MAT 532, Real Analysis I

Fall 2018

Christopher Bishop

Professor, Mathematics
SUNY Stony Brook

Office: 4-112 Mathematics Building
Phone: (631)-632-8274
Dept. Phone: (631)-632-8290
FAX: (631)-632-7631

Time and place: TuTh 1:00-2:20, Physics P-122

August 29, ROOM CHANGE: Mat 532 will now meet in ESS 183 (Earth and Space Sciences; other side of the big torus from the math building).

Problem sets:

        Due Sept 6: 1.2:3,4 and 1.3:8,10,12,14
        Due Sept 13: 1.4: 17,18,19 and 1.5: 30,31,33
        Due Sept 20: 2.1: 3,4,7,9 and 2.2: 13,15,16
        Due Sept 27: 2.3: 19,20,21,25 and 2.4: 33, 36
        Due Oct 4: 2.4: 39,44 and 2.5: 46,47,48,50
        Due Oct 11: 3.1: 2,3,6 and 3.2: 9, 11, 13, 17
        Due Oct 25: 3.4: 22,23,25 (25 will be easier after next Tuesday's lecture)
        Due Nov 1: 3.5: 30,31,37,40
        Due Nov 8: 4.6: 64, 65 and 4.7 68, 69, 70
        Due Nov 29: 5.1: 4,8,9,11,12, and 5.2: 19,22,25
        Due Dec 6: 5.3: 27,30,32,38,39 and 5.4: 45,47,48

The final exam will have three parts. The first part will ask for five definitions or statements of theorems. The second part will ask for five examples. These questions will be taken mostly from the material that followed the first midterm. The third part consists of doing three proofs: there are three pairs of problems and you will chose one of each pair. At least one of the pairs involves the material from Chapter 5 (including Hilbert spaces), but not necessarily a homework problem (as I mentioned as a possbility in class once).

We will use the text `Real Analysis' by by Gerald Folland, second edition, published by Wiley. I hope to cover Chapters 1-3, and parts of 4 and 5. Chapter 0 is prerequisite material but I may discuss it briefly if needed.

My office hours will be Tu-Th 9:30-11 in my office, 4-112 in the Math Building, and by appointment.

Grader is Jack Burkart.

This is an introductory course on measure theory, with a bit of point set topology and functional analysis thrown in.

Homework problems will be handed in at class each Thursday.

Midterm will be in-class, Tuesday, October 16, regular room.

Final is Thursday, Dec 20, 2018, 11:15-1:45 in the usual room, ESS 183.

The following is a tentative lecture and homework schedule .

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

Here are the midterms and finals for a 2-semester course from Rudin's 'Principles of Mathematical Analysis'. These should give you an idea of what would be good to know entering this course: midterm 1 , final 1 , midterm 2 , final 2 ,

Additional links

Hugh Woodin, The Continuum Hypothesis, Part I

This gives an introduction to set theory with a discussion of the the role of the axiom of choice and the existence of non-measurable sets.

Hugh Woodin, The Continuum Hypothesis, Part II

This continues the previous article and discusses in what sense the continuum hypothesis can be considered true or false, even through it is formally independent of ZFC.

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

Disability Support Services (DSS) Statement:

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website: ]

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Send me email at: bishop at

Link to history of mathematics