This is the second semester of a one year honors course in real analysis. The subject matter of real analysis is 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. Topics for the second semester include function spaces and applications, multivariable differentiation and integration and an introduction to Lebesgue measure and integration. 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 4-6.
|Midterm Exams (3)||25% each|
|Midterm I||Friday, February 20|
|Midterm II||Friday, April 3|
|Midterm III||Friday, May 8|
Homework will be due about every 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.