Math 417 - Honors Real Variables, I

Instructor

Volker Runde

Office hours

TBA

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%).