Math425

Assignments

Math 425: Integration Theory

MWF 10:00-10:50 a.m. 427 HB

Instructor: Rolf J. Ryham

Office: 452 HB

Phone: (713) 348-2385

Course Description

Lebesgue theory of measure and integration. Topics to be covered will include some set and real variable theory, construction of Lebesgue measure on the real line, measurable functions, the Riemann and Lebesgue integrals, classical Lp Banach spaces, approximation and continuity in these spaces and Fourier analysis.

Textbook

Real Analysis by H. L. Royden.

Other References

Real and Complex Analysis by Walter Rudin,

Measure and Integral by Wheeden and Zygmund,

Lebesgue Integration on Euclidean Space by Frank Jones.

Fourier Series, by Hardy and Rogosinski.

Homework

will be assigned roughly once per week. It will account for 40% of the course grade. Students may (and are encouraged) to solve homework problems together. However, solutions turned in for credit must represent the student's own solution of the problem, i.e. a proof copied from a classmates paper or the internet is not accebtable. Repeated instances of copying or plagiarism will be dealt with according to Rice policy.

Midterm

An in class (50 minute), closed book and closed note examination will be scheduled for October 10. It will account for 25% of the course grade. A student may reschedule the exam only in the event of a documented family or medical emergency.

Final

An in class (150 minute), closed book and closed note, cumulative exam will be given in the period of December 12 - December 19 (final exam week).

Although the date and time of the exam is currently not known, please make plans to be in the Rice area during this week. The final accounts for 35% of

the course grade and may not be rescheduled accept in the event of a documented family or medical emergency.

Accommodations

Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All discussions will remain confidential. Students with disabilities should also contact Disability Support Services in the Ley Student Center.