MAT 532, Real Analysis I

Fall 2017

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

We will use the text `Real Analysis' by by Gerald Folland, secondedition, 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 10-11 in my office, 4-112 in the Math Building, and by appointment.

Grader is Dahye Cho. Her office hours are Monday 4-6 in MLC and Tuesday 4:30-5:30 in S-240A (big office to left of outside door on SL level of Math Building). You may see her with questions about how problem sets were graded, and to submit "re-dos" for partial credit.

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 Tuesday.

The following is a tentative lecture and homework schedule .

problem set for Chapter 0.

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

Final location TBA.

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: http://www.stonybrook.edu/ehs/fire/disabilities ]

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Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/commcms/academic_integrity/index.html

Critical Incident Management Statement:

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.

Send me email at: bishop at math.sunysb.edu

Link to history of mathematics