mat336 - syllabus

### MAT 336 History of Mathematics Fall 2006

Index
Course Description
Syllabus
Homework
Schedule of Presentations

## MAT 336 Syllabus

The texts for MAT 336 will be
• 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)
with "documents" chosen from the texts and from:
• 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)
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.
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.
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!
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

Anthony Phillips
Math Dept SUNY Stony Brook
tony at math dot sunysb dot edu
December 4 2006