This is the first semester of a one year honors course in real analysis. The subject matter will be familiar. Essentially it is calculus, both single and multivariable, which means the theory of functions on the real line or in real n-dimensional space. But the emphasis will be on achieving a deep understanding of the theorems and the proofs which back them up. Along the way we will cover the basics of set theory, the topology of metric spaces, function spaces and Lebesgue measure. We will take the time to appreciate the many examples, counterexamples and paradoxes which illuminate the theory.
Real Mathematical Analysis, by Charles Pugh. I will try to cover Chapters 1-4 in the first semester.
|Midterm Exams||20% each|
|Midterm I||Monday, October 6|
|Midterm II||Monday, November 17|
|Final Exam||Tuesday, December 16, 8am-10am|
Homework will be due about every two or three weeks. Students are encouraged to work together on the assignments but everyone should write up their own version of the solutions. Not all of the assigned problems will be graded. To see the assignments as they become available, click on the link above.