A Document-based History of Mathematics Course (Implementation in Spring 2006 Abbreviated syllabus for 1-credit Honors College course, Spring 2008 )

MAT 336 Syllabus

• B: The History of Mathematics, an introduction by David Burton (6th Ed.,WCB McGraw-Hill 2007)
  Please note (1/23/06) the sections referred to below are from the 4th edition; they will be updated soon.
• D: William Dunham, Journey through Genius (Wiley 1990, Penguin 1991)

• S: Dirk Struik, A Source Book in Mathematics, 1200-1800 (Harvard, 1969)

  Week 1 Primitive counting; Positional and non-positional number systems. Mayan calendars. Babylonian number recording. (B: 1.1, 1.3, 2.5)
  document VAT 7858 (Berlin Museum; Christian Siebeneicher's website at Bielefeld)
  document NBC 7344 (Yale Babylonian Collection; Duncan Melville's website at St. Lawrence University)
  document YBC 7289 (Yale Babylonian Collection; Casselman's website at UBC)
  document YBC 6967 (Yale Babylonian Collection; Eleanor Robson's translation and analysis).

  Week 2 The decoding of Plimpton 322. (B: 2.6)
  document Plimpton 322 (Columbia Rare Book Collection; David Joyce's website at Clark University
  Bill Casselman's website at the University of British Columbia
  Eleanor Robson's analysis; Numerical evidence for Robson's analysis; Ernest Moyer's attack on Robson).
  

  Week 3 Egyptian number recording and Arithmetic. (B: 1.2, 2.1, 2.2, 2.3)
  document The Rhind Papyrus (St Andrew's website)

  Week 4 Thales and Pythagoras; Euclid. (B: 3.1, 3.3, 4.1, 4.2)
  document Euclid's calculation of the volume of a cone. (Euclid's Elements website, XII, 10; see diagram of proof.)
  

  Week 5 Euclid and Archimedes. (B: 4.3, 4.5)
  document Archimedes "On moments" palimpsest

  Week 6 Arab, Indian and Chinese mathematics during the "dark ages." (B: 5.5)
  document Table of sines from the Aryabhatiya (Narasimha in Nature Dec 20/27 2001)
  document Al-Khwarizmi on quadratic equations (S)
  

  Week 7 Fibonacci; Cardano and Tartaglia. (B: 6.2, 7.2, 7.3)
  document Word problems from the 1478 "Treviso Arithmetic" (B)
  document Cardano's solution of the cubic (D)

  Week 8 Galileo and Descartes. (B: 8.1, 8.2)
  document Galileo on uniformly accelerated motion (S)
  document Descartes on the theory of equations (S)
  

  Week 9 Newton and Leibnitz. (B: 8.3, 8.4)
  document Leibnitz on the Fundamental Theorem of Calculus (S)

  Week 10 Probability: Pascal to Laplace. (B: 9.1, 9.2)
  document Pascal on "Pascal's triangle" (S)
  

  Week 11 Euler and the Bernoullis. (B: 10.2)
  document Euler's calculation of the sum of the 1/n² series (D)

  Week 12 Gauss, Bolyai and Lobachevsky (B: 10.3, 11.1, 11.2)
  document Gauss' proof of the Fundamental Theorem of Algebra (S)

  Week 13The beginning of Modern Algebra: Hamilton, Cayley and Sylvester. (B: 11.4)
  document Cayley on the definition of Group
  document Cayley's "proof" of the Cayley-Hamilton Theorem

  Week 14 Nineteenth-Century Analysis: Cauchy, Fourier, Cantor. (B: 12.2)
  document (see Notes on spherical trigonometry and navigation).
  document "On an elementary question in set theory" (1890-91)
  document Cantor on the cardinality of a power set: |P(S)|>|S| (D)

  ---

  Anthony Phillips
  Math Dept SUNY Stony Brook
  tony at math dot sunysb dot edu
  November 23 2008