Math 6310, Real Analysis 1
Semester 1, 2013-14
Course Lecturer
Dr. Judith Packer, Dept. of Mathematics
Tel: (303) 492-6979
Office: Math 227
Email: packer@colorado.edu
URL: http://spot.colorado.edu/~packer
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, Lebesgue outer measure on R,
Lebesgue measurable subsets of R , Lebesgue measurable extended real-valued functions,
definition of the Lebesgue integral, convergence theorems in Lebesgue integration,
functions defined by integrals and convolution, diffentiation of monotone functions,
functions of bounded variation, absolute continuity, review of metric space theory,
the Ascoli-Arzela Theorem, and if time permits, the Stone-Weierstrass Theorem.
Prerequisite:
Math 3130, 3001 and 4001, or instructor consent.
Course Text:
We will use the text "Real Analysis", by H.L. Royden and Patrick Fitzpatrick, 4th Edition, Prentice Hall, covering most of Chapters 2 - 7.
Fitzpatrick has a web page devoted to the book, including a link to an errata page at
http://www-users.math.umd.edu/~pmf/RealAnalysis/index.html
Assessment:
Lecture Hours and Venue:
MWF 10 a.m.-11 a.m. ECCR 131.
Office Hours:
TBA
Homework:
Some Important Names associated with Real Analysis :
Back to the home page of Judith A. Packer
Last modified August 22, 2013.