Math 140A

Foundations of Analysis

Fall 1998

This course may be thought of as a deeper look at the theory of functions of a single real variable, a topic with which you are already familiar. However, the approach taken here will be less computational, with a far greater emphasis on proof and on gaining a better understanding of the basic principles. In addition, you will be expected to do a certain amount of mathematical writing, in your homework assignments and on your exam papers. As a ''warm-up'' we'll look at the real number system from an axiomatic point of view. The main topics to be discussed this term revolve around issues of convergence: limits, continuity, and the basics of metric spaces. We'll also cover differentiation of real functions.

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September 1, 1998; updated September 24, 1998