Stony Brook University   MAT 336: History of Mathematics
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Readings are assigned from:
Burton:David Burton, History of Mathematics: An Introduction
Dunham:William Dunham, Journey through Genius: The Great Theorems of Mathematics
Struik:Dirk Struik, A Source Book in Mathematics, 1200-1800, on reserve in Math Library
 
WEEKTOPIC & READING
Week 1
(1/22-1/26)
Primitive counting. Positional and non-positional number systems. Babylonian number recording.
Reading: Burton 1.1, 1.3
Document: YBC 7289 (Yale Babylonian Collection; Casselman's website at UBC)
Week 2
(1/29-2/2)
Babylonian MultiplicationTables; the decoding of Plimpton 322.
Reading: Burton 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, see also Eleanor Robson's analysis)
February 2: Sign-up for in-class presentation
Week 3
(2/5-2/9)
Egyptian number recording and Arithmetic.
Reading: Burton 1.2, 2.1, 2.2, 2.3
Document: The Rhind Papyrus (St Andrew's website)
Week 4
(2/12-2/16)
Development of Greek mathematics.
Reading: Burton 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.)
February 16: Deadline for e-mail with Paper 1 topic.
Week 5
(2/19-2/23)
Mathematics in the Hellenistic world.
Reading: Burton 4.3, 4.5
Document: Archimedes "On moments" palimpsest (read all parts 1-4)
Week 6
(2/26-3/2)
Arab, Indian and Chinese mathematics of the first millennium.
Reading: Burton 5.3, 5.5
Document: Table of sines from the Aryabhatiya (Narasimha in Nature Dec 20/27 2001)
Document: Al-Khwarizmi on quadratic equations (Struik)
March 2: Deadline for email of detailed outline of Paper 1.
Week 7
(3/5-3/9)
Italian mathematics of the late middle ages and the Renaissance.
Reading: Burton 6.2, 7.2, 7.3
Document: Word problems from the 1478 "Treviso Arithmetic"
Document: Cardano's solution of the cubic (Dunham)
Week 8
(3/12-3/16)
Mathematics of the humanistic era.
Reading: Burton 8.1, 8.2
Document: Descartes on the theory of equations (Struik)
Document: Galileo on uniformly accelerated motion (Struik) (see full text at Michael Fowler's website at University of Virginia: part 1, part 2)
Week 9
(3/19-3/23)
The birth of calculus.
Reading: Burton 8.3, 8.4
Document: Leibnitz on the Fundamental Theorem of Calculus (Struik)
March 19: Paper 1 due.
Week 10
(3/26-3/30)
The beginnig of probability.
Reading: Burton 9.1, 9.2, 9.3
Document: Pascal on "Pascal's triangle" (Struik)
March 30:Deadline for email of 3-sentence description of Paper 2 topic.
Week 11
(4/9-4/13)
Number theory in the 17-18 centuries.
Reading: Burton 10.2, 10.3
Document: Euler's calculation of the sum of the 1/n2 series (Dunham)
Document: Gauss' proof of the Fundamental Theorem of Algebra (Struik)
Week 12
(4/16-4/20)
Analysis in the 19th century.
Reading: Burton 11.3
Document: Cauchy on the derivatives and differentials of functions
Week 13
(4/23-4/27)
The beginning of modern Algebra.
Reading: Burton 11.4
Document: Cayley on the definition of Group
Document: Cayley on the Cayley-Hamilton Theorem
April 27: Deadline for detailed outline of Paper 2.
Week 14
(4/30-5/4)
The beginning of set theory.
Reading: Burton 12.2, 12.3
Document: Cantor, "On an elementary question in set theory" (1890-91)
Document: Cantor on the cardinality of a power set: |P(S)|>|S| (Dunham)
May 4: Paper 2 due.
 
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