History of Mathematics

Instructor: Franz Lemmermeyer
Office: FEN 116

Textbook

Homework

• Sept. 29 problems
• Oct. 16 problems; solutions.
• Oct. 30 problems; solutions.
• Dec. 22 problems; solutions.

Exam Averages

Midterm 1: 86/100
Midterm 2: 61/100
Final: 60/100

The final exams can be seen 
Fri Jan 16, 13:00-14:00    
Mon Jan 19, 13:00-14:00
Tue Jan 20, 13:00-14:00
in my office FEN 116.

Links

• Biographies of Mathematicians
• Euclid's Elements online
• Babylonian Mathematics
• Egyptian Mathematics
• Greek Mathematics
• On who burned down the Library of Alexandria: from bede (Christian) and ehistory
• Articles on the discovery of zero:
  • Boyer I
  • Boyer II
  • Datta
• An excellent article on the controversy about the discovery of the solution of the cubic
• A summary of geometry (includes things we did not talk about - don't worry about it).

Schedule

• Th Sept 25: Timeline. The development of number systems
• Mo Sept 29: number system
• Th Oct 02: Thales, Euclid, axioms; Euclid Book I, Proposition 1
• Mo Oct 06: Euclid Book I, Proposition 2; ruler and compass; collapsing compass.
• Th Oct 09: Eudoxus, Euclid and circles, method of exhaustion; Review
• Mo Oct 13: Midterm I
• Th Oct 16: Archimedes: circle
• Mo Oct 20: Archimedes: spiral and parabola
• Th Oct 23: Archimedes: parabola; notes on
  • exhaustion (F.L.)
  • exhaustion and limits (J.P. Seldin)
  • exhaustion and integration (from J. Rotman)
• Mo Oct 27: three classical unsolved problems
• Th Oct 30: Descartes, Gauss, Wantzel
• Mo Nov 3: Solving cubics and quartics: del Ferro, Tartaglia, Cardano, Ferrari. Here's D. Allen's essay about mathematics in the Renaissance.
• Th Nov 6: Cardano's solution of the cubic
• Mo Nov 10: presentation: Pythagoras
• Th Nov 13: (Ferrari's solution of the quartic) presentation: Zeno; Greeks and infinity;
• Mo Nov 17: presentation: Diophantus; here is a short summary.
• Th Nov 20: class canceled
• Mo Dec 1: Diophantus and negative numbers (S. Sertöz)
• Th Dec 4: Presentation on Diophantus part II
• Mo Dec 8: review
• Th Dec 11: midterm 2
• Mo Dec 15: Presentation Greek mathematics and mathematicians;
• Th Dec 18: Presentation on Indian and Chinese mathematics; presentation on Thales.
• Mo Dec 22: presentation on Fermat's Last Theorem.
• Th Dec 25: presentation on the Euler-Diderot incident. Galois theory
• Mo Dec 29: Gauss and the construction of the regular 17-gon.
• Th Jan 01: New Year's Day
• Mo Jan 05: presentation on non-Euclidean geometry; presentation on Wittgenstein
• Th Jan 08: presentation on Euler and the Basel problem; presentation on Bernoulli's evaluation of the integral of x^x; presentation on calendars. review.
• Mo Jan 12, 16:00 Final SBZ03, SBZ04

Presentations

• Development of Calendars [Yildirim, Topan, Korkmaz]
• Thales: his biography, philosophy, and mathematics [Alkis]
• Pythagoras and the Pythagoreans [D. Can]
• Classification of the Platonic solids and the structure of our universe[O. Boztas, C. Korkmaz, A. Kayrur]
• The paradoxa of Zeno and infinity in Greek philosophy [Y. Sengül, M. Ö. Özcakir, A. Tokuc]
• Eratosthenes and Aristarch: circumference of the earth, distance earth-moon and earth-sun.
• Some problems of Diophantus (1. Diophantus' Notation 2. Some problems (classical) 3. Some problems (modern) 4. Diophantus and negative numbers [K. Bozkurt, E. Yavas, Ö. Öztürün]
• How do we know about Greek mathematicsand mathematicians? [Sanli, Altundag, Öztürk]
• Asian, Chinese, Indian, and Arabic (Islamic) Mathematics [B.G. Tüker; C. Pekdemir; S. Yücelyigit; M. Akkus, U. Genc]
• The incident of Euler- Diderot; Galois and Bell [N. Misir, B. Evci, H.S. Aksu]
• Euler's summation of 1 + 1/4 + 1/9 + 1/16 + ... (Basel problem; see the books by Dunham; Polya)
• Progress in the calculation of pi (History; Machin's formula and group laws on conics; Grave's problem (Ribenboim, Catalan's conjecture, p. 138ff); Gauss and the AGM) [H. Basan, H. Islek, A. Hayta, M.K. Ozbek]
• Construction of regular pentagon and 17-gon with ruler and compass [E. Karabudak, Ö. Cavusoglu]
• Fermat's Last Theorem; Fermat and the proof for n=4 [Sahinoglu];
• Non-Euclidean geometry [B. Bosna, P. Pekcagliyan]