WEEK | TOPIC & READING |
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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) |
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Egyptian number recording and Arithmetic. |
Reading: Burton 1.2, 2.1, 2.2, 2.3 |
Document: The Rhind Papyrus (St Andrew's website) |
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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. |
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Mathematics in the Hellenistic world. |
Reading: Burton 4.3, 4.5 |
Document: Archimedes "On
moments" palimpsest (read all parts 1-4) |
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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. |
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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) |
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The birth of calculus. |
Reading: Burton 8.3, 8.4 |
Document: Leibnitz on the Fundamental Theorem of Calculus (Struik) |
March 19: Paper 1 due. |
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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. |
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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) |
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Analysis in the 19th century. |
Reading: Burton 11.3 |
Document: Cauchy on the derivatives and differentials of functions |
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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. |
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