Math 108: History of Mathematics Fall, 2003
Prof. J. Grabiner
Office phone: 73160; Secretary: 621-8218; email jgrabiner@pitzer.edu Office Fletcher 224; Office Hours posted

Required Books:
    Victor J. Katz, A History of Mathematics: An Introduction (2d ed., Harper Collins, 1998)
(This is the best one-volume history in existence, and it is worth buying, and keeping, even at the "new" price.)
    Plato, Meno (Bobbs-Merrill pb)
    René Descartes, Discourse on Method (Bobbs-Merrill pb)
    Jacques Hadamard, Psychology of Invention in the Mathematical Field (Dover pb)
     
Topics and Assignments:
Lectures will focus on specific topics, and will reflect the instructor's view of what is most important; Katz will provide an overview and some details.
  Sept. 3 Introduction to the course
  Sept. 8, 10
Mathematics in Egypt and Babylon; Mathematics in Africa, the Americas, & the Pacific.
Katz, 1-45, 332-341.
Recommended: H. Frankfort, Before Philosophy; O Neugebauer, Exact Sciences in Antiquity
M. Ascher, Ethnomathematics; Carl Boyer and Uta Merzbach, A History of Mathematics; B. L. van der Waerden, Science Awakening; A. Aaboe, Episodes from Early Mathematics.
  Sept. 15, 17 From Pythagoras to Euclid.
Katz, 46-58
Plato, Meno (all) for Wed. discussion
Recommended: W. Knorr, The Evolution of the Euclidean Elements; W. Knorr, The Ancient Tradition of Geometric Problems; David Fowler, The Mathematics of Plato's Academy.
  Sept. 22, 24

 

Euclid and His Time
Katz, 58-101;
Recommended: Aaboe, op. cit., and (superb!) Knorr, The Evolution of the Euclidean Elements; T. L. Heath, ed., The Thirteen Books of Euclid's Elements (Euclid, in full and in English).

  Feb. 29, Oct. 1 Archimedes
Katz, 102-134. (See more assigned reading 5 lines down)
Recommended: T. L. Heath, ed., The Works of Archimedes; E. J. Dijksterhuis, Archimedes (2d edition has updated
bibliography)
Apollonius, Diophantus, Hellenistic Mathematics
Katz, 135-191.
Recommended: J. Klein, Greek Mathematical Thought and the Origin of Algebra
  Oct. 6: No Class (Yom Kippur)
Oct. 8, 13 China and India; Mathematics in the Islamic World
Katz, 192-237; 238-287.
Recommended: George Gheverghese Joseph, The Crest of the
Peacock: NonEuropean Roots of Mathematics; Frank J. Swetz and T. Kao, Was Pythagoras Chinese? Right Triangle Theory in China; J. L. Berggren, Episodes in the Mathematics of Medieval
Islam, N. L. Rabinovitz, Probability and Statistical
Inference in Ancient and Medieval Jewish Literature
  Oct. 15 The Latin Middle Ages
Katz, 288-326; 327-331.
Recommended: M. Mahoney, "Mathematics," and J. Murdoch and E. Sylla, "The Science of Motion," in D. Lindberg, ed., Science in the Middle Ages
  Oct. 20 Fall Break
  Oct. 22 The Renaissance, and the Scientific Revolution.
Katz, 342-384, 385-430. Also Katz 544-595.
Recommended: O. Ore, Cardan: The Gambling Scholar; J. Klein, Greek Mathematical Thought and the Origin of Algebra; Judith Grabiner, "Mathematics," in P. F. Grendler, ed., Encyclopedia of the Renaissance (6 vols., 1999), vol. 4, 66-72.
On the Scientific Revolution, recommended: I. B. Cohen, The Newtonian Revolution
 
