Sidoli, Nathan Camillo
Spring, 2021
Office hours: Thursday, 4th and 5th

Office: 11-1409
03-5286-1738
[email protected]

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 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 5

    General Introduction

  • No reading.
  • Week 2: Apr 12

    Greek mathematics

  • Reading: Asper, M., The two cultures of mathematics in ancient Greece.
  • Week 3: Apr 19

    Mathematics education in the Greco-Roman world

  • Reading: Sidoli, N., Mathematics education.
  • Week 4: Apr 26

    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 3

    No Class

  • No Reading.
  • Week 5: May 10

    Euclid’s Elements, II

  • Reading: TBA.
  • Week 6: May 17

    Euclid’s Elements, III

  • Reading: TBA.
  • Week 7: May 24

    Euclid’s Elements, IV

  • Reading: TBA.
  • Week 8: May 31

    Euclid’s Elements, V

  • Reading: TBA.
  • Week 9: Jun 7

    Euclid’s Elements, VI

  • Reading: TBA.
  • Week 10: Jun 14

    Euclid’s Elements, VII

  • Reading: TBA.
  • Week 11: Jun 21

    Hilbert’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 28

    Hilbert’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 5

    Non-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 12

    Non-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 19

    Presentations and discussions

  • No Reading.