Math 6131 – Real Analysis, Fall 2008

Jan Mandel

Department of Mathematical and Statistical Sciences
University of Colorado Denver

This web page http://www-math.cudenver.edu/~jmandel/classes/6131f08 serves as the class syllabus and source of further information. Homework, material covered, and handouts will be in the homework file. Photographs and scans will be in the photos directory.

NOTE: This class deals with different topics than the PhD prelim in

Applied Analysis and it is thus not suitable for the preparation for that exam. Rather, the knowledge and the skills required by the prelim are expected in this class.

Prerequisites: MATH 4320 or MATH5070. Basic knowledge of the properties of reals and metric spaces. A good level of mathematical maturity and understanding of proof techniques.

Textbook: R. M. Dudley, Real Analysis and Probability, Cambridge University Press, 2nd ed, 2003, ISBN 978-0-521-00754-2 paperback
Time and location:  Monday and Wednesday 1-2:15 UCD 641
Office hours: Monday 9:30-10:30, Wednesday 10:30-11:30. I am also available Monday 10:30-12:30 where there is no CCM colloquium, and Wednesday 11:30-12:30 when there is no faculty meeting.
Contact: Phone 303-556-4475; email jan.mandel@ucdenver.edu. I am usually pretty good at answering email even at late hours.

Objectives

 

Material to be covered

 

Selected parts of chapters 1-6, plus some topics from other chapters if time allows. Material already known from Math 5070 will be left for reading or reviewed very briefly.

 

The book develops measure theory without topology. This has the advantage that we get a simpler theory without wondering if the topology is really needed, and the connections are treated later. Topology is developed in more generality than the reals or metric spaces. In addition to being an important topics in its own right, the theory of general topological spaces is needed to create many examples and for the exercises.

 

Learning philosophy

Do not trust anything until you have verified it - this includes what I say and what is in the book. This will take great time and effort. Before you apply a theorem, check if the assumptions are satisfied.

My role is to bring the book alive. Yours is to use the lectures to help you understand the book when you study by yourself and solve problems.

 

You do not need to study parts of the book that are skipped in class unless they are explicitly assigned for reading.

 

Grading

 

Always copy the statement of the problem first. Show clearly all your work. Do not write irrelevant things. Do not write incorrect statements and expect me to pick only the correct ones. Points will be taken off for incorrect statements even if they are not relevant to the problem being solved. It is not enough that you understand the mathematics correctly – you also need to write it so that it can be verified and understood. The point of most problems is the justification rather than a formal solution, so formal solutions count for little even if correct.

There will be homework most Mondays due the following Monday, and in-class midterm and final. The midterm will be on October 22. The final will be as determined by the Auraria finals schedule.

All work will be graded on the scale 0-4: 0=nothing relevant, 1=understands definitions and the problem, or a correct formal solution 2=good progress or a correct partial solution, 3=some minor glitch, 4=OK

The final score will be determined by 40% homework, 30% midterm, 30% final. The letter grades will be A >= 90,  A- >= 85, B+ >= 80, B >= 75, B- >=70,  C+ >= 65, C >= 60, C- >= 55, D+ >= 50, D >= 45, D- >= 40.

 

 

Fall 2008 CLAS Academic Policies

 

The following policies pertain to all students and are strictly adhered to by the College of Liberal Arts and Sciences (CLAS).

