Office Hours: Monday/Wednesday/Friday 9:00am - 10:00am or by appointment.
Class Meeting Time: MWF 3:00pm - 4:00pm
Lecture Location: Cupples I, Room 207
Math 5051 is an introduction to graduate real analysis and serves as the basis for the Ph.D. qualifying exam in analysis. Topics covered include: measures, sigma-algebras, outer measures (on abstract measure spaces), Borel measures; integration, measurable functions, integrals, monotone convergence theorem, Fatou's lemma, dominated convergence theorem, Fubini's theorem (on abstract spaces), Lebesgue integral on Euclidean space; decomposition and differentiation of measures, signed measures, Lebesgue-Radon-Nikodym theorem, functions of bounded variation. Basic ideas of functional analysis will also be covered.
Prerequisites for the course are Math 4111, 4171, and 4181, or permission of the instructor.
The syllabus for the course will be discussed the first day of class and then will be available here.
Textbook:Measure and Integral: An Introduction to Real Analysis by Richard Wheeden and Antoni Zygmund.
Attendance: Attendance is required for all lectures. The student who misses a class meeting is responsible for any assignments and/or announcements made. Office hours will not be utilized to re-teach material presented in class.
There will be no opportunities for make-up tests after the fact. In the event of an absence due to travel representing WUSTL, such as an intercollegiate sports competition, you must notify the professor at least two weeks in advance to arrange an early test or other alternative. Otherwise, such absences will be treated as personal.
Homework: This course will have daily homework assignments which should be done before the next class. Homework will be colleceted and graded.
Exams: This course will have two mid-term exams, and a comprehensive final exam. The mid-term exams will be take home, while the final exam will be in class. Dates of exams are:
Exam 1: Friday, September 30 (tentative)
Exam 2: Friday, November 4 (tentative)
Final Exam: Thursday, December 15 6:00pm - 8:00pm
Grade Computation Computation of your course grade is explained in detail on the syllabus. The usual ten-point scale will be used (A: 90-100, B: 80-89, C: 70-79, D: 60-69, F: 0-59), however, if necessary, adjustments will be made to arrive at a standard grade distribution for the course. On an individual basis, significant improvement over the semester will be taken into account. For students taking the course with the Pass/Fail option, the threshold for a passing grade will be a "C".
Learning Disabilities: It is the right of any student with a certified learning disability to request necessary accommodation. Such requests must be made well in advance of the time that the accommodation is required and a letter of documentation from the CornerStone office must be presented at the time of any request.
Academic Honesty: It is expected that all students are aware of their individual responsibilities under the WUSTL Academic Integrity Policy, which will be strictly adhered to in this class.