A survey of topics in the history of mathematics from the ancient Babylonians to the twenty-first century. Each session will be focused on one particular mathematician and one work that the mathematician wrote. We will devote two sessions to each topic, the first consisting of an overview of the relevant history of mathematics, and the second devoted to the particular subject under consideration. The topics considered have stimulated lively historical discussion and even controversy, and in many cases have resulted in a novel historical interpretation of some part of past mathematics.

A survey of selected topics in the history of astronomy. Proceeding chronologically, we survey major achievements in astronomy, from the planetary tables of the Selucid Babylonians to the big- bang model of contemporary cosmology. Attention will be paid to developments that have provoked historical debate and discussion, or have resulted in a novel historical interpretation of past astronomy. Particular emphasis will be placed on the development of cosmology: the shift from the Ptolemaic to Copernican astronomy in the Scientific Revolution, and the rise of big-bang cosmology in the twentieth century. <\p>

The course will provide a survey of a selected topic in the history of mathematics 1700-1900. Examples of subjects that have been covered in the past include the development of conceptual foundations of analysis, the history of complex analysis, historical perspectives on existence theorems in mathematics, and the history of mathematical logic. Emphasis will be placed on the technical and conceptual development of mathematics, although philosophical and social influences on mathematical practice will also be considered.

A survey of ancient, medieval and early modern mathematics, with emphasis on technical development as well as historical background. Topics to be covered include the development of axiomatic geometry by the Greeks, the establishment of mathematical astronomy in antiquity, algebraic techniques in Arabic mathematics, mathematical methods in the new astronomy of Copernicus and Kepler, and coordinate geometry and the calculus in the 17th century. The grade for the course will be based on assignments, a mid-term test, and a final examination.

An historical study of selected topics in the development of mathematics from 1700 to the present. Subjects to be covered include the history of the function concept, the arithmetization of analysis in the 19th century, the invention of non-Euclidean geometry, the emergence of abstract algebra, the development of set theory. Attention will also focus on some particular topic in analysis, geometry and topology, algebra, modern probability theory, number theory or combinatorics. An attempt will be made to give a sense of the problems and developments in these areas to students without extensive mathematical expertise. The grade for the course will be based on an essay, a mid-term and final test.

This course will delve into conceptions of the universe from 1800 to the present, with attention to theoretical and observational sources of changing ideas. History of large telescopes, stellar spectroscopy, and radio astronomy. Relativistic conceptions of space and time, models of stellar evolution, discovery of extra-galactic nebulae, the Hubble red-shift and the microwave background radiation. Philosophical and religious implications will also be examined. Evaluation will be based on class tests, assignments, and essays.