MATHEMATICS 110.605
Theory of Functions of a Real
Variable
Fall 2009 |
Prof. C. Sogge
á Textbook: Richard L. Wheeden and Antoni Zygmund, Measure and Integral: An Introduction to Real Analysis
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Coverage: This
course will be a one-semester treatment of standard real-variable theory. The goal will be to at least cover the
first nine chapters of Wheeden and Zygmund fairly thoroughly. We shall also cover the first chapter
of my book, ÒFourier Integrals in Classical AnalysisÓ.
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Prerequisites: A
good advanced calculus course, as well as equivalents of 110.405 and 110.413 is
required. The ability to write
logically correct and linguistically coherent proofs in the language of
mathematics is essential.
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Grading: The final grade will
be based on weekly homework assignments (20%), and two exams each worth 40%.
You may work with other members of the class on the homework assignments, but
you may not get help from the Help Room or other students on problems that are
assigned.
Homework
Assignments (Due in Class on Mondays)
Assignment 1 (Due
9/14): Chapter 1, Problems: 3, 8, 10, 12, 15, 17, 18
Assignment 2 (Due
9/21): Chapter 2, Problems: 1, 4, 5, 6, 7, 9, 10, 14
Assignment 4 (Due
9/28): Chapter 3, Problems: 2, 7, 8, 9, 10, 17, 23
Assignment 5 (Due
10/5): Chapter 4, Problems: 1, 2, 5, 6, 8, 9
Assignment 6 (Due
10/12): Chapter 5, Problems: 1, 2, 3, 4, 5, 6, 9
Assignment 7 (Due
10/21): Chapter 5, Problems: 10, 11, 12, 16, 18
Assignment 8 (Due
10/28): Chapter 6, Problems: 1, 2, 3, 5, 6; Chapter 7: 1, 2, 3, 4
Assignment 9 (Due
11/9): Chapter 7, Problems: 5, 6, 7, 8, 12, 14
Assignment 10 (Due
11/16): Chapter 8, Problems: 8, 2, 3, 4, 5, 6, 8
Assignment 11 (Due 11/23):
Chapter 8, Problems: 10, 11, 12,
15, 17, 18