Math 8201 Real Analysis
Syllabus

Spring 2019
Prof. Peckham


Syllabus

The goal of the course is to define (and understand) the Lebesgue Integral on Rn. In order to do this, we first need to spend a considerable amount of time deciding how to measure the ``volume'' of sets in Rn. In the process, we will build a collection of subsets which are "measurable." The Lebesgue integral of a function can then be defined "with respect to Lebesgue measure." A variety of applications will be considered.

The theoretical core material is covered in Chapters 1 -- 8 of the text. We will choose topics beyond these chapters according to the interests of the class (including the instructor). Some supplemental material, not included in the text, will occasionally be presented in lecture.

Course Prerequisites

Real Variables (Math 5201) or equivalent or permission of the instructor.

Grading (Dates and topics are tentative)

Note: Tests may be given from 5-7pm, outside of standard class times, in order to allow for extra time. A regular class will be cancelled for any test taken outside class time.
Exam 1:	   		Thurs. March 7		Ch's 1-4 	10%
Exam 2:	   		Thurs. April 25		Ch's 5-8	15%
HW sets":		due every week or 2:			55%
Final Problem Set:				Cumulative	20%
Total:							     	100%

General policy statement

Lectures, material in the text, homework sets, and tests are all intended to complement each other. No one is a replacement for any of the others. You are, in general, expected to learn material which is covered via any of these sources.

Homework Sets and Ground Rules

Homework will be turned in roughly every two weeks. All work should be neatly written, well-organized, and complete. For proofs, it is generally OK to quote results that we have already covered in the course.

For regular homework sets, you are encouraged to exchange ideas with each other, but each person should write up his/her solutions completely in his/her own words. It is never appropriate to give a written version of a problem/proof to another classmate, except to have the classmate read and evaluate your work with you present. It is OK to verbally explain your ideas to another classmate, as long as the classmate then writes up his/her work on his/her own. In this case, the student providing the help should be acknowledged on the writeup of the person who received the help. The acknowledgement should be specific about what help was received. One person copying a classmate's solutions - even when acknowledged - is expressly forbidden and will result in both students receiving zeroes for that complete homework set and facing academic disciplinary action.

Using supplementary texts and websites. The goal of the course is to develop your own problem-solving and critical thinking abilities. It is always best to work out problems on your own as much as possible. If, however, you use ideas from other textbooks, or from the web you MUST provide a full reference - book and page number, or website and specific location of the resource you used. Failure to provide proper attribution will result in a zero for that problem set, and academic disciplinary action. Every assignment should either have a statement: "Outside resources used: None", or a list of resources used for each problem, stating any resources from the web, other people, or other texts than the class textbook, etc. For more information, see the UMD Student Conduct Code.

It is often instructive to read the problems at the end of each section and think about how you would solve them, even if you don't actually attempt to solve them.

Assignments will be posted on the Course Web Page

Grace Days: Each student will have 5 grace days for the semester for handing in late HW sets. This days can be split between any number of assignments (up to 5). After 5 grace days have been used, a deduction will be made of 10% per day, with weekends counted as one day.

Missed Exams or Quizzes

Missed quizzes or exams will be assigned a zero score unless you provide a valid written, signed (by a Doctor, for example) excuse for your absence; unless it is not possible to do so, you must provide verbal notice ahead of time to your instructor for an absence. Arrangements for a makeup should be made as soon as you know you will miss. Do not wait for the next class. You can leave the instructor a message 24 hours a day by phone or email. Oversleeping, poor preparation, slight colds, and cold weather are not valid excuses.

Student Learning Outcomes

By the end of the course, students should
  1. be familiar with topics in measure theory and integration theory
  2. be able to apply results of theorems to solve problems
  3. be able to read, understand, and write sophisticated analysis proofs
Problems sets and tests will evaluate all three of these Student Learning Outcomes.

Disabilities

Please inform me of any disabilities of which I should be aware in order to provide for equitable participation.

Mental Health Statement

(Statement suggested by UMD Health Services and Counseling.) As a student you may experience a range of issues that can cause barriers to learning, such as strained relationships, increased anxiety, alcohol/drug problems, feeling down, difficulty concentrating and/or lack of motivation. These mental health concerns or stressful events may lead to diminished academic performance or reduce a student's ability to participate in daily activities. University of Minnesota services are available to assist you with addressing these and other concerns you may be experiencing. You can learn more about the broad range of confidential mental health services available on campus via the UMD Health Service Counseling website at this link.

This page (http://www.d.umn.edu/~bpeckham/www) is maintained by Bruce Peckham (bpeckham@d.umn.edu) and was last modified on Thursday, 24-Jan-2019 10:58:37 CST.