ADVANCED MATHEMATICAL ANALYSIS
MATH 109
Fall 2011
Dr. Ray Rosentrater
Office: Winter Hall 302
Phone: 6185
Office hours:
Tues. 2:00 – 3:30
Wed. 3:30 – 4:30
Thurs. 10:30 – 11:45
Prerequisites:
Mathematical Analysis (MA 108)
Texts:
Burk, A Garden of Integrals, Mathematics Association of America. (Required)
Recommended Resources
Taylor, General Theory of Functions and Integration.
DePree and Swartz, Introduction to Real Analysis.
Royden, Real Analysis.
Objectives: By the end of the course you should be able to
1. Articulate the wide variety of approaches to integration and explain the implications of the
different approaches.
2. Learn mathematics by reading, fill in gaps as needed.
3. Write effective mathematics.
Overview:
The idea of the integral is introduced in Elementary Calculus. The integral under discussion in
Elementary Calculus is the Riemann integral. There are, however, other generalizations and
approaches to integration. This course will explore some of the alternate integrals and their
properties. A tentative schedule is
Week
1-2
3-4
5
6-9
10
11-13
Topic
Overview and Cauchy Integration
Riemann (& Darboux) Integration
Reimann-Stieltjes Integration
Lebesque Integration
Lebesque-Stieltjes Integration
Henstock-Kurzweil (Gage) Integration
Evaluation: Evaluation will be based on the following criteria.
Regular Homework
Class Contribution
Regular Exams (2)
Cumulative Final
30%
30%
20% (10% each)
20%
Homework: Homework will be assigned more or less daily. Assignments will generally be due the
following class period. Solutions are to be written up using mathematical typesetting software and
should conform to disciplinary presentation standards.
Class work: We will use a seminar format in this course. Each day you will be assigned reading for
the next class period. You are responsible for both reading and understanding the material. In
particular, you are responsible for filling in any gaps in the proofs. During class, we will review
the reading and members of will be called upon to supply the missing details. Your class
contribution score will be based primarily on your responses. Toward the end of the course, you
may be assigned a class period during which you will lead the discussion and call on your
classmates for explanations.
Approximately weekly, I will distribute a copy of a submitted solution to be critiqued by the class.
Absence: While attendance is expected and absence is unwise, there is no formal penalty for absence.
Responsibility is expected. Clearly, you cannot get credit for class contribution when you are not
present. If you are forced to miss class for some reason, make arrangements for your homework
to be brought to class for you.
Dishonesty: Dishonesty of any kind will result in loss of credit for the work involved. Major or
repeated infractions will result in dismissal from the course with a grade of F. Collaboration is
encouraged, but mere copying of another's work is dishonest. Give credit on all collaborative
work. In particular, your homework solutions should credit any assistance you have received from
classmates, faculty, or online resources.
Students with Special Needs: Students who have been diagnosed with a disability (learning, physical
or psychological) are strongly encouraged to contact the Disability Services office as early as
possible to discuss appropriate accommodations for this course. Formal accommodations will only
be granted for students whose disabilities have been verified by the Disability Services office.
These accommodations may be necessary to ensure your full participation and the successful
completion of this course. Please contact Sheri Noble, Interim Coordinator of Disability Services
(x6186, snoble@westmont.edu) as soon as possible.