Office: 4-112 Mathematics Building
Phone: (631)-632-8274
Dept. Phone: (631)-632-8290
FAX: (631)-632-7631
Time and place: MWF 11:45-12:40, Harriman Hall 115
We will follow the text `Measure, Integral and Probability' by Marek Capinski and Ekkehard Kopp (Springer-Verlag, Springer Undergraduate Mathematics Series, ISBN 1-85233-781-8). We should cover all of Chapters 1-5, and perhaps parts of Chapters 6,7,8 as time permits.
This is definitely a course with proofs. Homework problems will be asssigned for each section and there will be an inclass midterm on Friday, Oct 27 and a final at a time to be set (Scheduled time is Monday Dec 18 at 2-4:30).
Please hand homework in on or before due date. I will try to discuss the problems on the following meeting. Incorrect problems may be rewritten and handed back in for partial credit.
MIDTERM in class on MOnday , Oct 29.
Midterm 1 sample exam in PDF
Midterm 1 sample exam in postscript
Chapter 1: Motivation and preliminaries
Problem set 1 is due Wed, Sept 12
Problem set 1 in PDF
Problem set 1 in postscript
Problem set 1 in TeX
Chapter 2: Measure
Problem Set 2a due Oct 1
Problem set 2a in PDF
Problem set 2a in postscript
Problem set 2a in TeX
Problem Set 2b due Oct 8
Problem set 2b in PDF
Problem set 2b in postscript
Problem set 2b in TeX
Chapter 3: Measureable functions
Problem Set 3 --- Due Oct 15
Problem set 3 in PDF
Problem set 3 in postscript
Problem set 3 in TeX
Chapter 4: Integral --- Oct 31
Problem Set 4
Problem set 4 in PDF
Problem set 4 in postscript
Problem set 4 in TeX
Chapter 5: Spaces of Integrable functions
Problem Set 5 --- Due Nov 26
Problem set 5 in PDF
Problem set 5 in postscript
Problem set 5 in TeX
Chapter 6: Product measures
Chapter 7: The Radon-Nikodym theorem
Chapter 8: Limit theorems
Here are some `fun' problems to think about:
- Given a set X in the real numbers, how many different sets
can you generate by taking complements and closures repeatedly?
-Show that every real number in the interval [0,2] Can be written
as the sum of two real numbers in the Cantor middle thirds set.
template.tex
postscript output for template.tex
Send me email at:
University final exam schedule
Link to Schroder-Bernstein theorem
Link to Freilng's dart argument against CH
Link to history of mathematics
Some specific topics from the history of math site: history of `e' , The Brachistochrome problem , Isaac Newton , Gottfried Willhelm von Leibniz , A brief history of calculus , The fundamental theorem of algebra , A brief history of mathematics , Jean Fourier , The number `Pi' , Discovery of Neptune and Pluto , ,