Real Analysis 2

Spring 2018

Schedule

Lecture Office hour Problem session
Wednesday – Thursday
10:00 am – 12:00 pm
Tuesday
11:00 am – 12:00 pm
Friday
11:00 am – 12:00 pm

Content

In this course we study the modern techniques of Real Analysis, from measure theory to the basics of functional analysis, as well as applications to Fourier Analysis.

Syllabus

PDF

Homeworks & remarks

Real Analysis 2, 2018

Bibliography

DM Bressoud, A radical approach to Lebesgue’s theory of integration, Cambridge, 2008
S Igari, Real analysis with an introduction to wavelet theory, AMS 1998
GB Folland, Real analysis: modern techniques and their applications, Wiley & Sons, 1999
J Franks, A (terse) introduction to Lebesgue integration, AMS, 2009
DA Salamon, Measure and integration, EMS, 2016
B Simon, A comprehensive course in Analysis, Part 1: Real Analysis, AMS 2015
B Simon, A comprehensive course in Analysis, Part 3: Harmonic Analysis, AMS 2015
B Simon, A comprehensive course in Analysis, Part 4: Operator Theory, AMS 2015
EM Stein & R Shakarchi, Real Analysis: measure theory, integration, and hilbert spaces, Princeton, 2005
EM Stein & R Shakarchi, Functional analysis: introduction to further topics in analysis, Princeton, 2011
ME Taylor, Measure theory and integration, AMS, 2006

Midterm evaluations

There will be two midterm evaluations, each with (optional) homework and a written examination.

Homework (40%)

Problems will be assigned weekly and must be submitted each Friday by 11:00 am.

Written exam (60%)

A written one-hour exam will evaluate the material of the course, focusing on the previous 8 weeks.

Calendar

  • First midterm: April 13
  • Second midterm: June 8

Final evaluation

The final evaluation will consist of a final project and a final written examination.

Project (50%)

Each student will be assigned a final project, extending the results from class. A report must be submitted before the written examination.

Exam (50%)

A two-hour written examination, evaluating the material of the course.

Date

June 27, 10:00 am

Additional examinations

  • Extra: July 4, 10:00 am
  • Regularization: August 8, 10:00 am