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.
| Day-by-day | ||
|---|---|---|
| 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 In the case of Skinner, the range of historical reference might be daunting, but please at least read sections I and VI (VI starts on page 86 of Visions), which, respectively, set out Skinner's methodological agenda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 .
