Remus Radu

Synopsis

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.

Lectures

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

Instructor

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

Teaching Assistant

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

Textbook

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

Other resources:

• 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).

Grading Policy

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.

Exams

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.