# MAT 532, Real Analysis I

# Fall 2017

# Christopher Bishop

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.

Midterm will be in class, Tuesday, October 24.

The following is a tentative
lecture and homework schedule .
Last revised Sept 21, 2017.

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 ]

### Academic Integrity Statement:

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