Home page for Math 509, Advanced Analysis

Spring 2018

Instructor: Charles L. Epstein

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The Course

In this course we continue our study of the foundations of analysis. The goal of this course is to further develop your instincts as a mathematical analyst. This entails understanding the basic concepts and techniques of analysis, as well as developing intuition and proficiency in the construction of rigorous proofs.  We continue the study of the Fourier transform and its applications, which we began in the Fall. We then turn to Advanced Calculus in several variables, culminating with Green's theorem. Using Green's theorem we will then introduce the basic concepts of functions of a complex variable.  I have not yet selected the textbook.  For part of the course we will use Strichartz (the textbook from the fall), as well as other sources for the complex analysis unit. Fourier Series  and  Complex Analysis by E.M. Stein and R. Shakarchi are excellent (though somewhat advanced) references. 

A problem set will be assigned every week, on Thursdays. We may have a take home final exam. 

Syllabus for the course

Lecture Notes


Problem Sets