GE 1331-0

Brief

This course introduces the logic and development of Western (mainly European) mathematics, from ancient Egyptian and Babylonian mathematics, to Greek legacies (especially philosophies of mathematics and Euclid’s Elements), through medieval Islamic and European mathematics and Renaissance developments, to the invention of modern calculus. Except mathematics per se, this course also discusses the interactions between mathematics and society in Western civilisations. For example, in ancient Egyptian and Babylonian societies, what kind of people participated in mathematical activities? Did they have similar or distinct mathematical conceptions from those in modern times? How did Greek philosophies help shape the forms and contents of Euclidean geometry? What was the relationship between Islamic culture and their mathematics? Also, we discuss the concept developments of modern calculus.

Description

Course keywords: history of mathematics, European mathematics, Greek philosophy and mathematics, philosophy of mathematics, geometry, calculus Text Books: There is no designated textbook for this course, but the reading materials and the professor’s slides are all included in the scope of the examinations. References: 1.Victor Katz, A History of Mathematics (New York: Pearson, 3rd edition 2017). 2.G.E.R. Lloyd, Early Greek science: Thales to Aristotle (New York: W. W. Norton & Company, 1974). 3.G.E.R. Lloyd, Greek science after Aristotle (New York: W. W. Norton & Company, 1975). 4.Stewart Shapiro, Thinking about Mathematics: The Philosophy of Mathematics (Oxford: Oxford University Press, 2000). Teaching Method: Reading materials are designated for each week. Students are encouraged to read them before class, and the professor will discuss the contents with the students in class. There is a 90-minute open-book examination at mid-term. Before the end of the term there are group presentations, for which each group has to discuss with the professor beforehand about which topic they want to present. In the final week there is again be a 90-minute open-book examination. Syllabus: Week 1 Introduction Week 2 Ancient Egyptian society and mathematics Bunt, Jones, and Bedient (1988), pp.1-41. Week 3 Babylonian society and mathematics Bunt, Jones, and Bedient (1988), pp.42- 64. Week 4 Ancient Greek culture and early Pythagorean school Katz (2017), pp.46-51; Lloyd (1974), pp.24-35. Week 5 Mathematics in Greek philosophy:Plato vs Aristotle Shapiro (2000), pp.49- 72. Week 6 Euclid’s Elements (I) Katz (2017), pp.58-94. Week 7 Euclid’s Elements (II) Week 8 Mid-term examination Week 9 Hellenistic mathematics: Archimedes to Heron Katz (2017), pp.102-115; 156- 167; Lloyd (1975), pp.33-52. Week 10 The Islamic world and mathematics(Group presentation proposals) Katz (2017), pp.238-287. Week 11 Medieval European society and mathematics Katz (2017), pp.288-326. Week 12 Renaissance society and mathematics Katz (2017), pp.342-384. Week 13 The development and controversies of calculus in the 17th century Katz (2017), pp.468-543. Week 14 Group presentation I Week 15 Group presentation II Week 16 Final examination Evaluation: Classroom participation 10% Mid-term examination 30% Group presentation 30% Final examination 30% Website: All materials are uploaded in the university platform eLearn. AI rules: Students need to specify if he or she uses any AI app in the written examination.

Timetable

Scores

Average Percentage 89.47

Std. Deviation 4.83

Remarks

本課程為16週課程

Restrictions

Compulsory

Elective

Cross Discipline

First Specialization

Second Specialization