Math 513: Modern Analysis II
Fall 2004
- Instructor: L. Peterson
- Section information:
Section 1, call number 07692, 8:00-8:50 A.M., MWF, Witmer 305
- Prerequisite: Math 512
- Office: 322 Witmer Hall. You
may leave messages for me in the Math Office, Room 313 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. I will announce my
formal office hours in class and post them on my Web site. Please
fill in the information below.
- Mondays:
- Tuesdays:
- Wednesdays:
- Thursdays:
- Fridays:
These office hours do not apply during university recesses and
holidays, on Reading and Review Day (December 10, 2004), or during
final exam week.
- Phone numbers: 777-4609
(office), 795-8984 (home), 777-2881 (Mathematics office)
- E-mail address:
lawrence.peterson@und.nodak.edu
- URL for Web site:
http://www.und.nodak.edu/instruct/lapeters.
- Textbook: Real
Analysis, Third Edition, by H.L. Royden (Pearson Education, 1988).
- Grading:
- Midterm exams: 40%
- Final exam: 30%
- Homework: 30%
- Homework: Homework will be an
important part of the course. You may work together, 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. 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.
- Problem solutions: A file
folder in the Mathematics Learning Center will contain solutions to
past homework problems. You may borrow them for a few minutes at a
time. A photocopier is available in Room 211, Witmer Hall.
- 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.
- Course objectives:
- To develop the ability to understand mathematical proofs and to
construct well-written proofs
- 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 develop a better understanding of real analysis for its own
sake
- Course content: This course is
the second semester of our two-semester course in modern analysis.
During this second semester, we will continue our study of measure
and integration theory. In the first semester of this course, you
studied Lebesgue measure and integration. Portions of the second
semester will deal with measure and integration in general, as
opposed to the specific case of Lebesgue measure and integration.
The course will also deal with metric spaces. You may have seen
metric spaces in other courses. A metric space is a set together
which a function that defines the “distance” between any
two elements of the set. Two important examples of metric spaces
are Banach spaces and Hilbert spaces. These spaces are vector
spaces with certain properties. We will see that certain sets of
functions are actually Banach spaces or Hilbert spaces, and we will
use measures and integrals to define these sets of functions. I
hope to cover the following material from our textbook:
- Chapter 5
- Chapter 6
- Chapter 7, sections 1 through 8
- Chapter 10, sections 1, 2, 3, 4, and 8
- Chapter 11
- Chapter 12, sections 1, 2, 4, 5, 8, and 9
This course plan is subject to change.
- Comments and concerns: Let me
know if you have any comments about the class. If you need
accommodations in this course because of a disability, if you have
emergency medical information to share with me, or if you need
special arrangements in case the building must be evacuated, please
make an appointment with me as soon as possible.
- Final Exam: The final exam for
this course will occur from 8:00 A.M. to 10:00 A.M. on Wednesday,
December 15, 2004, in the usual classroom.
Links
-
Lawrence J. Peterson home page
-
Mathematics Computer Lab home page
-
Department of Mathematics home page
-
University of North Dakota home page
Notes on Web Page
-
Contact Person: Larry Peterson
E-mail: lawrence.peterson@und.nodak.edu
Phone: (701) 777-4609
Date of most recent update: 18 August 2004
University of North Dakota home page