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 Others## Course 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’sFoundations of Geometry, and some of Lobachevski’sTheory 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, IReading: 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, IIReading: TBA. Week 6: May 17Euclid’s

Elements, IIIReading: TBA. Week 7: May 24Euclid’s

Elements, IVReading: TBA. Week 8: May 31Euclid’s

Elements, VReading: TBA. Week 9: Jun 7Euclid’s

Elements, VIReading: TBA. Week 10: Jun 14Euclid’s

Elements, VIIReading: TBA. Week 11: Jun 21Hilbert’s Geometry, I

Reading: David Hilbert’s Foundations of GeometryChap. 1 (pp. 1-7).Supplementary Reading: Hartthorne, R., Geometry: Euclid and BeyondChap. 2 (pp. 65-81).Week 12: Jun 28Hilbert’s Geometry, II

Reading: David Hilbert’s Foundations of GeometryChap. 1 (pp. 7-16).Supplementary Reading: Hartthorne, R., Geometry: Euclid and BeyondChap. 2 (pp. 81-96).Week 13: Jul 5Non-Euclidean Geometry, I

Reading: Nicholas Lobachevski’s Theory of Parallelspp. 11-16 (up to section 19).Supplementary Reading: Hartthorne, R., Geometry: Euclid and BeyondChap. 7 (pp. 373-387).Week 14: Jul 12Non-Euclidean Geometry, II

Reading: Nicholas Lobachevski’s Theory of Parallelspp. 16-21 (from section 19).Supplementary Reading: Hartthorne, R., Geometry: Euclid and BeyondChap. 7 (pp. 373-387).Week 15: Jul 19Presentations and discussions

No Reading.