This exam will test your working knowledge of basic real, complex and functional analysis. You will be required to demonstrate an ability to use standard results and techniques to solve problems, including special cases of standard theorems which do not require long arguments.
We will not emphasize the memorization of statements of theorems nor of long proofs of standard theorems.
The student is urged to work on the problems in the relevant sections and chapters in the reference books.
Syllabus (updated Fall 2020).
There will typically be 12 problems, 7 from real analysis and 5 from complex analysis. Students must designate 10 to be graded.
 Natanson, Theory of Functions of a Real Variable.
 Kolmogorov and Fomin, Introductory Real Analysis.
 Royden, Real Analysis.
 Rudin, Real and Complex Analysis, 2nd edition.
 Friedman, Foundations of Modern Analysis.
 Folland, Real Analysis.
 Wheeden and Zygmund, Measure and Integral, an introduction to real analysis.
 Stein and Sharkarchi, Real Analysis, Measure Theory, Integration and Hilbert Spaces.
 Stein and Sharkarchi, Fourier Analysis.
 Ahlfors,Complex Analysis
 Conway, Functions of One Complex Variable
 Schaum's Outline of Complex Variables