SUNY Stony Brook

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 , ,