2026 Spring Course Syllabus - Mathematics 8042.001

Real Analysis II

3

In-person

TTh 2:00 PM-3:20 PM

Wachman 617

Wachman 1022

By appointment.

Textbook: “Measure and Integral: An Introduction to Real Analysis", Second Edition, by R. Wheeden and A. Zygmund (Chapman & Hall/CRC Pure and Applied Mathematics) ISBN-13: 978-1498702898.

There will be regular homework assignments (20%), which must be uploaded online to Canvas; two midterms (25% each) February 26 and April 23; and a final exam (30%) April 30.

Real Analysis I or knowledge of Lebesgue measure and integration in n-dimensional spaces.

This is the second semester of a year-long course covering the core areas of analysis. It focuses on the development of measure and integration in abstract spaces, differentiation of integrals, Hilbert spaces, basic functional analysis,  Hausdorff measure, and Fourier transform. Emphasis will be on exercises and problems. The course will prepare students to take the Real Analysis section of the qualifying exam.

1. Abstracts measures and integration

2. Differentiation and maximal functions

3. Lp-spaces

4. Outer measures

5. Basic functional analysis

6. Fourier transform

Midterm 1: February 26

Midterm 2: April 23

Final Exam: April 30

Attendance is required

This is the second semester of a year-long course covering the core areas of analysis. It focuses on the development of measure and integration in abstract spaces, differentiation of integrals, Hilbert spaces, basic functional analysis,  Hausdorff measure, and Fourier transform. Emphasis will be on exercises and problems. The course will prepare students to take the Real Analysis section of the qualifying exam.