Measure and Integration
MAA 5616 Fall 2017
www.math.fsu.edu/~kercheva/Courses/17Fall/MAA5616syllabus.html
201 LOV
MWF 10:10--11:00 am

instructor
Prof. Alec N. Kercheval
contact me
214-A Love Building; 644-8701 (office); 644-2202 (front desk)
webpage: http://www.math.fsu.edu/~kercheva/
Note: See the course Blackboard page for handouts and other materials.
office hours MWF 2-3 pm; or by appointment
eligibility
This course is designed for graduate students in mathematics who are preparing for the Analysis PhD qualifying exam. Students should have already taken MAA 5406 Theory of Functions of a Complex Variable, or have permission of the instructor.
primary textbooks
We will use the following required texts in this course:
  • Terence Tao, An Introduction to Measure Theory, American Mathematical Society, Graduate Studies in Mathematics vol 126, 2011.
  • Terence Tao, An Epsilon of Room, I: Real Analysis American Mathematical Society, Graduate studies in Mathematics vol 117, 2010.
Recommended for supplementary reading:
  • Stein and Shakarchi, Real analysis: measure theory, integration, and Hilbert spaces, Princeton Lectures in Analysis III, Princeton Univ. Press, 2005.
  • Folland, Real Analysis: Modern Techniques and their Applications, 2nd ed, Wiley, 2007.
  • Royden and Fitzpatrick, Real Analysis, 4th edition, Pearson, 2010.
objectives
This course contains a part of the common culture of mathematics that every graduate student in mathematics should study and every mathematician should know. It represents the culminating point of view on the real number system that began back in calculus, and is required background for anyone wishing to understand current research in analysis, probability, stochastic processes, and differential equations. The purpose of the course is to give the student a foundation for research in analysis or further study in applications.

In this semester we will aim to discuss most of the core topics, including measures and sigma-algebras, Lebesgue integration on Euclidean and abstract spaces, measurable functions and Littlewood's three principles, differentiation and absolute continuity, product measures and integrals, signed measures and the Radon-Nikodym theorem, L^p spaces, and Hilbert spaces as time permits.
homework
Homework will be assigned regularly, discussed in class, and turned in. The homework grade will be based on complete of the written assignments and on student in-class presentation of homework solutions.
exams
There will be a one hour midterm exam on a date to be announced, and a comprehensive final exam at the University's designated final examination time: Monday, May 1, 2017, 5:30 - 7:30 pm.
grading
Your course grade will be a weighted average of total homework grade (15%), midterm grade (35%), and final exam grade (50%). Faithful attendance is expected. Borderline grades will be resolved positively by good class participation and negatively by inconsistent attendance.
makeups
An unexcused missed exam receives a zero. Those with prior permission or sufficient documentation will substitute an oral exam.

Academic Honor Policy: The FSU Academic Honor Policy outlines the University's expectations for the integrity of students' academic work, the procedures for resolving alleged violations of those expectations, and the rights and responsibilities of students and faculty. Students are responsible for reading the Academic Honor Policy and for living up to their pledge to ''. . . be honest and truthful and . . . strive for personal and institutional integrity'' at FSU. (The FSU Academic Honor Policy is at http://registrar.fsu.edu/bulletin/grad/info/integrity.htm.)

In this class, you are permitted to work together with classmates on homework problems, but you must turn in only work written by yourself. All exams and any other assignments must reflect only your own work unassisted by others.

Audio, video, or photographic recording of class activity is not permitted except by express permission of the instructor.

University Attendance Policy: Excused absences include documented illness, deaths in the family and other documented crises, call to active military duty or jury duty, religious holy days, and official University activities. These absences will be accommodated in a way that does not arbitrarily penalize students who have a valid excuse. Consideration will also be given to students whose dependent children experience serious illness.

Americans With Disabilities Act: Students with disabilities needing academic accommodation should: (1) register with and provide documentation to the Student Disability Resource Center (SDRC) and (2) bring a letter to the instructor indicating the need for accommodation and what type. This should be done during the first week of class. This syllabus and other class materials are available in alternative format upon request.

For more information about services available to FSU students with disabilities, contact: SDRC, 874 Traditions Way, 108 Student Services Building, FSU, Tallahassee, FL 32306-4167, (850) 644-9566 (voice), (850) 644-8504 (TDD), sdrc@admin.fsu.edu, http://www.disabilitycenter.fsu.edu

FSU's Syllabus Change Policy: Except for changes that substantially affect implementation of the evaluation (grading) statement, this syllabus is a guide for the course and is subject to change with advance notice.