The experience was extremely rewarding, and I highly recommend it to anyone who has the opportunity. Feel free to contact me for more information or any of the materials I used. The following list of readings conveys a sense of what we discussed.

September 1

Plato, Meno

Euclid, The Elements, Book I, through Proposition 3

September 6

Euclid, The Elements, Book I, through Proposition 10

Excerpts from Plato, The Republic

September 8

Excerpts from the Republic

Continue reading Book I of the Elements

September 13

Finish reading Book I of the Elements.

September 15

Lear, Jonathan, "Aristotle's Philosophy of Mathematics"

September 20

Euclid's "geometric algebra" in Book II.

Eudoxus' theory of Propositions in Book V.

(Various secondary sources as well.)

September 27

Read the definitions in Book VII of Euclid, and excerpts from VII and IX (number theory).

October 4

Read the section on Al-Khwarizmi in Struik's sourcebook.

Read the section on Cardano from the Laubenbacher and Pengelley book.

Read the introduction to the section on Viète in the Struik sourcebook.

October 6

Start reading Descartes' "Rules for the direction of the mind."

October 11

Henk Bos on Descartes' rules

Descartes' Rules 13-21.

October 13

Excerpts from Descartes' Geometry.

October 18

Excerpt from Galileo's Two New Sciences, third day

October 20

Excerpts from Descartes' Geometry (from Struik)

Bos, on Descartes (excerpt from Redefining Geometrical Exactness)

October 25

Continue reading Descartes.

October 27

Continue reading Descartes.

November 1

Start reading Newton's Principia: the Central Argument:

Read the Forward and Preliminaries.

Read Newton's Preface to the Reader, on page 3.

Skim the definitions from pages 5-27.

November 3

Continue reading the guide to the Principia:

Read the laws of motion on pages 29 to 30, and the first two corollaries on 31 and 32.

Start reading Book I, from pages 47 to 71.

November 8

Continue reading through the Principia. In particular:

Read Lemma 8 on page 91.

Read Lemma 9 on page 94.

Read Lemma 10 on page 99.

Read Lemma 11 on page 108.

Read the Scholium on pages 119 to 121, and notice that Spencer was right and I was wrong in the last class.

November 10

Start reading Section 2 on page 123, and see if you can understand Propositions 1-4.

November 15

Read Proposition 6 on page 178 of Densmore, and Corollary 1 on page 182.

(See also the excerpt from the book by Guicciardini.)

November 17

This is the big day! We will work our way through Proposition 11 on page 227 of Densmore.

November 22

Read the Leibniz excerpt from Struik.

November 29

Dedekind, "Continuity and irrational numbers."

December 1

Read Dedekind's "Letter to Keferstein"

Following the sketch there, read the following excerpts from "The Nature and Meaning of Numbers" (also in the Essays on Numbers):

Preface

Sections 1-3, on "systems," or sets of objects

The definition of a "chain" in Section 37

The "proof" that there exists an infinite system, in Section 66

The notion of a "simply infinite system" in Sections 71 and 73

December 6

Read the first few sections of Cantor's "Theory of transfinite numbers."

December 8

Read as much of Chapter I of Hilbert's Foundations of Geometry as you can. Focus on:

The introduction, and the very first definition.

Theorems 3 and 5.

Theorem 8.

Axiom III, 1.