Math 6310, Real Analysis 1
Semester 1, 2022-23
Course Lecturer
Dr. Judith Packer, Dept. of Mathematics
Tel: (303) 492-6979
Office: Math 227
Email: packer@colorado.edu
URL:
Course Syllabus: For course syllabus, click here! This syllabus contains all university rules and regulations.
Course Information:
This course is meant to familiarize the student with the analysis of functions of a single real variable, with an emphasis on Lebesgue measure
and Lebesgue integration on the real line, together with their relationship to differentiation.
Topics to be covered include:
the historical development of the Lebesgue integral, a review of set theory,
the structure of open sets and Borel sets on the real line, Lebesgue outer measure on R,
Lebesgue measurable subsets of R,
measurable extended real-valued functions, definition of the Lebesgue integral,
convergence theorems in Lebesgue integration, product measures,
functions defined by integrals and convolution, differentiation of monotone functions, functions of
bounded variation, absolute continuity, review of metric space theory, L^p spaces.
Prerequisite:
Math 3001 and 4001, or instructor consent.
Course Text:
We will use the text "Real Analysis", by H.L. Royden and P.M. Fitzpatrick, Prentice Hall, 2010,
4th edition, covering most of Chapters 2--7, and more if time permits.
The text "Real Analysis, Modern Techniques and Their Applications", by G.B. Folland, 2nd Edition,
John Wiley and Sons, is also useful.
Assessment:
- Homework Assignments (every two weeks or so): 30 %
- In-class mid-term exam - Wednesday, September 28, 3:25 - 4:20 p.m.: 20 %
- In-class mid-term exam - Monday, November 2, 3:25 - 4:20 p.m.: 20 %
- In-class final exam, Wednesday, December 14, 1:30 p.m. - 4:00 p.m. : 30 % .
Lecture Hours and Venue:
MWF 3:35 p.m.-4:25 p.m. MATH 220.
Office Hours:
MWF 11 a.m. - 12 p.m. in MATH 227, or by appointment on ZOOM.
Homework:
Homework will be assigned biweekly, and is due uploaded to the class Canvas website at 11:59 p.m., on the due date.
Some, but not all of the problems will be graded. Show
all your work. You are allowed to work with classmates, but your final write-up must be your own.
Homework Assignments:
- Assignment 1, due Friday Sept. 2, 2022 .
- Assignment 2, due Wednesday Sept. 21, 2022 .
- Assignment 3, due Friday Oct.14, 2022..
- Assignment 4, due Friday Oct. 28,2022. .
- Assignment 5, due Friday Nov. 18, 2022 .
- Assignment 6.
Some Important Names associated with Real Analysis :
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Last modified August 19, 2022.