Approximately 100 years ago, Henri Lebesgue described a new theory of integration to handle many important, possibly discontinuous, functions of several variables. This discovery has proven to be one of the most influential mathematical events of history. For example it greatly advanced the development of probability theory and Fourier analysis. Remarkably, though enjoying many extensions and generalizations, it retains its original formulation while in actve use today. In this course, we will carefully develop Lebesgue's integration theory. This applies to quite general measures, though we will focus on the important Lebesgue measure on Rn which roughly describes n dimensional volume. Some of the topics to be covered are as follows:
Office: HB 430; Office hours: 9-10 MWF
(and others by appt.)
T:10-1:30,4-5, W:10-1,1-2,3-5, Th:10-1:30,4-5, F:10-11,3-4
Telephone: ext 3280
Frank Jones, Lebesgue Integration on Euclidean Space, Jones and Bartlett Publishers Inc., 1993. (available from the Rice bookstore or Dr. Jones (HB448). This resource gives an excellent careful treatment and is a great source of exercises. In Math 425 we will cover approximately 1/2 of this text. Some other commonly used texts are Bartle, Elements of Integration and Lebesgue Measure, Royden, Real Analysis, Rudin, Real and Complex Analysis, and and Wheeden and Zygmund, Measure and Integral.
The final grade for the course will be determined as follows:
Midterm exam 25%
Final exam 40%
There will be a homework assignment each week when there is not an hour exam scheduled. All homework is usually due each Wednesday, one week after it is assigned. In doing any problem in the text you may find it useful to use the results of previous problems in the text. The homework is not pledged. You are encouraged to discuss the homework, and to work together on the problems. However each student is responsible for the final preparation of his or her own homework papers.
Note the changes in Homework 4.
Note Homework 5 now due Monday Oct. 3 because of Rita.
Note the change in Problem 8 of Homework 8.
Midterm Exam. This is a take-home exam that will be distributed in sealed envelopes Monday Oct.17. It will be due back Monday Oct.24 at 10AM. After opening the envelope you should work for no more than the next 2 hours. You may use the textbook or notes. Be sure and hand in all the work you do on each problem. Good luck!
Final Exam. This is a take-home final that will be distributed in sealed envelopes Friday December 2. It will be due back at the end of Finals period Wednesday Dec.14, 4PM. After opening the envelope you should work for no more than the next 4 hours. You may use the textbook or notes or old homeworks. Be sure and hand in all the work you do on each problem. Good luck!
The final contains a few homework problems and a few problems similar to those on the midterm exam.
The last homework #11 is graded and outside the door of HB430.
page is maintained by Robert Hardt, email@example.com.
Last edited 12/6/05.