Math 3010: Topics in the History of Mathematics, Spring 2016

Meeting: MWF 2:00-2:50, AEB 350 (3 credit hours)

Instructor: Stefan Patrikis, office JWB 309, email (my last name)

Office hours: Monday 3-4, Wednesday 3-4, held in AEB 350

Please read the syllabus.

I will collect here a list of helpful links.

Date Topic and Supplements Assignment due
M 1/11 Introduction and overview None
W 1/13 Method in the history of ideas Read the syllabus.
Look over Katz Table A.1 (Timeline of Mathematics).
Read Katz 945-947 (General References in the History of Mathematics)
F 1/15 Egypt Read Katz 1.1
M 1/18 No class: Martin Luther King Day Apropos of our discussion on 1/13, compare the approaches to the history of mathematics and, more broadly, the history of ideas, proposed by
(1) a legendary mathematician, Andre Weil, by reading his essay History of Mathematics: Why and How; and
(2) a leading contemporary intellectual historian, Quentin Skinner, by reading his essay Meaning and understanding in the history of ideas (This is a link to a library resource: follow the link, click "View It," log in using your uid, and then read the essay, which appears as chapter 4 of volume 1 of Skinner's Visions of Politics.)
You may find both of these essays rather hard-going, for different reasons. In the case of Weil, if you come to an unfamiliar mathematical notion, just press on and don't worry about it--you'll still get the methodological gist. In the case of Skinner, the range of historical reference might be daunting, but please at least read sections I and VI (VI starts on page 86 of Visions), which, respectively, set out Skinner's methodological agenda and deliver his (rousing!) conclusion.
W 1/20 Mesopotamia Read Katz 1.2
F 1/22 China: historical overview Hand in Katz Problems 1.4, 1.10, 1.17, 1.27 (show your work for all problems!)
Read Katz 7.1-7.2
M 1/25 China: arithmetic and algebra through the Han Review ``Euclid's" algorithm (Katz page 198-199)
W 1/27 China: geometry of the Han classics Read Katz 7.3
F 1/29 Song China: polynomial equations Hand in Katz problems 7.6, 7.8, 7.9 AND the following two questions: use iterated division (``Euclidean algorithm") (1) to compute gcd(95, 133);
and (2) to solve (in integers) 49x+33y=1.
Read Katz 7.4
M 2/1 Song China: number theory Read Katz 7.5
W 2/3 More modular arithmetic: Fermat's little theorem Review modular arithmetic and the Chinese Remainder Theorem
F 2/5 China: catch-up and wrap-up Hand in Katz problems 7.18, 7.23, 7.25, 7.26
Read Katz 7.6
M 2/8 Greece: introduction Read Katz 2.1-2.2
W 2/10 Greece: the mathematical universe; and
three famous construction problems
Read Plato, Timaeus, 27d-36d and 51b-56e (log in to library resources and read pages 16-24 and 44-51 in this edition; note that the online reader allows you to save up to 60 pages).
Read sections I and II (the first 4 pages) of Tegmark, "The Mathematical Universe," (Foundations of Physics 38:101-150) available here.
F 2/12 Introduction to library resources Hand in pset 4.
M 2/15 No class: Presidents' Day Holiday Read Plato, Republic, Book 6. Focus on 506e-511e. Available (after library login) here.
W 2/17 Greece: the regular polyhedra, Theaetetus, and Plato Read Plato, Republic, Book 7. Focus on the place of mathematics in the educational system of the kallipolis. Available (after library login) here.
F 2/19 Greece: Aristotle and logic. Introduction to Euclid. Hand in pset 5.
Read Katz 2.3, 3.1, 3.2. Please also read the final paper guidelines and timeline.
M 2/22 Midterm Exam
W 2/24 Euclid's Elements: geometry Read Katz 3.3, 3.4
F 2/26 Euclid's Elements: ratio and number theory Hand in Katz problems 3.2, 3.15, 3.16, 3.17
Read Katz 3.5, 3.6, 3.7
M 2/29 Eudoxus and exhaustion. Archimedes Hand in final paper topic, sources, and source analyses (see the posting on 2/19).
Read Katz 3.8-4.3
W 3/2 Conics Read Katz 4.4-4.5. Read Katz 22.2 (especially 22.2.1)
F 3/4 Finish conics; Ptolemy and astronomy Redo the first four (i.e., the mathematical) midterm problems.
M 3/7 The decline of Rome Hand in first draft of introductory paragraphs for final paper (see 2/19).
W 3/9 Zeno, Cantor, Russell, Gödel Read Katz 22.2, 25.1. Read Lewis Carroll's dialogue, ``What the Tortoise Said to Achilles".
F 3/11 Zeno, Cantor, Russell, Gödel, continued Hand in pset 8.
M 3/21 Decimal place-value: India to the Islamic world Hand in partial draft of final paper (see 2/19).
W 3/23 Algebra in the Islamic world, Part I Read Katz 8.1-8.2, 8.4, 9.1-9.3
F 3/25 The Abbasid translation movement Read Katz 8.3, 8.7, 8.8, 9.4-9.6
M 3/28 Algebra in the Islamic World, Part II Reread Katz 9.3.5-9.3.6
W 3/30 Trigonometry, planar and spherical, in the Islamic World Read Katz 9.6
F 4/1 From Arabic to Latin: the reawakening of the mathematical tradition in the Latin West HW 9 due: Katz 9.10, 9.16, 9.19, 9.25
Read Katz 10.1
M 4/4 Guest Lecture, Dragan Milicic: Renaissance astronomy through Kepler Read Katz 13.0, 13.3
W 4/6 Guest Lecture, Evelyn Lamb: Renaissance algebra and the drama of the cubic equation Read Katz 12.1-12.3
F 4/8 Guest Lecture, Sean McAfee: the life and work of Galois HW 10 due: Katz 10.31, 10.34, 10.41, 10.42
Read Katz 21.2
M 4/11 Algebraic symbolism in the early modern period Read Katz 12.4-12.5
W 4/13 Analytic Geometry: Fermat and Descartes Read Katz 12.4-12.5, 14.1-14.2
Begin Descartes, Discourse on the Method, available through your library login here.
F 4/15 Beginnings of the theory of probability HW 11 due: Katz 12.30, 12.32
Finish Descartes, Discourse on the Method (see 4/13).
Read Katz 14.3
M 4/18 Calculus: Beginnings Read Katz Chapter 15
W 4/20 Calculus: Newton and Leibniz Read Katz 16.1
F 4/22 Calculus: Newton and Leibniz Read Katz 16.2
M 4/25 Conclusion Submit final paper
F 4/29 Final Exam, 1-3pm See the review sheet.

Homework solutions: HW1, HW2, HW3(part 1),HW3(part2), HW4, HW5, HW6, HW7/Midterm, HW8, HW9 page 1, HW9 page 2, HW9 page 3, HW10 .