Office: 4-112 Mathematics Building
Phone: (631)-632-8274
Dept. Phone: (631)-632-8290
FAX: (631)-632-7631
Time and place: Tu-Th 10:00-11:20am, Library W4530
Grader: David Hu
Final Exam: Friday, Dec 11, 2015 11:15am-1:45pm, W4530 Melville Library (usual lecture room)The Grader will have a Review Session to go over the problem sets 1-4 on Tuesday, Oct 13 at 6-8pm in P-131 of the Math Tower.
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 cover 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.
Office Hours: Tu 9-10, Th 9-10 and 1-2
Links to the problems sets will be posted here later.
Problem Set 1, Prerequisites, Due Thursday, Sept 3
Problem Set 2, Measure zero sets, Due Tuesday, Sept 15
Problem Set 3, Measurable sets, Due Thursday, Sept 25
Problem Set 4, Measurable functions,
Due Thursday, October 8
Midterm Review.
This describes the format of the Midterm on Thursday, Oct 15
(same time and place as class usually meets).
Problem Set 5, Lebesgue integration,
Due Thursday, October 29
Problem Set 6, L^p spaces, Due Thursday, November 13
Problem Set 7, Product measures , Due Tuesday, December 1
Alternate treatment of Fubini's theorem
Final Review.
This describes the format of the Final exam on Friday, Dec 11
(same place as class usually meets).
Fractals in probability and analysis
Chapter 1 contains a simple proof of the strong law of
large numbers
Send me email at:
University final exam
Hugh Woodin, The Continuum
Hypothesis, Part I
Hugh Woodin, The Continuum
Hypothesis, Part II
paper giving careful proof of Banach-Tarski paradox
Wikipedia article on the Banach-Tarski paradox
Wikipedia article on Carleson's a.e. convergence theorem
Wikipedia article on Weierstrass' nowhere differentiable function
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 , ,