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, Phyics P-127
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). I hope to the entire book, at a rate of about 1 chapter every two weeks.
This is definitely a course with proofs. Homework problems will be asssigned for each section and there will be an in-class midterm and a final.
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.
Hugh Woodin, The Continuum
Hypothesis, Part I
Hugh Woodin, The Continuum
Hypothesis, Part II
FINAL is scheduled for Tuesday, Dec 13, 2:15-4:45
Chapter 1: Motivation and preliminaries
Problem set 1 is due Friday, Sept 16. Rewrites for full credit due Friday, Sept 23.
Problem set 1 in PDF
Problem set 1 in TeX
Wikipedia article on the Banach-Tarski paradox
Wikipedia article on Carleson's a.e. convergence theorem
Wikipedia article on Weierstrass' nowhere differentiable function
Chapter 2: Measure
Problem Set 2a due Monday, Sept 26
Problem set 2a in PDF
Problem set 2a in TeX
Problem Set 2b due Monday Oct 3
Problem set 2b in PDF
Problem set 2b in TeX
Chapter 3: Measureable functions
Problem Set 3 --- Due Friday Oct 14
Problem set 3 in PDF
Problem set 3 in TeX
Chapter 4: Integral ---
Problem Set 4
Problem set 4 in PDF
Problem set 4 in TeX
Chapter 5: Spaces of Integrable functions
Problem Set 5 --- Due
Problem set 5 in PDF
Problem set 5 in TeX
Chapter 6: Product measures
Problem Set 6 --- Due Mon, Nov 28
Problem set 6 in PDF
Problem set 6 in TeX
Chapter 7: The Radon-Nikodym theorem
No problem set for this chapter
The final will be 2:15-4:45pm in Rooom 4-130 of the math building (our usual
classrooom).
Sample final
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.
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 , ,