Abstract

0. PREFATORY THOUGHTS. I am known as a complex analyst, yet I have never had a course in complex variable theory. This lacuna in my education has perhaps had an effect on the way that I view the subject. I see the elegant subject of complex function theory as a stage for the setting of beautiful problems. Once these problems are apprehended or understood, they are of ten best solved by stripping away the complex variables and bringing in tools from other parts of mathematics. That is the point of view that I promulgate in the present article. I illustrate the point with examples from real analysis, group theory, abstract algebra, partial differential equations, geometry, and other subjects as well.

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