20472 History of Mathematics: From Ancient Greece to Euler's Time 1
Credits: 4 intermediate credits in Mathematics
Prerequisites: none
Required: The ability to read scientific texts in English, and one of the following: Infinitesimal Calculus I, Differential and Integral Calculus I 1
Recommended: Bibliographic instruction in the Library
The course is based on a series of recorded lectures by Prof. Leo Corry, and on guided readings.
The history of mathematics is a dynamic field of academic research, characterized by significant controversy over the explanation and understanding of historical-mathematical issues. The course examines the processes of creation and implementation of mathematic knowledge in their cultural context, thus enabling students to understand the complexity of the factors that influence the development of ideas.
The course summarizes key processes in the developments of mathematical thought from ancient Greece to the 18th century. It examines the affinity between the development of mathematical ideas unique to each era and the intellectual framework and institutions in which they arose. Mathematics is shown to be a system of knowledge that develops out of deliberation and coping with problems; a system that often reaches a dead end; that occasionally achieves an ideological breakthrough; and that has periods of gradual development. The course provides a different view of mathematics to that which is familiar from courses whose aim is to impart knowledge in its various areas. The course is likely to provide mathematics teachers with an interesting perspective on subjects with which they deal on a daily basis in their work.
Topics: Introduction: The history of mathematics – what is it?; Ancient Greek mathematics: the sources, key problems, techniques; The foundations of Euclid: structure and goals; Archimedes and Apollonius; Late Greek mathematics: Diophantus and algebra; Islamic mathematics and its influences; Jewish mathematicians of the Middle Ages; Mathematics of the Renaissance and the beginning of the modern era: new algebra; Preparing for calculus: Cavalieri, Roberval, Pascal, Barrow and others; The beginning of calculus: Newton and Leibniz; Mathematics after Newton and Leibniz.
1Students lacking the appropriate background but wish to choose this course are advised to consult an academic advisor.