  • Every student MUST check and verify their schedule prior to the published drop/add deadlines._ Failure to verify a schedule is not sufficient reason to justify a late add or drop later in the semester._ It is the student’s responsibility to make sure that their schedule is correct prior to the appropriate deadlines.
  • CLAS students must use their email.cudenver.edu email address._ Email is the official method of communication for all University of Colorado Denver business._ All email correspondence will take place using your CU-Denver email address._ Go to http://www.cudenver.edu/registrar to update and/or change your email address.
  • Students are NOT automatically added to a course off a wait list after wait lists are dropped._ If a student is told by a faculty member that they will be added off the wait list, it is the responsibility of the student to complete the proper paperwork to add a course.
  • Students are not automatically notified if they are added to a class from a wait-list._ Again, it is the responsibility of the student to verify their schedule prior to any official dates to drop or add courses.
  • Students must complete and submit a drop/add form to make any schedule changes._ Students are not automatically dropped from a class if they never attended, stopped attending or do not make tuition payments. _
  • Late adds will be approved only when circumstances surrounding the late add are beyond the student’s control and can be documented independently._ This will require a petition and documentation from the student._ Late adds will only be approved if the student has not taken any exams, quizzes, or has not completed any other graded assignments._ Independent verification of this from the professor of record will be required._ Please note that the signature of a faculty member on an add form does not guarantee that a late add petition will be approved._ Petitions are available in NC 2024.
  • Late drops will be approved only when circumstances surrounding the late drop have arisen after the published drop deadlines, are beyond the student’s control, and can be documented independently._ This will require a petition and documentation from the student._ Pre-existing circumstances (circumstances that existed prior to the published drop deadlines) regarding illness, work, family, or other confounding issues will not be considered adequate reason to drop or withdraw from courses after the published University and/or College drop deadlines._ Please note that the signature of a faculty member does not guarantee that a late drop petition will be approved._ Petitions are available in NC 2024.
  • Students wishing to graduate in fall of 2008 must meet with their academic advisor by the end of the drop/add period to obtain a graduation application._ This application must be completed and submitted by 5 PM on September 3, 2008._ You can obtain an application ONLY after meeting with your academic advisor. There are no exceptions to this policy or date.
  • Students are responsible for completing financial arrangements with financial aid, family, scholarships, etc. to pay their tuition._ Students will be responsible for all tuition and fees for courses they do not officially drop using proper drop/add procedures and forms._

______ Students who drop after the published drop/add period will not be eligible for a refund of______________________ the COF hours or tuition.

 

 

 

Important Dates

 

  • August 11, 2008; First day of Class
  • August 17, 2008 ; Last day to be added to a wait list using the SMART system.
  • August 17, 2008: Last day to add a course using the SMART system.
  • August 11 – September 3, 2008; Students are responsible for verifying an accurate fall 2008 course schedule via the SMART registration system._ Students are NOT notified of their wait-list status by the university._ All students must check their scheduled prior to September 3, 2008 for accuracy.
  • August 18, 2008: LAST DAY TO DROP WITHOUT DROP CHARGE.
  • August 18, 2008: Wait Lists are dropped._ Any student who was not added to a course automatically from the wait list by this date and time MUST complete a drop/add form to be added to the class._ Students are NOT automatically added to the class from the wait list after this date and time._ If your name is not on the official student roster, you are not registered for the course.
  • August 19, 2008: First day instructor may approve request to add a student to a full course with a Schedule Adjustment Form.
  • August 24-29: CAMPUS CLOSED due to Democratic National Convention._ Classes resume on September 2, 2008.
  • September 3, 2008 at 5 PM; Last day to add structured courses without a written petition for a late add._ This is an absolute deadline and is treated as such. This deadline does not apply to independent study, internships, and late-starting modular courses.
  • September 3, 2008 at 5 PM; Last day to drop a fall 2008 course with a tuition refund minus the drop charge and no transcript notation._ Drops after this date will appear on your transcript._ This is an absolute deadline and is treated as such.
  • September 3, 2008 at 5 PM; Last day to completely withdraw from all fall 2008 courses with a tuition refund and no transcript notation. Drop charge applies. Drops after this date will appear on your transcript._ This is an absolute deadline and is treated as such.
  • September 3, 2008 at 5 PM; Last day to request pass/fail option for a course.
  • September 3, 2008 at 5 PM: Last day to request a no credit option for a course.
  • September 3, 2008 at 5 PM: Last day to register for a Candidate for Degree.
  • September 3, 2008 at 5 PM: Last day to petition for a reduction in thesis or dissertation hours.
  • September 3, 2008 at 5 PM: Last day to apply for fall 2008 graduation._ You must make an appointment and see your academic advisor before this date to apply for graduation.
  • September 15, 2008: Early Alert starts for Faculty
  • September 24, 2008: Early Alters ends at 5:00 P.M.
  • October 27, 2008 at 5 PM; Last day for non CLAS students to drop or withdraw from all classes without a petition and special approval from the student’s academic Dean._ This is treated as an absolute deadline.
  • November 7, 2008 at 5 PM; Last day for CLAS students to drop or withdraw from all classes without a petition and special approval from the student’s academic Dean. Students still need signatures from the faculty and Dean._ This is treated as an absolute deadline.
  • After November 7, 2008 all schedule changes require a petition._ Petitions are available in NC 2024.
  • No schedule changes will be granted once finals week has started._ There are NO exceptions to this policy.