In Ideas in Mathematics we shall examine the ideas, concepts, and paradigms which have significantly influenced the growth of modern mathematical thought, with emphasis on an appreciation for the creative side of mathematics and the fundamental role it has played in the development of modern civilization. Topics will be drawn from across the spectrum of mathematical thought and treated from a historical and cultural as well as mathematical perspective.
In particular, during this term we shall
- study contributions of the Greeks to mathematics (In this portion of the course we shall, among other things, read a portion of Euclid's Elements, look at important mathematical developments in the centuries preceding Euclid, and consider some of the monumental contributions of Archimedes in the century following Euclid.);
- consider the importance of the development of analytic geometry in the first half of the seventeenth century as a prelude to
- The Calculus which Newton and Leibnitz developed in the last half of the seventeenth century;
- see how ideas initiated by the ancient Greeks Zeno and Eudoxus were developed by the nineteenth century mathematicians Georg Cantor and Richard Dedekind;
- finally, consider selected gems of modern mathematics.