MAT 336 History of Mathematics Spring 2020 (Section 01)

MAT 336 Detailed Syllabus and Schedule. Updated 3/19/2020

• B: The History of Mathematics, an introduction by David Burton (7th Ed.,WCB McGraw-Hill 2011)
• D: William Dunham, Journey through Genius (Wiley 1990, Penguin 1991)

Starting March 30, instruction will be online.

• Classes will be conducted via Zoom at the old scheduled times, but will be recorded for later playback.
• Student presentations will be made to the instructor via Zoom or otherwise, and shared with the class at a later time. Note that student presentation schedule has had to be changed: revised schedule here.
• Homework will take the place of quizzes. It will be submitted using Google forms. Stay tuned for detailed instructions.

For an overview linked to dates in world history, you may refer to the Time-line for the History of Mathematics compiled by William H. Richardson of Wichita State University.

Note: This schedule may be modified as the term progresses.

Homework exercises are recommended, and may help with next week's quiz.Starting 3/30, homework will be collected and graded.

Week 2 (Feb 3) Babylonian Multiplication Tables; the decoding of Plimpton 322. (B: 2.5, 2.6)
document VAT 7858 (Berlin Museum; Christian Siebeneicher's website at Bielefeld); also here
document NBC 7344 (Yale Babylonian Collection; Duncan Melville's website at St. Lawrence University); also here
document MS2184/3 and MS3866 (Schøyen collection) shown here.
document Plimpton 322 (Columbia Rare Book Collection; David Joyce's website at Clark University)
Egyptian number system; use of the 2/n table.
Quiz on base-60 and cuneiform numbers.
Students choose presentation topics.
Homework: B2.5, #1,2,4,9,11; B2.6, #2,8

Week 3 (Feb 10) Egyptian number recording and Arithmetic. (B: 1.2, 2.1, 2.2, 2.3)
document The Rhind Papyrus (St Andrew's website). Full text, translation and documentation, (A. B. Chase, Mathematical Association of America).
document Moscow Papyrus, problem 14. Nice picture here; Translation into hieroglyphics and English with analysis, from Wayne Aitkin's page at Cal State, San Marcos.
In-class presentations begin.
No quiz this week.
Homework: B2.3 ## 1, 2, 4, 5, 20, 22.

Week 4 (Feb 17) 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.)
Student presentations continue.
Quiz on Egyptian Mathematics.
Homework: Read Section 4.2. Check that "Euclid's construction for the golden section of a line segment" works, i.e. that AC/CB=CB/AB. Problem 12.

Week 5 (Feb 24) Euclid and Archimedes. (B: 4.3, 4.5)
document Archimedes "On moments" palimpsest.
"The Method of Archimedes" covers the volume of the sphere.
"The Method of Archimedes: propositions 13 and 14" the volume of the "hoof," using calculus.
"The Archimedes Codex" a review by J. L. Berggren of a modern history of the manuscript.
Student presentations continue.
No quiz this week.
Term paper topics and list of references (at least one besides our text) will be due March 10, two weeks from now.
Prof. Chas' Guidelines for term paper. Follow these.
Homework: B 4.3, ##15,16,17; 4.4 ##1,2.

Week 6 (Mar 2) Arab, Indian and Chinese mathematics during the "dark ages." (B: 5,3, 5.5)
document Table of sines from the Aryabhatiya (Narasimha, R. Sines in terse verse. Nature 414, 851 (2001) link). Further explanation here.
document al-Khwarizmi: "Compendium of Calculation by Completion and Reduction" (This translation was published by Frederic Rosen in 1831; quadratic equations start on page 12).
Student presentations continue.
Quiz on Greek mathematics.
Homework: B 5.5 ##1, 2, 10, 11, 14

Week 7 (Mar 9) 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.
Term paper outline due March 10. Use this link to submit your outline. Note that you can return to this form to edit it. Automatic 10-point deduction from term paper grade for missing this deadline.
Homework: Work the five problems from the Treviso Arithmetic. Check that you get the given solutions. Homework is due 4/2 and should be submitted online.

Week 8 (Mar 30) Galileo and Descartes. (B: 8.1, 8.2)
document Descartes and "cartesian coordinates:" original (from La Geometrie), translation and analysis.
document Galileo's Arithmetic.
Student presentations continue.
Homework due April 9.

Week 9 (Apr 6) Newton and Leibnitz. (B: 8.3, 8.4)
document From Newton letter to Oldenburg, October 24, 1676, re Binomial Theorem
document A page from Newton's notebooks
document Newton's mathematical approach to Bible Study
document Leibniz on refraction original text
Student presentations continue.
Homework due April 16: see Assignments on Blackboard.

Week 10 (Apr 13) Number theory from Fermat to Euler and Gauss. (B: 10.2, 10.3)
document Euler on the Bridges of Königsberg (partial translation). Original text
document Gauss on quadratic reciprocity
Student presentations continue.

Week 11 (Apr 20) Cauchy and Fourier. (B: 11.3)
document Cauchy on the "Cauchy-Riemann equations"  Original text: p.1, p.2, p.3.
document Fourier on the movement of heat in a ring
Thurs 4/23 Deadline for detailed outline (including all worked-out mathematics) of term paper.
Submit your outline here.
Missed deadline: paper gets automatic one-third-grade deduction.

Week 12 (April 27) The beginning of Modern Algebra (B: 11.4) and non-Euclidean geometry
document Cayley on Group Theory
document (see Notes on spherical trigonometry and navigation).
Student presentations continue.

Week 13 (May 4) 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.
Term paper due by end of business, Friday May 8.