MTH 471 "Real Analysis"

Syllabus: General measure spaces, integration over general measure spaces, general L^p spaces, construction of particular measures, measure and topology.

Prerequisites: MTH 265H and, preferably, MTH 240H.

Textbook: H. L. Royden and P. M. Fitzpatrick, Real Analysis (4th edition), Prentice Hall, 2010. Together with the textbook, "Problems in mathematical analysis III - Integration" by Kaczor and Nowak can be found on reserve in Carlson Library.

Course philosophy: This is an introductory graduate course on the general theory of measure and integration. Unlike the theory of Lebesgue measure and integration, which relies heavily on the topology of the ambient space, the emphasis here is to start with a set of axioms, which are also satisfied by the Lebesgue measure, and construct a new theory strictly based on the axioms, without any topological information. Nevertheless, throughout the course, we will often pendulate between the concrete case of the real line and the abstract setting of the general theory. Our main focus will be part III in the textbook.

This course is challenging and requires time commitment. Proficiency will be achieved only by completing the reading assignments and working out the practice problems. Please take full advantage of my office hours.

Grading: Quizzes 30%, Midterm 30%, Final 40%.

Quizzes

Exams

The Final is scheduled for Wednesday, 12/17, from 19:15 to 22:15, and it will be a comprehensive exam.

Course policies

1. The course average is not based on a curve, nor on previously fixed scales. It will reflect how well the class is doing, and it will be high if everyone is working hard on the practice problems and is performing well on quizzes and exams.

2. Incomplete "I" grades are almost never given. The only justification is a documented serious medical problem or a genuine personal/family emergency. Falling behind in this course or problems with workload on other courses are not acceptable reasons.

3. If you miss the Midterm with a valid excuse (e.g., illness or emergency), you must notify the instructor and provide supporting documentation verifying your excuse as soon as possible. For a valid excuse with supporting documentation, the Final will count as your make-up test (i.e., the Final will count towards 70% of your grade). If you miss the Final, you are in trouble. No make-up exams will be given for any reason. If you miss an exam without a valid excuse (and supporting documentation), you will receive a score of 0 on that test.

4. You are responsible for knowing and abiding by the University of Rochester's academic integrity code. Any violation of academic integrity will be pursued according to the specified procedures.

Tentative weekly schedule: