History of Mathematics Math 478/678

In this course we will look at the axiomatic method --- the cornerstone of modern mathematics --- through the historical development of several important mathematical topics. In particular, we will discuss the following topics: The development of geometry concentrating mostly on Euclidian axioms; Numbers, including the Peano axioms for natural numbers, integers and the fundamental theorem of arithmetic, rational numbers as an example of a field, and the long history to the rigorous notion of real numbers; Polynomials as the ``nicest'' functions, including the discovery of complex numbers, fundamental theorem of algebra, and ``infinite'' polynomials, aka power series, that were invented by Isaac Newton; and finally Probability theory, including the axioms of Kolmogoroff, classical probability, and the (basic version of) central limit theorem.

Spring 2020:
I plan (tentatively) to include the following topics:

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