Announcements:

• Final Exam: Tuesday, May 8, 4:00-7:00 (Hill 423)

Lecturer: Prof. Roe Goodman

Text: (required) Gerald B. Foland, Real Analysis: Modern Techniques and Their Applications (2nd ed.),
    ISBN #0-471-31716-0, Wiley-Interscience/John Wiley Sons, Inc., 1999.

This course is a continuation of 640:501 from Fall 2006. The goal is to give an introduction to core topics in real and functional analysis that every professional mathematician should know.

Homework Assignments: Here is the list of   homework problems.

Topics: The course will cover material from Chapters 4-8 of Folland's book:

• Topological Spaces
  Basic properties, compact spaces, Stone-Weierstrass theorem
• Introduction to Functional Analysis
  Normed vector spaces, Hahn-Banach theorem, bounded linear transformations, Closed graph and Open mapping theorem, applications of Baire category theorem, Hilbert spaces, topological vector spaces, weak and weak* convergence
• Lp Spaces
  Integral inequalities, duality, bounded integral operators
• Introduction to Fourier analysis
  Schwartz space, convolutions, Fourier transform and Fourier series, Plancherel theorem, Poisson summation formula, Lp and pointwise convergence of Fourier series
• Integration on Locally Compact Spaces
  Continuous functions and Radon measures on locally compact spaces, dual of C(X), vague convergence of measures

Grading: There are weekly graded homework assignments, an in-class midterm exam (closed book) on March 7, and a final exam (closed book) on May 8.