The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.

Michael C. Reed received the Bachelor’s degree in mathematics from Yale (1963) and the Ph.D. in mathematics from Stanford (1969). He has worked in many branches of mathematics including functional analysis, mathematical physics, partial differential equations, and the applications of mathematics to human physiology and medicine. He is currently Arts and Sciences Distinguished Professor of Mathematics at Duke University, where he uses Fundamental Ideas of Analysis to teach undergraduate and graduate students.