Sidoli, Nathan Camillo
Spring, 2021
Office hours: Thursday, 4th and 5th
Office: 11-1409
03-5286-1738
[email protected]
I will put announcements about the class in this space. Please check here periodically as the term progresses.
First Year Seminar:
Geometry, Euclid and OthersCourse Description
In this course, we will explore some of the historical contexts of Greek mathematics, read some of Euclid’s Elements of Geometry, some of Hilbert’s Foundations of Geometry, and some of Lobachevski’s Theory of Parallels. We will be focusing on the techniques of proving propositions and will go through the arguments in detail. Students taking this class will develop an understanding of some basic geometry, and appreciation of logically structured arguments, be exposed to some of the ideas of formalized axiomatic geometry, as well as non-Euclidean geometry. Students will develop experience presenting mathematics in front of others.
Required Texts
Euclid: Fitzparick, R., trans., 2008, Euclid’s Elements of Geometry. Hilbert: Unger, L., trans., 1971, Hilbert’s Foundations of Geometry. Lobachevski: Halsed, G.B., trans., 1914, Lobachevski’s Theory of Parallels. Grading
Classroom presentations 70% Active participation 30% General Format
The class meets once a week for a seminar discussion. Attendance and participation in class are mandatory and graded. Each week some students will present the mathematics from the reading on the board to everyone else. We will work very slowly through the arguments so that everyone understands. The goal of the presentations will be comprehension, not polish.
Topics, Readings and Assignments
Week 1: Apr 5General Introduction
No reading. Week 2: Apr 12Greek mathematics
Reading: Asper, M., The two cultures of mathematics in ancient Greece. Week 3: Apr 19Mathematics education in the Greco-Roman world
Reading: Sidoli, N., Mathematics education. Week 4: Apr 26Euclid’s Elements, I
Reading: TBA. Supplementary material: For Euclidean constructions see, Euclid: The Game!. (It sometimes takes a long time to load.) Holiday: May 3No Class
No Reading. Week 5: May 10Euclid’s Elements, II
Reading: TBA. Week 6: May 17Euclid’s Elements, III
Reading: TBA. Week 7: May 24Euclid’s Elements, IV
Reading: TBA. Week 8: May 31Euclid’s Elements, V
Reading: TBA. Week 9: Jun 7Euclid’s Elements, VI
Reading: TBA. Week 10: Jun 14Euclid’s Elements, VII
Reading: TBA. Week 11: Jun 21Hilbert’s Geometry, I
Reading: David Hilbert’s Foundations of Geometry Chap. 1 (pp. 1-7). Supplementary Reading: Hartthorne, R., Geometry: Euclid and Beyond Chap. 2 (pp. 65-81). Week 12: Jun 28Hilbert’s Geometry, II
Reading: David Hilbert’s Foundations of Geometry Chap. 1 (pp. 7-16). Supplementary Reading: Hartthorne, R., Geometry: Euclid and Beyond Chap. 2 (pp. 81-96). Week 13: Jul 5Non-Euclidean Geometry, I
Reading: Nicholas Lobachevski’s Theory of Parallels pp. 11-16 (up to section 19). Supplementary Reading: Hartthorne, R., Geometry: Euclid and Beyond Chap. 7 (pp. 373-387). Week 14: Jul 12Non-Euclidean Geometry, II
Reading: Nicholas Lobachevski’s Theory of Parallels pp. 16-21 (from section 19). Supplementary Reading: Hartthorne, R., Geometry: Euclid and Beyond Chap. 7 (pp. 373-387). Week 15: Jul 19Presentations and discussions
No Reading.