Math 417 - Honors Real Variables, I
Instructor
Office hours
Syllabus
- elementary set theory (including cardinalities)
- construction of the real numbers
- Lebesgue measure and integral in one dimension (possibly in several
dimensions if there is enough time)
- functions of bounded variation and the Riemann-Stieltjes integral
Textbooks
The book I'm planning to follow mostly is
- H. L. Royden, Real Analsysis, Third Edition. Prentice-Hall, 1988.
Since it is rather expensive, I won't require it. Another useful text on the
subject is
- C. D. Aliprantis and O. Burkinshaw, Principles of Real Analysis,
Third Edition. Academic Press, 1998.
The following two books are not immediately related to the course, but are
worth looking into on occasion:
- K. R. Davidson and A. P. Donsig, Real Analysis with Real
Applications. Prentice-Hall, 2002. (The second part of the book
presents interesting applications of analysis.)
- K. Saxe, Beginning Functional Analysis. Springer Verlag, 2002.
(Even though this book is on functional analysis, it covers also some
real analysis, in particular, the N-dimensional Lebesgue integral.)
Grading
The grade will be based on weekly homework assignments (30%), an in-class-midterm on October 21 (20%), and a final (50%).
Last update: 1/14/06.