Math 6310, Real Analysis 1
Semester 1, 2018-19
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!
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, the notion of a measure space, sigma-algebras of subsets,
outer measures, Borel measures on R,
measurable extended real-valued functions, integraion of a non-negative measurable function with respect to a measure,
integration of real and complex-valued integrable functions,
convergence theorems in integration, product measures, Lebesgue measure on R and R^n,
functions defined by integrals and convolution, sgined measures, absolute continuity and mutual singularity of one measure with respect to another,
the Lebsesgue-Radon Nikodym Theorem, complex measures, differentiation on Euclidean space, functions of bounded variation on R .
Prerequisite:
Math 3001 and 4001, or instructor consent.
Course Text:
We will use the text "Real Analysis, Modern Techniques and Their Applications", by G.B. Folland, 2nd Edition, John Wiley and Sons, covering most of Chapters 0- 3.
Assessment:
- Homework Assignments (every two weeks or so): 25 %
- In-class mid-term exam - Wednesday, October 3, 3 - 3:55 p.m.: 20 %
- In-class mid-term exam - Monday, November 5, 3 - 3:55 p.m.: 20 %
- In-class final exam, Tuesday, December 18, 7:30 p.m. - 10 p.m. : 35 % .
Lecture Hours and Venue:
MWF 3 p.m.-3:50 p.m. ECCR 108.
Office Hours:
MWF 1 p.m. - 2 p.m.
Homework:
Some Important Names associated with Real Analysis :
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Last modified August 28, 2018.