Stony Brook University

Office: 4-112 Mathematics Building

Phone: (631)-632-8274

Dept. Phone: (631)-632-8290

FAX: (631)-632-7631

Meeting ID: 974 0855 8490, Passcode: textbook author

For audio only use phone nummber: 646 876 9923 US (New York)

Find your local number .

The final exam will have 5 problems. The first problem has five subparts that asks for examples of various objects from Chapters 4, 5 and 7. For example, give an example of a meager set with full measure. You do not need to prove your examples are correct. The other four problems require a proof of some sort. You will have a choice of four from five possibilities: two from Chapter 8 (Fourier analysis), two from Chapter 9 (Distributions) and one from Chapter 10 (probability)

You may use the textbook during the exam, but no other sources (books, people, notes,...). Please review the following problems from the text. A few of these (or variations) will appear on the final exam: 8.8, 8.18, 8.32, 8.34, 8.35, 9.10, 9.11, 9.25, 9.33, 10.14, 10.15.

Meeting ID: 625 069 4063 Passcode: 653434

Jordan Rainone (grader): Monday 1-2pm personal Zoom link .

CHAPTER 4 SLIDES - Topology

CHAPTER 4 SLIDES, ANNOTATED The slide plus any corrections, skteches,... I made in class. Much larger file.

CHAPTER 5 SLIDES - Functional analysis

CHAPTER 7 SLIDES - Radon measures

CHAPTER 8 SLIDES - Fourier analysis

CHAPTER 9 SLIDES - Distributions and Sobolev spaces

CHAPTER 10 SLIDES - Topics in Probability Theory

Prof Varolin's notes on existence and uniqueness for ODE

Slides based on Varolin's ODE notes

My plan to is have problems sets due every other week. My hope was that this was less stressful than weekly assignments, although the total number of problems would be the same. Tentatively, problems sets are due on the Friday following the week(s) when we cover the relevant section. Due dates may change depending on the schedules for other core classes, and the grader.

Late problem sets will be accepted, but with a penalty determined by the grader.

Although it is not required, you may wish to consider writing up your solution in TeX, since eventually you will probably use this to write your thesis and papers.

The not too short introduction to LaTex

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

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Link to history of mathematics