Sidoli, Nathan Camillo

Spring, 2024

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 part of Euclid’s

Elements of Geometry, some of Lobachevski’sTheory of Parallels, and some of Hilbert’sFoundations of Geometry. 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.

## Classroom Etiquette

Please follow basic rules of decorum – do not sleep, eat, or carry on individual conversations in class. Finally, DO NOT use mobile phones, smart phones, or laptops in class. (Unfortunately, a large percentage of students use their laptops to do unrelated things during class, and this distracts both them and everyone behind them.)

## Topics, Readings and Assignments

Week 2: Apr 22Introduction to Greek mathematics

Readings: Asper, M., The two cultures of mathematics in ancient Greece. Week 3: Apr 29Euclid’s

Elements, IReading: TBA. Supplementary material: For Euclidean constructions see, Euclid: The Game! (It sometimes takes a long time to load.) Holiday: May 6 (子供の日)No Class

No Reading. Week 4: May 13Euclid’s

Elements, IIReading: To be announced (TBA). Week 5: May 20Euclid’s

Elements, IIIReading: TBA. Conference Trip: May 27No Class

No Reading Week 6: Jun 3Euclid’s

Elements, IVReading: TBA. Week 7: Jun 10Euclid’s

Elements, VReading: TBA. Week 8: Jun 17Euclid’s

Elements, VIReading: TBA. Week 9: Jun 24Euclid’s

Elements, VIIReading: TBA. Week 10: Jun 26 (Make-up class, different day)Non-Euclidean Geometry, I

Reading: Nicholas Lobachevski’s Theory of Parallelspp. 11-16 (up to section 19).Supplementary Reading: Hartshorne, R., Geometry: Euclid and BeyondChap. 7) (pp. 373-387).Supplementary material: See Tibor Marcinek’ss Geogebra website of the Poincaré Disk for a model of the hyperbolic plane. Week 11: Jul 1Non-Euclidean Geometry, II

Reading: Nicholas Lobachevski’s Theory of Parallelspp. 16-21 (from section 19).Supplementary Reading: Hartshorne, R., Geometry: Euclid and BeyondChap. 7 (pp. 373-387).Week 12: Jul 8Hilbert’s Geometry, I

Reading: David Hilbert’s Foundations of GeometryChap. 1 (pp. 1-7).Supplementary Reading: Hartshorne, R., Geometry: Euclid and BeyondChap. 2 (pp. 65-81).Week 13: Jul 15Hilbert’s Geometry, II

Reading: David Hilbert’s Foundations of GeometryChap. 1 (pp. 7-15, 25-26).Supplementary Reading: Hartshorne, R., Geometry: Euclid and BeyondChap. 2 (pp. 81-96); Chap. 7 (pp. 295-300).Week 14: Jul 22Presentations and discussions

No Reading.