Instructor: Kevin McLeod Office: EMS E481 Office hours: TR 8:30—9:20 (in the Northwest Quadrant) (or by appointment) Phone: 229-5269 e-mail: kevinm@uwm.edu |
Class meeting time: TR 11:00 AM-12:15 PM, EMS E495 Text: Gerald B. Folland, Real Analysis (2nd Edition). |
Course Description
Last semester, in MATH 711, we learned how to integrate. More specifically, we studied the abstract theory of measurable spaces, measurable functions, and the Lebesgue integral. Towards the end of the semester, we spent some time on differentiation, and learned that absolutely continuous functions are the most general class for which the Fundamental Theorem of Calculus holds. This leaves us in the uncomfortable position that there are many functions which are differentiable almost everywhere (with respect to Lebesgue measure) but which cannot be recovered by integrating their derivatives.
Since not all functions that analysts need to work with are absolutely continuous, the question arises as to whether there might be some replacement or generalization of the derivative (henceforth to be known as the “classical” derivative) which would enable us to carry out the operations of calculus with a broader class of functions. There are in fact several such generalizations, and we will study the most important one in Chapter 9 of our textbook. The theory is quite abstract, however, heavily dependent on the concept of dual spaces, and Chapter 7 will provide a useful stepping stone to the more general theory. (Chapter 8 discusses the Fourier Transform.)
I will try to keep lecturing to a minimum, and devote class time to discussion and problem solving. As a result, you will be expected to read the textbook in a timely fashion, as necessary to participate in the class discussions. At least once per week, I will ask you to e-mail me with one or more questions you have about your reading. I will review those e-mails prepare a brief lectures or other activities for any common questions, as I feel necessary. I will also save those e-mails; at the end of the semester they will be used as evidence that you were completing the reading assignments, and will count towards the homework portion of your grade.
Evaluation
Your grade for the course will be based on the following factors:
- Homework In addition to the textbook (and possibly other) readings, you will be assigned written homework regularly, some of which you will be expected to hand in. Of the homework you hand in, approximately half will be treated summatively; i.e. you will be given a grade which will contribute to your final grade for the course. (The other half will be treated formatively: you will be given feedback, but no score.) 25%.
- Class participation You will be expected to contribute to the class discussion, to the extent of leading discussions on topics from the text or homework problems. (For this reason alone, regular class attendance will be essential.) 25%.
- Exams There will be two exams, a midterm and the final exam. 25% each.
Average Time Investment
The amount of time that an average student should expect to spend on this
class is as follows:
- Classroom time (face to face instruction): 45 hours
- Time taking exams (midterm, final exam): 15 hours
- Time for preparation and study for exams: 10 hours
- Time completing reading and other homework assignments: 80 hours
Total number of hours: 150.
Students with disabilities
If you feel you are a student with a disability, please feel free
to contact me early in the semester for any help or accommodation
you may need.
University policies
You should keep yourself informed of important dates in the University calendar.
The Secretary of the University has a page dedicated to university policies for religious observances, grade appeal procedures, military service and other matters. You should also familiarize yourself with the information on the Dean of Students Office webpage concerning proper student conduct at the university, both academic misconduct and non-academic misconduct. You will be held responsible for the information and policies contained at these links.