MAT 336 History of Mathematics Fall 2006

Index Course Description Syllabus Homework Schedule of Presentations

MAT 336 Syllabus

• B: The History of Mathematics, an introduction by David Burton (6th Ed.,WCB McGraw-Hill 2007)
• D: William Dunham, Journey through Genius (Wiley 1990, Penguin 1991)

• S: Dirk Struik, A Source Book in Mathematics, 1200-1800 (Harvard, 1969) -on reserve in Math-Physics Library.

  Week 1 (Sept 6) Primitive counting; Positional and non-positional number systems. Mayan calendars. Babylonian number recording. (B: 1.1, 1.3) document YBC 7289 (Yale Babylonian Collection; Casselman's website at UBC)

  Week 2 (Sept 11) Babylonian Multiplication Tables; the decoding of Plimpton 322. (B: 2.5, 2.6)
  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 Plimpton 322 (Columbia Rare Book Collection; David Joyce's website at Clark University, University of Swansea website)
  Thursday: Sign up for in-class presentation topics.
  Quiz on base-60 and cuneiform numbers.

  Week 3 (Sept 18) Egyptian number recording and Arithmetic. (B: 1.2, 2.1, 2.2, 2.3)
  document The Rhind Papyrus (St Andrew's website)
  Quiz

  Week 4 (Sept 25) Thales and Pythagoras; Eucl id. (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.)
  Student presentations begin.
  Fri. 9/29: Deadline for email of Paper 1 topic.
  Topic must be approved for paper to be accepted.
  Missed deadline: paper gets automatic one-third-grade deduction (e.g. from B- to C+).
  Quiz

  Week 5 (Oct 2) Euclid and Archimedes. (B: 4.3, 4.5)
  document Archimedes "On moments" palimpsest.
  Student presentations continue.
  Quiz

  Week 6 (Oct 9) Arab, Indian and Chinese mathematics during the "dark ages." (B: 5,3, 5.5)
  document Table of sines from the Aryabhatiya (Narasimha in Nature Dec 20/27 2001)
  document Al-Khwarizmi on quadratic equations (S)
  Fri. 10/13 Deadline for email of detailed outline of Paper 1. Detailed outline must include at least one non-text, non-web reference.
  Missed deadline: paper gets automatic one-third-grade deduction.
  Student presentations continue.
  Quiz

  Week 7 (Oct 16) 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)
  Student presentations continue.
  Quiz

  Week 8 (Oct 23) Galileo and Descartes. (B: 8.1, 8.2)
  document Descartes on the theory of equations (S)
  document Galileo on uniformly accelerated motion (S)
  Student presentations continue.
  Quiz

  Week 9 (Oct 30) Newton and Leibnitz. (B: 8.3, 8.4)
  document Leibnitz on the Fundamental Theorem of Calculus (S)
  NOTE CHANGE! Thursday November 2: Paper 1 due.
  Late submission: paper gets automatic one-third-grade deduction.
  Student presentations continue.
  Quiz

  Week 10 (Nov 6) Probability: Pascal to Laplace. (B: 9.1, 9.2, 9.3)
  document Pascal on "Pascal's triangle" (S)
  Fri. 11/10 Deadline for email of 3-sentence description of Paper 2 topic.
  Missed deadline: paper gets automatic one-third-grade deduction.
  Student presentations continue.
  Quiz

  Week 11 (Nov 13) Number theory from Fermat to Euler and Gauss. (B: 10.2, 10.3)
  document Euler's calculation of the sum of the 1/n² series (D)
  document Gauss' proof of the Fundamental Theorem of Algebra (S)
  Student presentations continue.
  Quiz

  Week 12 (Nov 20) Cauchy and Fourier. (B: 11.3)
  document (see Notes on spherical trigonometry and navigation).
  Wed 11/29 Deadline for detailed outline of Paper 2. Note change!
  Missed deadline: paper gets automatic one-third-grade deduction.
  Student presentations continue.
  No class Thursday. No quiz this week

  Week 13 (Nov 27) The beginning of Modern Algebra: Hamilton, Cayley and Sylvester. (B: 11.4)
  document Cayley on the definition of Group
  document Cayley on the Cayley-Hamilton Theorem
  Student presentations continue.
  Quiz

  Week 14 (Dec 5) Cantor and the infinite (B: 12.2, 12.3)
  document Cantor: "On an elementary question in set theory" (1890-91)
  See also: Cantor on the cardinality of a power set: |P(S)|>|S| (D)
  Student presentations continue.
  Quiz

  Week 14 (Dec 12) Review
  Thurs 12/15 Paper 2 due.
  Late submission: paper gets automatic one-third-grade deduction.
  Regular schedule of Tues & Thurs classes. Final week exercises.
  Quiz

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  Anthony Phillips
  Math Dept SUNY Stony Brook
  tony at math dot sunysb dot edu
  December 4 2006
  link updated January 29 2008
  link updated October 5 2010