NEWS

• HW 5 is now posted here and on Canvas.

Syllabus

Topics. We begin with a review of Riemann integration, followed by a concrete development of measurable functions, measures, the Lebesgue integral, integrable functions, L^p spaces, modes of convergence, decomposition of measures, product measures, and Lebesgue measure. Fourier series and integrals are a major application.

Time. Classes meet Mondays, Wednesday, and Fridays, 10:00 am to 10:50 am, in Wilson Hall room 214.
Lectures will be livestreamed via Zoom and videorecorded. Find the recordings under Zoom/CloudRecordings on the Canvas webpage for this class.

Prerequisites. Math 4101, or the permission of the instructor.

Text. The lectures will follow the book An Introduction to Lebesgue Integration and Fourier Series by Howard J. Wilcox and David L. Myers, published by Dover Books, ISBN 978-0-486-68293-8 (1994).

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 submit your solutions electronically via Canvas and GradeScope by 11:00pm on the due date. Late homework will not be accepted.

Problem sets will be assigned as follows:

HW #1, due Fri, Jan 30 (Solutions) HW #2, due Fri, Feb 13 (Solutions) HW #3, due Fri, Feb 27 (Solutions)	HW #4, due Fri, Mar 27 (Solutions) HW #5, due Fri, Apr 10 HW #6, due Fri, Apr 24

The lowest HW score (of the six) will be dropped. The remaining five HW percentages will be averaged with equal weights.

Tests. Midterm examination: Friday, March 6, 2026, in class. Cumulative final examination: May 4th, 2026, 10:30am-12:30pm, in the classroom.

Grading. One letter grade will be assigned for homework, each worth the same with the lowest HW score dropped, one for the midterm examination, and one for the final examination. These three will contribute in respective shares 40%, 30%, and 30% to the course grade.
There will be no make-up exams or early or late exams. The final exam score will replace the midterm exam score if that improves the course score so it is possible to miss the midterm without failing the course.

Letter grades, computed from the course score, will be at least the following:

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 Mondays and Wednesdays from 11:00-12:00, that is, after class, or make an appointment for other times.