Announcements

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’s Theory of Parallels, and some of Hilbert’s Foundations 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 1: Apr 15

General Introduction

Readings: Sidoli, N., Mathematics education.

Week 2: Apr 22

Introduction to Greek mathematics

Readings: Asper, M., The two cultures of mathematics in ancient Greece.

Week 3: Apr 29

Euclid’s Elements, I

Reading: 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 13

Euclid’s Elements, II

Reading: To be announced (TBA).

Week 5: May 20

Euclid’s Elements, III

Reading: TBA.

Conference Trip: May 27

No Class

No Reading

Week 6: Jun 3

Euclid’s Elements, IV

Reading: TBA.

Week 7: Jun 10

Euclid’s Elements, V

Reading: TBA.

Week 8: Jun 17

Euclid’s Elements, VI

Reading: TBA.

Week 9: Jun 24

Euclid’s Elements, VII

Reading: TBA.

Week 10: Jun 26 (Make-up class, different day)

Non-Euclidean Geometry, I

Reading: Nicholas Lobachevski’s Theory of Parallels pp. 11-16 (up to section 19).

Supplementary Reading: Hartshorne, R., Geometry: Euclid and Beyond Chap. 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 1

Non-Euclidean Geometry, II

Reading: Nicholas Lobachevski’s Theory of Parallels pp. 16-21 (from section 19).

Supplementary Reading: Hartshorne, R., Geometry: Euclid and Beyond Chap. 7 (pp. 373-387).

Week 12: Jul 8

Hilbert’s Geometry, I

Reading: David Hilbert’s Foundations of Geometry Chap. 1 (pp. 1-7).

Supplementary Reading: Hartshorne, R., Geometry: Euclid and Beyond Chap. 2 (pp. 65-81).

Week 13: Jul 15

Hilbert’s Geometry, II

Reading: David Hilbert’s Foundations of Geometry Chap. 1 (pp. 7-15, 25-26).

Supplementary Reading: Hartshorne, R., Geometry: Euclid and Beyond Chap. 2 (pp. 81-96); Chap. 7 (pp. 295-300).

Week 14: Jul 22

Presentations and discussions

No Reading.