Math 300 A Concise History of Mathematics

Instructor: Ali Sinan Sertöz

Homepage: http://www.fen.bilkent.edu.tr/~sertoz
Phone: 290 1490
Office: Science Building, room 121.

Schedule: Monday  16:40-17:30  SAZ-19
                 Thursday 14:40-16:30  SBZ-04

Text Book: W. S. Anglin, Mathematics: A Concise History and Philosophy,
                    Undergraduate Texts in Mathematics, Springer-Verlag 1994.

Syllabus: Numbers in brackets denote the chapters from the book around which the discussions will proceed.

  1. 24-27 September 2001: (1,2)
    General discussion about methods. Given a certain era, what is known then? Which civilization is attributed with the discovery? What are the other civilizations doing then? What is the significance of that knowledge then, and now?
    What are the evidences on which we build all these discussions?

    The Moscow papyrus, the Rhind papyrus, Plimpton 322 tablet.

  2. 1-4 October 2001: (3,4,5,6,7)
    Thales, Pythagoras and Euclid
    Elements.

  3. 8-11 October 2001: (8,9)
    More on Elements.
    Concept of infinity in ancient times.

  4. 15-18 October 2001: (10,11,12)
    Plato, Aristotle, Eudoxus.

  5. 22-25 October 2001: (13,14,15)
    Ruler and compass constructions.
    More on Elements.

  6. 1 November 2001: (16,17)
    Archimedes, Apollonius.

  7. 5-8 November 2001: (18,19,20,21)
    Early Medieval mathematics.

  8. 12-15 November 2001: (22,23)
    Late Medieval mathematics.

  9. 19-22 November 2001: (24,25)
    Finding roots of polynomials; cubics and quartics.

  10. 26-29 November 2001: (26,27,28)
    Napier, Galileo, Kepler, Desargues, Descartes, Fermat.

  11. 3-6 December 2001: (29,30,31)
    Pascal, Newton, Leibniz.

  12. 10-13 December 2001: (32,33)
    Euler, Lagrange.

  13. 20 December 2001: (34,35)
    Nineteenth century algebra and analysis.

  14. 24-27 December 2001: (36,37)
    Nineteenth century geometry and number theory.

  15. 2 January 2002: (38,39,40)
    Twentieth century: Hilbert's problem list.

Grading: Each student is required to prepare two term-projects; one on an ancient and one on a more recent mathematical concept or a mathematician. The grading will then depend on the creative approach and the depth and  breadth of the final work. There will be a written final exam where students will be able choose from a set of questions those which are akin to their interests and will have a chance of demonstrating their understanding and interpretation of this concise history of mathematics. No other homework or quizzes are planned. Assesment: Term projects are 35% each, final exam is 30%.

Optional: There will be optional extra hours where we may view videos from the department library about more recent topics of popular interest, or listen to extracurricular topics of interest presented by participating students.

There are numerous internet sources for the history of mathematics. One such link is the Index of Biographies.

 

A Sample Answer Paper for the Final Exam is available here in two formats:
DVI File         PDF File