Trent University
Mathematics 3820H
Mathematics from medieval to modern times

MATH 3820H is a survey of the history of mathematics from medieval times onwards, with a focus on the development of arithmetic and algebra and the evolution of proofs and abstraction.

Prerequisite: Mathematics 1120H.
Recommended: Mathematics 2200H or 2350H.

Take-home Final Examination - due Friday, 18 December, 2020.

Stefan's Exam Period Office Hours
Thursday, 10 December, 20:00-20:50
Friday, 11 December, 15:00-15:50
Monday-Thursday, 14-17 December, 15:00-15:50 & 20:00-20:50
Friday, 18 December, 15:00-15:50
(All on Zoom - check your email & the Blackboard announcement for the invitations.)

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

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.

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.

Fall 2014

• Course information:
  • Course Outline
  • Readings & Schedule
  • Project
• Assignment # 1, 2, 3, 4, 5, 6
• Take-Home Final Examination

Fall 2012

• Course information:
  • Course Outline
  • Project
  • Readings & Schedule
• Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
  Reading for Assignment 11
• Take-Home Final Examination

Some Resources

There is fair bit of material available online about the history of mathematics and related areas; a brief selection follows:

• Mathematics - History and Overview at the arXiv.org preprint archive.
• The Euler Archive
• Gauss' Works
• Historia Mathematica, a journal on the history of mathematics. Published by Elsevier. Available at Bata Library, in print and/or electronic form, depending on the issue.
• History/Biography at The Math Forum
• History of Mathematics at Math Archives (University of Tennessee - Knoxville)
• History of Mathematics at Mathematics Resources on the Internet by Bruno Kevius
• History of mathematics article at Wikipedia
• The History of Mathematics, maintained by David R. Wilkins
• MacTutor history of mathematics archives
• The Newton Project
• The Newton Project - Canada
• Wilbour Hall, an archive of "public domain materials that are essential for the study of ancient and early modern mathematics and mathematical astronomy," maintained by Joseph Leichter.

Department of Mathematics

Trent University