MAT 336 History of Mathematics
Spring 2006
Index Course Description Syllabus Schedule of Presentations |
|
MAT 336 History of Mathematics
|
Index Course Description Syllabus Schedule of Presentations |
Week 1 (Jan 23) 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)
Week 2 (Jan 30) The decoding of Plimpton 322. (B: 2.6)
document
Plimpton 322 (Columbia Rare Book Collection; David Joyce's website at Clark
University,
University of Swansea website;
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).
Signup for in-class presentation topics.
Quiz on base-60 and cuneiform numbers.
Week 3 (Feb 6) 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 (Feb 13) 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)
Mon. 2/20: Deadline for email of Paper 1 topic.
Quiz
Week 5 (Feb 20) Euclid and Archimedes. (B: 4.3, 4.5)
document Archimedes "On moments" palimpsest.
Quiz on Euclid's control of the error
in approximating the area of a circle by the area of inscribed
polygons: each time you use his construction to double the number
of sides of the polygon, you divide by two his upper bound on the
error.
Week 6 (Feb 27) 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)
Student presentations begin.
Fri. 3/3 Deadline for detailed outline of Paper 1.
No quiz this week.
Week 7 (Mar 6) 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 on completing the square
in Old Babylonian mathematics (Robson's analysis of YBC 6967), in
Al-Khwarizmi and today.
Week 8 (Mar 13) Galileo and Descartes. (B: 8.1, 8.2)
document Descartes on the theory of equations (S)
Fri. 3/17 Paper 1 due. (postponed to 3/20, 5PM).
Student presentations continue.
Quiz
Week 9 (Mar 20) Newton and Leibnitz. (B: 8.3, 8.4)
document Leibnitz on the Fundamental Theorem of Calculus (S)
Student presentations continue.
Quiz
Week 10 (Mar 27) Probability: Pascal to Laplace. (B: 9.1, 9.2)
document Pascal on "Pascal's triangle" (S)
Fri. 3/31 Deadline for email of 3-sentence description of Paper 2 topic.
Student presentations continue.
Quiz
Week 11 (Apr 3) Euler and the Bernoullis. (B: 10.2)
document Euler's calculation of the sum of the 1/n2
series (D)
Fri. 4/7 Deadline for detailed outline of Paper 2.
Student presentations continue.
Quiz
Week 12 (Apr 17) Gauss, Bolyai and Lobachevsky (B: 10.3, 11.1, 11.2)
document Gauss' proof of the Fundamental Theorem of Algebra (S)
Student presentations continue.
Quiz
Week 13 (Apr 24) Cantor and the infinite (B: 12.2)
document Cantor on the cardinality of a power set: |P(S)|>|S| (D)
Student presentations continue.
Quiz
Week 14 (May 1) Review
Fri 5/5 Paper 2 due.
Student presentations continue.
Quiz