# MAT 532, Real Analysis I

# Fall 2018

# 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

###
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: 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
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including categories of academic dishonesty, please refer to the
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http://www.stonybrook.edu/commcms/academic_integrity/index.html

### Critical Incident Management Statement:

Stony Brook University expects students to respect the rights,
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to the Office of Judicial Affairs any disruptive behavior that
interrupts their ability to teach, compromises the safety of the
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Send me email at:
bishop at math.sunysb.edu
Link to
history of mathematics