History of Mathematics
Instructor: Franz Lemmermeyer
Office: FEN 116
I suggest Boyer, History of Mathematics. One copy is on reserve
in the library. Here are my reasons for
not picking Anglin, Mathematics: A concise History and Philosophy.
Midterm 1: 86/100
Midterm 2: 61/100
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.
- Th Sept 25: Timeline.
The development of number systems
- Mo Sept 29: number system
- Th Oct 02: Thales,
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;
- Mo Oct 13: Midterm I
- Th Oct 16: Archimedes: circle
- Mo Oct 20: Archimedes: spiral and parabola
- Th Oct 23: Archimedes: parabola; notes on
- 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
- 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:
- Th Dec 11: midterm 2
- Mo Dec 15: Presentation Greek
- 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.
- Mo Dec 29: Gauss and the construction of the
- 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
presentation on Bernoulli's
evaluation of the integral
of xx; presentation on calendars.
- Mo Jan 12, 16:00 Final SBZ03, SBZ04
If you're interested, please email me with your names and the
topic; you may suggest topics yourselves. Many of the sources above
come from the excellent online course on the history of mathematics
Allen at Texas A&M University.
- Development of Calendars [Yildirim, Topan, Korkmaz]
Thales: his biography,
philosophy, and mathematics [Alkis]
Pythagoras and the Pythagoreans [D. Can]
- Classification of the
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
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
[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]