Syllabus

Topics. This course is the second part of a rigorous introduction to mathematical analysis that begins with Math 4111. We will begin with Riemann integration, then study measurable functions, measures, the Lebesgue integral, integrable functions, L^p spaces, modes of convergence, decomposition of measures, product measures, and Lebesgue measure.

Time. Classes meet Tuesdays and Thursdays, 10:00 am to 11:30 am, in Cupples I, room 199.

Prerequisites. Math 4111, or the permission of the instructor.

Text. The lectures will follow the second half of the book Mathematical Analysis by Tom Apostol, second edition, published by Addison-Wesley, ISBN 0-201-00288-4 (1974).

Homework. You are encouraged to collaborate on homework, and to work additional exercises from the relevant problem sections, although the homework grade will be based only on the exercises listed below. Please return your solutions to the instructor by the end of class. Problem sets will be assigned as follows:

HW #1, due Thu, Jan 31 (Solutions) HW #2, due Thu, Feb 14 (Solutions) HW #3, due Thu, Feb 28 (Solutions)	HW #4, due Thu, Mar 28 (Solutions) HW #5, due Thu, Apr 11 (Solutions) HW #6, due Thu, Apr 25

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

Tests. Midterm examination: Thursday, March 7, 2013, in class. Cumulative final examination: Tuesday, May 7, 2013, 6-8 pm, in the classroom.

Grading. One letter grade will be assigned for homework, one for the midterm examination, and one for the final examination. These three will contribute equally to the course grade. Students taking the Cr/NCr or P/F options will need a grade of D or better to pass. Students auditing the course will need to attend at least 25 class sessions.

Office Hours. See the instructor in Cupples I, room 105a, on Tuesdays from 11:30-1:00 pm, that is, after class, or make an appointment for other times.