Stefan's History of Mathematics Archive Page

Trent University
Stefan's History of Mathematics Archive Page

Once there was Mathematics-Science 380 - History of Mathematics, a full-year course offered every other year. This was eventually split up into two half-courses, Mathematics-Science 381H - Ancient and classical mathematics and Mathematics-Science 382H - Mathematics from medieval to modern times, offered in alternate years, which were soon renumbered as Mathematics 3810H and 3820H, respectively. These were eventualy replaced by Mathematics 3830H - A Survey of the History of Mathematics, intended to be offered every other year.

MATH 3830H, Winter 2025

MATH 3830H Course Outline
Textbook: A Short Account of the History of Mathematics (4th Edition), by W.W. Rouse Ball, from Project Gutenberg. [Local copy.]
The Greek Alphabet
Herodotus on Egyptian geometry
Euclid's Axioms and Proposition I-1
Archimedes' Cattle Problem
The Algebra of Mohammed Ben Musa [i.e. al-Kwarizmi]
Project
Assignment # 1, 2, 3, π, τ, 4, 5, 6
Take-Home Final Examination

MATH 3810H, Winter 2022

MATH 3810H Course Outline
Supplementary text: A Short Account of the History of Mathematics (4th Edition), by W.W. Rouse Ball, from Project Gutenberg. [Local copy.]
The Greek Alphabet
Project
Assignment # 1, 2, 3, π, 4, 5, 6
Readings for Assignment # 2:
Words and Pictures: New Light on Plimpton 322 by Eleanor Robson
Plimpton 322 is Babylonian exact sexagesimal trigonometry, by Daniel F. Mansfield and N.J. Wildberger
Reading for Assignment #3:
Meno, by Plato, translated by Cathal Woods.
Reading for Assignment #5:
Archimedes, the Sand Reckoner by Ilan Vardi, including his translation of the Greek text
Take-Home Final Examination
Lectures and Notes (webm and pdf formats)
- (Pre-)History of mathematics - video and notes
- Ancient Egypt and the Egyptian Number System - video and notes
- Egyptian Fractions, Division, and Some Algebra - video and notes
- Ancient Egyptian Geometry - video and notes
- Ancient Mesopotamia and Their Number System - video and notes
- Mesopotamian Arithmetic and Algebra - video and notes
- Mesopotamian Geometry and Algebra - video and notes
- Beginning of Greek Mathematics - Thales - video
- Pythagoras - video
- Zeno of Elea and Hippocrates of Chios - failed to record
- Eudoxus of Cnidus - video [audio failed]
  Handout: Magnitudes and Proportions
- Lunes, Three Unsolved Problems, and Archytas of Tarentum - video
- Mathematics and Philosophy: Plato and Aristotle - video
- Euclid - video
  Handout: Excerpt from Book I of the Elements
- Euclid II - video
  Handout: Proposition I-47 - The Pythagorean Theorem
  Handout: Excerpt from Book VII of the Elements
- Euclid III - video
  Handout: Excerpt from Book VII of the Elements
  Handout: Proposition IX-20 - The Infinitude of Prime Numbers
- Euclid IV - video
  Handout: Proposition XII-2 - Areas of Circles are Proportional to the Squares of their Diameters
  Handout: Proposition XIII-12 - Area of an Equilateral Triangle Inscribed in a Circle
- Archimedes - video
  Handout: Archimedes in Plutarch's Life of Marcellus [excerpt]
- Archimedes II - video
  Handout: The Cattle Problem
  Handout: Quadrature of the Parabola
- Archimedes III - video
  Handout: The Method (a.k.a. Geometrical Solutions Derived From Mechanics)
- Ancient Greek and Hellenistic Astronomy - video
- Claudius Ptolemy - video
- Apollonius of Perga - video
- Eratosthenes of Cyrene - video
- Heron and Menelaus, both of Alexandria - video
- Diophantus - video
- Pappus of Alexandria - video
- The End Times - video

