Math 513: Modern Analysis II
Fall 2007
- Instructor: L. Peterson
- Section information:
Section 1, class number 9535, 2:00-2:50 P.M., MWF,
Witmer 211
- Prerequisite: Math 512 (Modern Analysis I)
- Office: 322 Witmer Hall
- Office hours:
Feel free to drop in anytime during normal business hours. If I am
available and not overly busy, then I can meet with you. My official
office hours are as follows:
| Mondays: | 11:00-11:50 A.M.
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| Tuesdays: | 1:00-1:50 P.M.
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| Wednesdays: | 11:00-11:50 A.M.
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| Thursdays: | 2:00-2:50 P.M.
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| Fridays: | 12:00 noon-12:50 P.M.
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These office hours do not apply during university recesses
and holidays, on Reading and Review Day (December 7, 2007), or
during final exam week. Additional office hours, including hours on
Reading and Review Day and during final exam week, are available by
appointment or, when possible, by drop-in.
- Phone numbers: 777-4609
(office), 795-8984 (home), 777-2881 (Mathematics office)
- Messages:
If you cannot reach me, you may leave recorded messages at my
777-4609 number. You may also leave a note for me in the Mathematics
office, Room 313 Witmer Hall.
- E-mail address:
lawrence.peterson@und.nodak.edu
- URL for Web site:
http://www.und.nodak.edu/instruct/lapeters. Use of the Web site is
optional. I will announce all assignments in class as well as on
the Web.
- Textbook:
Real Analysis, Third Edition, by H.L. Royden (Pearson
Education, 1988). You may purchase the text at Barnes & Noble in
Grand Forks. The textbook may also be available at the Dakota
Textbook Company, 415 North 42nd Street, Grand Forks, or from other
distributors. If Barnes & Noble has run out of copies of the book,
they may not order any more copies unless you go to the textbook
counter and ask them to order a copy specifically for you.
- Course content: This course is the second
semester of our two-semester course in modern analysis. During the
first semester, we studied the idea of the measure of a set of real
numbers as well as the Lebesgue integral of a real-valued function
of a single real variable. During the second semester, we will
continue this study, but we will also study measures of other types
of sets as well as the integrals of functions defined on these sets.
We will study dual spaces, linear functionals, Banach spaces,
the Hahn-Banach Theorem, the Radon-Nikodym Theorem, and Fubini's
Theorem.
As time permits, we will cover sections 6.2, 6.3, 6.4, 6.5, 10.1,
10.2, 10.3, 11.1, 11.2, 11.3. 11.4, 11.5, 11.6, 11.7, 12.1, 12.2,
and 12.4. We will also study the Hausdorff Maximal Principle in
Section 1.8, and we may spend a small amount of time
reviewing metric spaces in Chapter 7. In Section 10.3, we
will skip Proposition 5 and Theorem 8. If we run
out of topics, then we will probably study Hilbert spaces in
Section 10.8.
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Course objectives:
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To develop the ability to understand mathematical
proofs and to construct well written proofs
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To give students some of
the background in analysis that they may need in order to do original
mathematical research and to conduct master's degree independent
studies
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To provide some of the background in analysis that is
necessary for more advanced courses and studies
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To develop a better
understanding of real analysis for its own sake
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Grading:
- Midterm exams: 40%
- Final exam: 30%
- Homework: 30%
- Grading scale: 90% A, 80% B,
70% C, 60% D
- Homework:
Homework will be an important part of the course. You may discuss
your homework with other people, but do not copy another person's
solutions. If you receive significant help from another person, make
a note of this fact on the paper you hand in. If you are stuck, feel
free to come to see me or to raise questions in class. I hope to
grade all of the problem solutions that you hand in. Please hand in
homework by 4:20 P.M. on the announced due date.
If you do not hand in your homework during class, you
may bring your homework solutions directly to me in my office. If
the door to my office is closed, please give your papers to the
staff in the Mathematics Department office.
- Solution keys: A file folder
in the Mathematics Learning Center (Rooms 310 and 312, Witmer
Hall) will contain solutions to past homework problems. You may
borrow them for a few minutes at a time. Feel free to photocopy
them. There are photocopiers on the second floor of Witmer Hall and
at the Chester Fritz Library.
- Exams: There will be two
midterm exams and one final exam. The midterm exams will occur in
class during regular class periods on dates that I announce in
advance. The final exam will be
comprehensive with an emphasis on the material that we cover after
the second midterm.
- Absences from exams: If you
will be absent from an exam, call me in advance.
- Attendance policy: I want you
to succeed in this course. Please attend all class sessions if
possible. Please be respectful and considerate of other people in
the class.
- Final exam: The final exam for this course
will occur from 3:15 P.M. to 5:15 P.M. on Monday
December 10, 2007 in our usual classroom.
- Changes to policies: Course
policies, including all policies described in this syllabus, are
subject to change. I will announce any changes to the policies.
- Comments and concerns:
Let me know if you have any comments about the class. If you have
emergency medical information to share with me, if you need special
arrangements in case the building must be evacuated, or if you need
accommodations in this course because of a disability, please make an
appointment with me. If you plan to request disability accommodations,
you are expected to register with the
Disability Support
Services (DSS) office (190 McCannel Hall, 777-3425 voice/TTY).
Links
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Lawrence J. Peterson home page
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Department of Mathematics
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University of North Dakota
Notes on Web Page
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Contact Person: Larry Peterson
E-mail: lawrence.peterson@und.nodak.edu
Phone: (701) 777-4609
Date of most recent update: 21 August 2007
University of North Dakota home page