Oct. 27, 29

Analytic Geometry
Katz, 431-448, 448-503.
Descartes, Discourse on Method, all. (For discussion Monday, October 27)
Recommended: M. Mahoney, The Mathematical Career of Pierre de Fermat . C. Boyer, History of Analytic Geometry
  Nov. 3, 5. 17th-century mathematics before the calculus;
Newton and Leibniz
Katz, 448-467; 468-503. Then, 503-543.
Recommended: I. Hacking, The Emergence of Probability;
C. Boyer, History of the Calculus (covers antiquity - 19th c.)
M. Baron, Origins of the Infinitesimal Calculus (focus on 17th c.)
A. R. Hall, Philosophers at War: The Newton-Leibniz Controversy
  Nov. 10, 12 18th-century mathematics
Katz, 544-595, 596-648.
Recommended:; T. L. Hankins, Science and the Enlightenment; M. R. Kline, Mathematical Thought from Ancient to Modern Times (relevant chapters); H. Goldstine, History of Numerical Analysis from the 16th through the 19th century
  Nov. 17 Rigorization of the calculus.
Katz, 704-737. Handouts: translations from Cauchy.
Recommended: J. V. Grabiner, The Origins of Cauchy's Rigorous Calculus
Nov. 19 Mathematical creation (class discussion Tues.) based on Hadamard, Psychology of Invention in the Mathematical Field
  Nov. 24: Film, "The Proof" (on Fermat's Last Theorem) and discussion
  Nov. 26: to be announced
  Dec. 1, 3:

Women in Mathematics: Student Reports in Class.
Details and suggested sources will be forthcoming. Each student will have k minutes where k + 1 = total timenumber of students for the in-class report. Students not coming to present an in-class report will be required instead to hand in a documented 3-page written version, due Monday December 8 at the start of class.

Recommended: J.Alexanderson & D. Albers, Mathematical People; More Mathematical People; Claudia Henrion, Women in Mathematics (her bibliography is especially worth consulting); C. C. Gillispie, ed., Dictionary of Scientific Biography, 16 vols., the place to start for reliable biographies of any deceased scientific figure;
Ann H. Koblitz, Sofia Kovalevskaya: Scientist, Writer, Revolutionary; Constance Reid, Julia Robinson.
  Dec. 8, 10: Modern Mathematics; Bringing it All Together
Katz, (skim) chapters 15, 16, 17, 18. Choose one section based on your own mathematical background; problem and questions due Friday May 10. Seniors: Yours is due Monday, May 6. Senior finals TBA.
Recommended: T. Hawkins, Lebesgue's Theory of Integration; J. L. Richards, Mathematical Visions: Non-Euclidean Geometry in Britain; G. Moore, Zermelo's Axiom of Choice; Constance Reid, Hilbert, Sylvia Nasar, A Beautiful Mind (life of John Nash)
     
Written Assignments:
(i) Daily assignments:

 

 		 (a)

Hand in, at the START of class, on the day's assignment in Katz, a one-page outline or list of the most important points.

(b) At the end of each class, hand in one legible sheet of paper with (1) the key point of the day and (2) one question raised by the day's class.
(ii) Weekly assignments:   Every Monday (except Sept. 8, the first real week, and Dec. 1, the week reports are given), you will hand in the following:
(a) the solution of any problem in the previous week's chapter from Katz (your choice; it's most valuable if you pick the hardest one you can reasonably do);
(b) your answer to one of the discussion questions in the previous week's chapter(s) from Katz (again, your choice; pick something that interests you. Do not "share" this assignment with another student; work on your own). One page, double-spaced, should be enough for each question.
(c) either an outline of the material in the previous week's chapter(s) in Katz, or half a dozen intelligent sentences, in your own words, about the six individual topics in those chapter(s) that you found interesting. But if you do the six topics, they must not duplicate either the problem or the question you do from this chapter.
For both (a) and (b), GIVE THE PAGE AND QUESTION NUMBER! Please type (b) and, if possible, (c); make (a) as legible as possible.
     
(iii) Report:


 


   Each student will do a brief report the week of December 1-3. See calendar. More details will be provided closer to the date.
 
 
 
 
 
(iv) Final Examination Tuesday, December 16, 2 PM. Study suggestions will be provided. (short answer plus essay)
Grading algorithm: Grading algorithm: Weekly assignments 45%, daily assignments 15%, report 15%, final exam 25%.
Late work (without compelling reason) docked 10% per CALENDAR day.