Syllabus

Topics. This will be the second semester of a two semester graduate-level introduction to the theory of measure and integration in abstract and Euclidean spaces. We continue with an introduction to the basic ideas of differential calculus, operator theory, and analysis on manifolds. Math 5051 and 5052 form the basis for the Ph.D. qualifying examination in real analysis.

Prerequisites. Math 5051, or permission of instructor.

Time. Classes meet Tuesdays and Thursdays, 2:30 pm to 4:00 pm, in Cupples I, room 111.

Text. The lectures will follow the book Real and Functional Analysis, 3rd edition, by Serge Lang, ISBN 0387940014 (Springer, 1993). This textbook was also used in Math 5051.

Homework assignments: Solutions are due at the end of class on the due date. Late homework will not be accepted.

	(solved) HW #7, due Thu, Feb 1 (solved) HW #8, due Thu, Feb 15 (solved) HW #9, due Thu, Mar 8 (solved) HW #10, due Tue, Apr 3 (solved) HW #11, due Thu, Apr 12 (solved) HW #12, due Thu, Apr 26

Collaboration on homework is permitted and encouraged, but each student must submit individually written solutions.

Tests. There will be a final examination in Cupples I, Room 199 on Wednesday, May 9th, 2007 from 3:30-5:30pm. Students may choose to take the real analysis qualifying examination instead from 3:30-6:30pm.

Grading. One grade will be assigned for homework and one for the final examination. These grades will contribute as follows to the course grade: Homework 75%, Final Examination 25%. Students taking the Cr/NCr or P/F options will need a grade of C or better to pass.

Office Hours. See the instructor in Cupples I, room 105a, on Tuesdays 4-5pm, Wednesdays 3-4pm, or by appointment any time.