Math 512: Modern Analysis I, Spring 2010
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Section information: Section 1, class number
23438, 1:00-1:50 P.M., MoWeFr, Witmer 305
- Prerequisite: Math 432
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Instructor: L. Peterson
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Phone numbers: 777-4609 (office), 795-8984
(home), 777-2881 (Mathematics office)
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E-mail address: lawrence.peterson@und.edu
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URL: http://www.und.nodak.edu/instruct/lapeters.
This syllabus appears on my Web site. Use of the Web is optional. I
will announce all assignments in class as well as on the Web.
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Office: 322 Witmer Hall
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Office hours:
| Mondays: | 2:00-2:50 P.M.
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| Tuesdays: | 1:00-1:50 P.M.
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| Wednesdays: | 2:00-2:50 P.M.
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| Thursdays: | 1:00-1:50 P.M.
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| Fridays: | 2:00-2:50 P.M.
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These office hours do not apply during University recesses and
holidays, on Reading and Review Day (May 7, 2010), or during
final exam week.
- Textbook: Real Analysis, Third
Edition, H. L. Royden (Upper Saddle River, New Jersey: Prentice
Hall, 1988). Be sure to get the third edition. Let me know if you
have difficulty obtaining the book.
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Course content: Math 512 is the first
semester of our two-semester course in modern analysis. This
two-semester sequence will introduce you to many of the topics that
you may encounter in more advanced mathematical work. The primary
topic of Math 512 will be Lebesgue measure and integration. The
goal will be to develop a more general version of the integral that
you studied in elementary calculus. In Math 513, we will develop
an integral which is even more general than the integral we study in
Math 512. The second semester of the course will also include
some topics related to metric spaces, vector spaces, and linear
transformations.
In Math 512, we will cover as much of
chapters 1 through 6 of the Royden textbook as possible, but we
will skip Section 4.5. We may also skip other sections, but we
may return to some of these later. My tentative plan for
Math 513 is to finish Chapter 6 and then cover
sections 7.1, 7.2, 7.3, 7.4, 7.5, 10.1, 10.2, 10.3, 11.1, 11.2,
11.3, 11.5, 11.6, 12.1, 12.2, and 12.4. Time constraints will
probably force us to skip some of this material, however.
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Course objectives:
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To develop the student's 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
- To provide some of the background in analysis that is
necessary for more advanced courses and studies
- To improve the student's overall mathematical ability
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Exams: There will be two midterm exams and one
final exam. The midterm exams will occur in class during regular
class periods. The final exam will be comprehensive with an emphasis
on the material that we cover after the second midterm.
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Homework: Feel free to stop by my office if you
have questions about the homework. You may also raise questions in
class. A file folder in the Mathematics Learning Center
(rooms 310 and 312, Witmer Hall) will contain worked out
solutions to past homework problems. I will collect homework in class
on announced due dates. You will receive full credit if you hand in
the homework anytime up to 4:20 P.M. on the due date. If I am
not in my office, leave it in my mailbox.
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Grading:
- Midterm exams: 40%
- Final exam: 30%
- Homework: 30%
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Grading scale: 90% A, 80% B, 70% C, 60% D
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Comments and concerns: Let me know if you have
any comments or concerns about the class. This course will likely
have a very low enrollment. So if things are not going well for you,
I may be able to adjust the pace of the class or provide you with
additional help.
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Emergency information and special
arrangements: 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 request disability accommodations, please register with Disability Services for
Students. The DSS office is located in Room 190, McCannel Hall
(Telephone 777-3425, voice/TDD).
- Final exam: Our final exam will
occur in the regular classroom at the following time:
1:00-3:00 P.M., Wednesday, May 12, 2010.
Links
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Lawrence J. Peterson home page
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Mathematics Computer Lab home page
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Department of Mathematics home page
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University of North Dakota home page
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: 7 January 2010
University of North Dakota home page