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

The texts for MAT 336 will be

- 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" palimpsestWeek 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/n^{2}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 TheoremWeek 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