MATH 3820H, Fall 2020

MATH 3820H Course Outline & Schedule
The textbook: A Short Account of the History of Mathematics (4th Edition), by W. W. Rouse Ball, 1908. A version (pdf and T_EX) is available online (for free!) from Project Gutenberg at: http://www.gutenberg.org/etext/31246; you can also find a pdf copy locally. [From the Project Gutenberg License: This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org.]
Readings (other than the textbook):
- Week 1: Aryabhatiya [pp. 35-39]
- Week 2: The Algebra of Mohammed ben Musa (i.e. al-Kwarizmi) [pp. 1-21]
- Week 3: A History of Mathematical Notations, Vol. I, by Florian Cajori. [pp. 45-57 & 381-383]
- Week 4: Jerome Cardan: The Life of Girolamo Cardano, of Milan, Physician, Vol.I, by Henry Morley. [pp. 207-276]
- Week 5: Memoirs of John Napier of Merchiston, by Mark Napier. [pp. 435-507]
- Week 6: Dialogues Concerning Two New Sciences, by Galileo Galilei. [pp. 30-38]
- Week 7: Essay on Conics, by Blaise Pascal, trans. by Frances Clarke. [All five pages.]
- Week 8: An Account of the Book Entituled Commercium Epistolicum Collinii et Alliorum, de Analysi Promota, by Isaac Newton [writing anonymously], edited by D.R. Wilkins. [All thirty one pages.]
- Week 9: A Treatise of Fluxions, by Colin MacLaurin. [pp. 51-68]
  Supplementary: Leonhard Euler: His Life, the Man, and His Works, by Walter Gautschi
- Week 10: Elements of Algebra, Vol. I, by Leonhard Euler. [pp. 54-70 & 144-157]
- Week 11: A Contribution to the Mathematical Theory of Big Game Hunting, by H. Petard. [All of it.]
Lectures and notes:
- Indian history and Aryabhata - video, notes
- Bhaskara (I) and Brahmagupta - video, notes
- Early Islamic history, al-Kwarizmi, and ibn Qurra - video, notes
- Some of Thabit ibn Qurra's work in geometry - video, notes
- Yusuf al-Mutaman ibn Hud - video, notes
- Omar al-Khayyami - video, notes
- Two examples of Islamic mathematics - video, notes
- Math in medieval Europe - video, notes
- Fibonacci - video, notes
- Late medieval mathematics - video, notes
- The Renaissance - video, notes
- The solution of the cubic and quartic equations - video, notes
- The solution of the cubic and quartic equations II - video, notes
- Notation and some math elsewhere in Europe - video, notes
- Logarithms - video, notes
- The Astronomers - video, notes
- The Astronomers II - video, notes
- Cavalieri - video, notes
- The French Connection - video, notes
- The French Connection II - video, notes
- John Wallis - video, notes
- The Isaacs - Barrow and Newton - video, notes
- Gottfried Wilhelm Leibniz - video, notes
- Three Bernoullis - video, notes
- Three non-Bernoullis - video, notes
- Leonhard Euler - video, notes
  Supplementary: Leonhard Euler: His Life, the Man, and His Works, by Walter Gautschi
- Maria Agnesi - video, notes
- Joseph-Louis Lagrange - video, notes
- Laplace and Legendre - video, notes
- Carl Friedrich Gauss - video, notes
- The Rigourization of Calculus - video, notes
Project
Assignment # 1, 2, 3, π, 4, 5, 6
Take-home Final Examination

MATH 3810H, Winter 2020

MATH 3810H Course Outline
Project
Assignment # 1, 2, 3, 4, 5, 6
Take-Home Final Examination
Supplementary text: A Short Account of the History of Mathematics (4th Edition), by W.W. Rouse Ball, from Project Gutenberg. [Local copy.]
Instead-of-lecture notes:
Additional readings:
- The architect Kha's protractor, by Amelia Carolina Sparavigna.
- Words and Pictures: New Light on Plimpton 322, by Eleanor Robson.
- Plimpton 322 is Babylonian exact sexagesimal trigonometry, by D.F. Mansfield and N.J. Wildberger.
- Meno, by Plato, translated by Cathal Woods.
- Excerpts from Euclid's Elements:
  Taken from Euclid's Elements in Greek, with an English translation by Richard Fitzpatrick.
- Archimedes' Cattle Problem
- Geometrical Solutions Derived from Mechanics [also known as The Method], by Archimedes, trans. by J.L. Heiberg and L.G. Robinson. From Project Gutenberg. [Local copy.]
- The Sand Reckoner [PostScript] by Archimedes, translated with commentary by Ilan Vardi. [Local copy (pdf).]
The Greek Alphabet

MATH 3820H, Winter 2019

MATH 3820H Course Outline & Schedule
The textbook: A Short Account of the History of Mathematics (4th Edition), by W. W. Rouse Ball, 1908. A version (pdf and T_EX) is available online (for free!) from Project Gutenberg at: http://www.gutenberg.org/etext/31246; you can also find it (pdf) locally here. [From the Project Gutenberg License: This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org.]
Project
Assignment # 1, φ, 2, 3, π, 4, 5, 6
Take-Home Final Examination
Works to read from (other than the textbook):
- Week 1: Aryabhatiya
- Weeks 2 & 3: The Algebra of Mohammed ben Musa (i.e. al-Kwarizmi)
- Week 4: Jerome Cardan: The Life of Girolamo Cardano, of Milan, Physician, Vol.I, by Henry Morley.
- Week 5: Memoirs of John Napier of Merchiston, by Mark Napier.
- Weeks 6 & 7: Dialogues Concerning Two New Sciences, by Galileo Galilei,
  and Essay on Conics, by Blaise Pascal [trans. by Frances Clarke].
- Weeks 8 & 9: An Account of the Book Entituled Commercium Epistolicum Collinii et Alliorum, de Analysi Promota, by Isaac Newton [writing anonymously], edited by D.R. Wilkins.
- Week 10: A Treatise of Fluxions, Vol. I, by Colin MacLaurin.
- Weeks 11 & 12: Elements of Algebra, Vol. I, by Leonhard Euler.
- Exam: The Hindu-Arabic Numerals, by L.C. Karpinski and D.E. Smith.

MATH 3810H, Fall 2017

MATH 3820H, Fall 2016

MATH 3820H Course Outline & Schedule
The textbook: A Short Account of the History of Mathematics (4th Edition), by W. W. Rouse Ball, 1908. A version (pdf and T_EX) is available online (for free!) from Project Gutenberg at: http://www.gutenberg.org/etext/31246; you can also find it (pdf) locally here. [From the Project Gutenberg License: This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org.]
Project
Assignment # 1, 2, 3, π, 4, 5, 6
Take-Home Final Examination
- Reading for question 3: Bija Ganita by Bhaskara II.
- Initial reading for question 5: The Hindu-Arabic Numerals by L.C. Karpinski and D.E. Smith, at Project Gutenberg.