Foundations of Analysis
This course may be thought of as a deeper look at the theory of functions of a
single real variable, a topic with which you are already familiar.
However, the approach taken here will be less computational, with a far
greater emphasis on proof and on gaining a better understanding of
the basic principles. In addition, you will be expected to do a certain amount
of mathematical writing, in your homework assignments and on your exam papers.
As a ''warm-up'' we'll look at the real number system from an axiomatic point
of view. The main topics to be discussed this term revolve around issues of
convergence: limits, continuity, and the basics of metric spaces. We'll also
cover differentiation of real functions.
- Instructor: P. Fitzsimmons (firstname.lastname@example.org)
- AP&M' 5715, phone 534-2898
- Office Hours: MWF 10:30-11:30 am and 1:30-2:30 pm, or by appointment.
- Teaching Assistant: J. Lee (email@example.com)
- Text: W. Rudin, Principles of Mathematical
Analysis (Third Edition), McGraw-Hill, 1976.
(I plan to cover most of the topics found in chapters 1-5
of the text.)
There will be two
midterm exams (in the fourth and eighth weeks) and a final exam, with the following weights:
- Midterm #1: 20%
- Midterm #2: 20%
- Final: 35%
- In addition, there will be weekly homework
assignments, which will account for the remaining 25% of your grade.
The +/- system will be used
for letter grades.
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September 1, 1998; updated September 24, 1998