MAT336: History of Mathematics
Lectures 1 and 3 -Fall 2025
| Class | Topic | Assignments | Presentations |
|---|---|---|---|
| Aug 25 Lect 1 |
Math History Introduction – Info about the course | ||
| Aug 27 Lect 2 |
Reliable Sources – Counting Foundations | HW 0 and the topic choice form | Aug 28: Topic distribution will be posted. |
| Sep 1 | Labor Day – Monday, Sept. 1 | ||
| Sep 3 Lect 3 |
Cultural Counting Methods / Number Systems | HW 1: Sources and Intro. Reading: On the origin of numbers |
|
| Sep 8 Lect 4 |
Number Systems | ||
| Sep 10 Lect 5 |
Mathematics in Ancient Egypt | HW 2: Number Systems and Sources (including minimal bibliography). Reading: There notes until Question 2 in Section 1.1.2. |
|
| Sep 15 Lect 6 |
Mathematics in Ancient Egypt | ||
| Sep 17 Lect 7 |
Ancient Egypt / Mesopotamia | Quiz 1: Number systems. Reading: This text from the beginning to Section 1.5 Plimpton 322. | |
| Sep 22 Lect 8 |
Mathematics in Ancient Mesopotamia | ||
| Sep 24 Lect 9 |
Mathematics in Ancient Mesopotamia | Outline and Draft oft Slides. | |
| Sep 29 Lect 10 |
Inca and Mayan Mathematics | ||
| Oct 1 Lect 11 |
The earliest Hellenic mathematics | Proposal Creative Project HW 3 Egypt and Mesopotamia |
Unit Fractions & Rhind Papyrus |
| Oct 6 Lect 12 |
The earliest Hellenic mathematics | Thales & Shadow of the Pyramid | |
| Oct 8 Lect 13 |
The earliest Hellenic mathematics | Abstract and Outline of Paper Quiz 2: Egypt |
|
| Oct 13 | Fall Break (Oct 13–14) | ||
| Oct 15 Lect 14 |
Euclid’s Elements – Number Theory | Creative Project. Quiz 3: Mesopotamia |
The Two Earths of Eratosthenes |
| Oct 20 Lect 15 |
Euclid’s Elements – Axiom Systems |
Regular Polygons in Ancient Mathematics
Art and Mathematics: The Platonic Solids |
|
| Oct 22 Lect 16 |
Euclid’s Elements – Non-Euclidean | Baby Draft Paper (500 words) |
The Parallel Postulate and its Role in Geometry
The Story of the Binomial Theorem |
| Oct 27 Lect 17 |
Archimedes |
Ptolemy’s Theorem and Ancient Astronomy
Gauss and the Discovery of Ceres |
|
| Oct 29 Lect 18 |
Apollonius, Eratosthenes, Ptolemy, Diophantus | Draft Paper (750 words); HW 4: Euclid’s Elements |
Diophantus of Alexandria
Historical Development of Complex Numbers |
| Nov 3 Lect 19 |
Chinese Mathematics |
Curves Before Equations (Ancient through Early 17th Century)
Curves by Equations (17th Century on) |
|
| Nov 5 Lect 20 |
Chinese Mathematics (cont.) | Draft Paper (1000 words); Quiz 4: Euclid’s Elements. |
Right-Angled Triangles in Ancient China |
| Nov 10 Lect 21 |
Indian Mathematics |
Ancient Indian Square Roots
Ancient Chinese Square Root Algorithms |
|
| Nov 12 Lect 22 |
Indian / Islamic Mathematics | Draft Paper (1500 words) |
Early History of the Isoperimetric Problem
Steiner and the isoperimetric problem |
| Nov 17 Lect 23 |
Islamic Mathematics |
Ibn al‑Haytham and Early Algebra
Omar Khayyam: Geometric Algebra and Cubic Equations |
|
| Nov 19 Lect 24 |
Renaissance Mathematics | Paper (1500 words) |
Pascal and the Invention of Probability Theory
Descartes and the Geometrization of Algebra |
| Nov 24 Lect 25 |
Renaissance Math (cont.) |
The Invention of Analytic Geometry
Kovalevskaya’s Sine Anecdote |
|
| Nov 26 | Thanksgiving (Nov 26–28) | ||
| Dec 1 Lect 26 |
Calculus Origins |
The Origins of the Rule of False Position: From Ahmes to al-Khwarizmi
The rule of false position from Fibonacci to Cardano. |
|
| Dec 3 Lect 27 |
Selected Topics | HW 5: Review and reflection |
Königsberg Bridges and the Birth of Graph Theory
The Story of Fermat’s Last Theorem |
| Dec 8 Lect 28 |
Review / Last Day | Quiz 5: Review and reflection |
Ancient and Early Methods for Tangents (Sections 1 to 3)
Tangents and the Analytical Revolution (Sections 4 to 5) |