Math 525: Real Analysis II

Winter 2013

Instructor: Zhen-Qing Chen

Phone: (206) 543-1907 (Office)
Fax: (206) 543-0397
Office: Padelford Hall, Room C525
Email: zchen@math.washington.edu
Office hours: Tuesdays 11:00-11:50 am. and Fridays 1:30-2:20 pm. at Padelford Hall C525.

Lectures: MWF: 11:30 am.-12:20 pm., PDL C-36.

Teaching Assistant: Erik Slivken. Office hours: Mondays 4-6 pm at at PDL C-20, and Tuesdays by appointment. Email: slivken@math.washington.edu

Textbook: E. M. Stein and R. Shakarchi, Real Analysis: measure theory, integration, & Hilbert spaces. Princeton Univ. Press, 2005. ((required) Gerald B. Folland, Real Analysis, Second Edition. John Wiley & Sons, 1999. (recommended) E. M. Stein and R. Shakarchi, {\it Functional Analysis}. Princeton Univ. Press, 2011. (recommended)

Reference Book: H. L. Royden, Real Analysis, 3rd Edition.

Course Description

This is the second part of a year-long course on real analysis. This sequential course will cover the fundamental tools needed to work in the general field of analysis including probability theory and stochastic analysis. This quarter we will cover the following topics:

  • Differentiation and Integration (including Hardy-Littlewood maximal function, Lebesgue differentiation theorem, functions of bounded variation, and absolutely continuous functions and measures).
  • Hilbert spaces (including the Radon-Nikodym theorem as an application)
  • Topology (including Arzela-Ascoli and Stone-Weierstrass theorems)
  • $L^p$ spaces and Banach spaces.

    Prerequisite: Math 524 or its equivalent.

    Here is the Course Syllabus .

    Recommended preparation

    Read the textbook and the reference book before and after each lecture.

    Homework Assignments