Meeting: MWF 2:00-2:50, AEB 350 (3 credit hours)
Instructor: Stefan Patrikis, office JWB 309, email (my last name)@math.utah.edu
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 In the case of Skinner, the range of historical reference might be daunting, but please at least read sections I and VI (VI starts on page 86 of Visions), which, respectively, set out Skinner's methodological agenda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 .