MATH 110-2
Algebra Through History

Syllabus, day-by-day schedule

• Course syllabus (.pdf file)
• Detailed course schedule, revised 11/14

Information and announcements

• Solutions for the midterm exam.
• Review sheet for the final exam. The exam will be given at 11:00am on Wednesday, December 18 in our usual classroom, SW 321
• Exam Week Office Hours
  • Monday, 12/16 -- 10am - 12noon
  • Tuesday, 12/17 -- 1pm - 3pm
  • Wednesday, 12/18 -- 8am - 10am
  • Thursday, 12/19 -- 2pm - 4pm
• Solutions for the final exam.

Course materials

• Why is algebra hard? (class on 9/4)
• 2015 PISA results -- comparative achievement in reading, mathematics, science in different countries around the world
• Is the mathematics curriculum used in schools in Finland better?
• The Ishango bone, class on 9/6
• The Egyptian number symbols, class on 9/6
• Historical background on Old Babylonian mathematics and a representative table used in calculations.
• Materials on YBC 6967 -- a drawing of the actual cuneiform tablet with the numbers circled; English translation, and commentary by Eleanor Robson, from The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Victor J. Katz, ed.
• Euclid and the Elements, classes on 9/23 and 9/25
• Quotes about Euclid, class on 9/23
• Euclid, Elements, Book II, Propositions 1-5, class on 9/25
• Greek thinking about commensurability, magnitude, number, class on 9/27
• Some highlights of post-Euclid Greek mathematics, class on 9/30
• The Greek alphabetic number system, from mathsisgoodforyou.com
• Materials on Diophantos of Alexandria and the Arithmetica, classes on 10/2, 4, and 7
• Fermat's note to Diophantos II, 8, class on 10/9
• Andrew Wiles, class on 10/9
• Greek mathematics after Diophantos, class on 10/11
• Scene from Agora, class on 10/11
• Overview on mathematics in the medieval Islamic world, class on 10/21
• The Hisab al-jabr w'al-muqabala of Muhammad ibn Musa al-Khwarizmi, translated into Latin by Robert of Chester (12th century CE) -- note his version of the title(!), with English re-translation on facing pages (from www.wilbourhall.org), classes on 10/23 and 10/28
• Two case studies on Islamic mathematics, class on 11/1
• How Islamic mathematics was transmitted back to Europe, class on 11/4
• After Fibonacci, class on 11/6
• A "mathematical soap opera" -- Tartaglia, Cardano, Ferrari and the solution of cubic and quartic equations, contemporary testimony on Tartaglia's feud with Cardano, class on 11/8
• The Ottoman Empire
• Viète's Analytical Art, classes 11/15,18,20
• Original edition of Viète's Analytical Art
• Pappus of Alexandria (ca. 320 CE) on analysis and synthesis in geometry, class on 11/22 or 25.
• Facts about circles from elementary geometry, for class on 11/25.
• Book I of Descartes' La Géométrie, for class on 12/4, 12/6, 12/9
• What is algebra? What is algebra today?, class on 12/11.

Assignments

• First small group discussion, due Monday, September 16, no later than 5:00pm
• Individual problem set 1, due Friday, September 20, no later than 5:00pm
• Individual problem set 2, due Monday, October 7, no later than 5:00pm
• Information on Research Papers due at the end of the semester. Note deadline of November 15 for the proposal about the topic you want to research.
• Individual problem set 3, due Wednesday, November 6, no later than 5:00pm
• Individual problem set 4, due Friday, November 22, no later than 5:00pm
• Group assignments for Discussion 3, December 6 and 9. (Note: This is the final mathematical assignment for the semester; you should have enough time to complete it working entirely in class).

Downloading Information

Last modified: December 19, 2019