MATH 6131 Real Analysis (Fall 2006)

 

Mon. and Wed. 2:30-3:45pm; CU-bldg 641

 

Lynn S. Bennethum
Office: CU 638, Phone 556-4810
Office hours:  Mon. and Wed. 1:30-2:30 and 6:00-7:00 in CU 638, or by appointment.
e-mail: Lynn.Bennethum@cudenver.edu
home page: http://www-math.cudenver.edu/~bennethm
fax: 556-8550
home phone: (303) 683-6983 (Please call after 9am and before 9:30pm - I generally work at home on Fridays)

 

Textbooks:  Real Analysis by H. L. Royden, 3rd edition, 1988, Collier Macmillan

Goals of This Course:  Besides learning the material presented in the course, one of the goals is to improve your proof-writing ability.   This means not only intuitively understanding why your proofs work, but also writing up a proof so that others may follow it.  Thus feedback is critical.  Homework will be assigned for which you can practice writing proofs and I may give you feedback;  you may then re-write your proofs if you so desire for additional points (see Homework, below).   In addition, it is expected that by the end of the course you will be able to continue learning related material independently, and this is to be demonstrated by the final project.

Prerequisite: Advanced Calc II (Math 4320) or Applied Analysis MA 5070.  For most students, MA5070 is taken before Real Analysis, not so much for the content of Applied Analysis, but to gain more experience in writing proofs.  Unless you are strong in analysis (i.e. receive a grade of A- or better in your undergraduate Advanced Calc class or equivalent), it is strongly recommended that you take MA5070 before Real Analysis.

 

 

Grading:

Homework: 

300pts

2 Midterms (100 pts each): 

200pts 

Final Project: 

150pts

The lowest 50 pts will be dropped (i.e. if your worst score is a midterm score, it will be worth half of the other midterm).

Homework: Homework will be assigned weekly. Late homework will be accepted but with a penalty.  You may make up half of your missed points by re-working an assigned problem and turning it in within a week after you received the graded homework back.  So for example, suppose you received 10 pts out of a possible 20pts on a homework problem.  Then turning in the problem again, proven or worked correctly, would allow you to get an addional 5 pts towards your homework grade.

Midterms: Midterms will be in-class exams over the material covered in class.

Final Project:  This project involves a written and oral report over material generally chosen from Royden's Part 3: General Measure and Integration Theory.  The purpose of the project is to (1) help improve your oral and written communication skills and (2) demonstrate that you can learn material independently.
The oral report involves spending one-half to one class period "teaching" the rest of us about the material.  It is not expected that you would need external resources (books) to learn the topic, although if you would like to use other texts you are certainly welcome to.

Topics: Measure theory; Lebesgue measure, and Lebesgue-Stieltjes integration.

References:  Besides the textbook, some other references include:
   Principles of Mathematical Analysis by Walter Rudin (McGraw-Hill).  Also known as "Baby Rudin", this book covers what is normally covered in advanced calculus plus Lebesgue integration.  Rudin is known for being correct and concise, hence his books are great reference books but by many are considered difficult to learn from.
   Real and Complex Analysis, by Walter Rudin (McGraw-Hill) is Rudin's "adult" book.   This book covers measure theory and Lebesgue integration theory not just on the real line but over the complex space (and in general metric spaces).  Again, a great reference book.
    Real Analysis for Engineers , by Erham Cinlar and Robert Vanderbei; Available on the web - look under books.   These are real analysis notes written for engineering students.  This is easy to read, clear, with lots of examples.  I strongly recommend downloading these notes (although it is not small - 119 pages and the authors are still revising).
     Fundamentals of Real Analysis, New York, Springer-Verlag, 1999;   For an alternate source of the material at the same level as Royden.

Counterexamples in Analysis Bernard R. Gelbaum, and John M. H. Olmsted, Mineola, NY Dover, 1992.


Important Dates:
Sept.4: Labor Day. No classes.
Sept. 6: To add courses after this date, students need instructor's and dean's signature. Last day to drop a course with tuition adjustment. After this date, dropping a course requires instructors signature. is due at noon.

Oct. 30: Last day to withdraw from a course without dean’s approval.
Nov. 10: After this date, no WITHDRAWLS unless very special circumstances are involved. Student needs instructor's signature, then needs to petition the dean of his college.
Nov. 20 - Nov. 24 : Thanksgiving break. No classes.

 

Important Responsibilities for CLAS Students

·         CLAS students must always have an accurate mailing and e-mail address. Please go to: http://www.cudenver.edu/registrar to update.

·         Students must complete and submit a drop/add form to make any schedule changes. Students are not automatically dropped from a class if they stop attending or do not make tuition payments. The student is ultimately responsible for verifying their schedule prior to officially published drop dates.

·         Late adds will be approved only when circumstances surrounding the late add are beyond the student’s control and can be documented.  This will require a petition and documentation from the student.

·         Late drops will be approved only when circumstances surrounding the late drop are beyond the student’s control and can be documented.  This will require a petition and documentation from the student.

·         Students who wish to graduate in December of 2006 must meet with their academic advisor to obtain a graduation application.  The application must be completed and submitted by September 6, 2006.

·         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.

 

 

Fall 2006 Registration and Academic Deadlines

 

·                     August 24, 2006 (midnight) Last day to be added to the wait-list for a closed course.

·                     August 24 – September 6, 2006   Students are responsible for verifying an accurate fall 2006 registration via SMART.  Students are NOT notified of their wait-list status by the University.  All students must check their schedules prior to September 6, 2006 for accuracy.

·                     August 31, 2006 (midnight)   Last day to add courses via the web SMART system.

·                     September 6, 2006 (5:00 pm)   Last day to add structured courses without a written petition for a late add.  This is an absolute deadline. This deadline does not apply to independent study, internships, and late-starting modular courses.

·                     September 6, 2006 (5:00 pm)   Last day to drop a fall 2006 course for tuition refund and no transcript notation.  This is an absolute deadline.

·                     September 6, 2006 (5:00 pm)   Last day for undergraduates and graduates to apply for December 2006 graduation. This is an absolute deadline.

·                     September 6, 2006 (5:00 pm)   Last day to request pass/fail or no credit option.  This is an absolute deadline.

·                     October 30, 2006 (5:00 pm) Last day for NON-CLAS students to drop a fall 2006 course without a petition to their home college and receiving their Dean’s approval.

·                     November 10, 2006 (5:00 pm)   Last day for CLAS students to drop a fall 2006 course.  Treated as an absolute deadline.  Dean’s approval required.

·                     November 10, 2006 (5:00 pm)   Last day to withdraw (drop all courses) without a written petition.

 

   See Academic Calendar for details on registration/payment deadlines:

http://www.cudenver.edu/registrar