilbert spaces and Banach spaces. After developing the basic theory we will also give some applications to Probability. The main results will be the Monotone Convergence Theorem, the Dominated Convergence Theorem, the Radon-Nykodyn Theorem, and the Central Limit Theorem.

Click here to download a copy of the course syllabus. Please visit the course website on Blackboard to see your grades.

Tuesdays & Thursdays 10:00-11:20am in Melville Library W4535

Remus Radu

**Office:** Math Tower 4-103

**Office hours:** Wednesday 12:00-2:00pm in Math Tower 4-103

Monday 3-4pm in MLC, or by appointment

El Mehdi Ainasse

**Office:** Physics D-107

**Office hours:** Wednesday 4-5pm in Physics D-107

Monday 4-4:30pm, Wednesday 10-11am, and Friday 12-12:30pm in MLC

Marek Capinski & Ekkehard Kopp, *Measure, Integral and Probability*, 2nd ed., Springer-Verlag,
Springer Undergraduate Mathematics Series, ISBN 1-85233-781-8.

- G. Folland,
*Real Analysis: Modern Techniques and their Applications (2nd ed.)*, John Wiley, 1999. - E. Stein and R. Shakarchi,
*Real Analysis: Measure Theory, Integration, and Hilbert Spaces*, Princeton University Press, 2005. - Terrence Tao,
*An introduction to measure theory*, Graduate Studies in Mathematics, vol. 126, 2011.

The book is based on the notes posted on his blog (begin reading with Prologue & Note 1 -- bottom of the webpage).

Grades will be computed using the following scheme:

- Homework – 25%
- Midterm – 30%
- Final – 45%

Students are expected to attend class regularly and to keep up with the material presented in the lecture and the assigned reading.

There will be a midterm and a final exam, scheduled as follows:

- Midterm – Thursday, October 25, 10:00-11:20am, in Library W4535.
- Final Exam – Friday, December 16, 11:15am-1:45pm, room TBA.

Last updated October 2016