Instructor: Franz Lemmermeyer Office: FEN 116

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

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.

- 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:
- 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).

- 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

- 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]