This course provides a basic introduction to mathematical thinking and elementary mathematical concepts. We will survey the history of mathematical discoveries from the antiquity to the end of Renaissance by analyzing case studies and situating them in the context of advances in philosophy, logic, physics and technology. For example, how developments in banking system, bookkeeping methods and maritime navigation advanced the theory of magnitudes which in turn contributed to developments in Kinematics and what is now called linear algebra. By looking at different case studies and examining thoughts and methods behind these discoveries, the course aims to portray mathematics in a different light as a field where intuitive thinking, formal rigor and creative experimentation come hand in hand.
The course consists of two modules, each of four weeks.
Each module of the two-part seminar will be composed of four two and a half hour sessions, each of which will be conducted as an extended seminar. During this period material blogged the previous week will be discussed alongside the set material. Based upon the set readings, online news and commentary, and ongoing class discussion, students will be expected to contribute ~400 words of content to the seminar blog on relevant topics. (This will additionally be posted to the google classroom page for everyone to read and comment upon as they wish, providing some preliminary threads for the group discussion). The final assessment will consist of a 2500 word extended essay on a topic agreed upon with the instructor in advance.
Image: Rafael, School of Athens, 1509-1511