Türkçe'deki notlarım aşağıdadır (my notes in Turkish are below).
notes here refers to course lecture notes or other
so-called expository writing. I may blame my calculus teacher (about
whom I wrote a blog
article) for first giving me the idea that the best teachers create
their own textbooks. I do not necessarily agree with this any more, at
least not in all cases; but the fact remains that, in teaching a course,
I am usually not satisfied to follow anybody's textbook but my own.
Expository writing may be based on historical
research. It is possible that mathematical research—the
discovery of new theorems—may result; I cite my paper, monograph on Euclid's number theory,
arguing for a (more or less) new and (I think) better way of
understanding this theory.
In English (İngilizce’de)
- Finite Fields 2017 | 2016 (for a course at the Nesin Mathematics Village)
- Linear algebra notes (in html, for an undergraduate course, original in 2000)
- Groups and Rings, for a first-year graduate course.
- See also my courses in projective and hyperbolic geometry (based on Pappus and Lobachevski):
- Foundations of Mathematical Practice (236 pages, size A5, September 24, 2010), for a first-year undergraduate course.
- Minimalist Set Theory (166+ pages, 2011), for a third-year undergraduate course.
- Recursion and Induction: Notes on Mathematical Logic and Model Theory (109 pages, size A4, September 17, 2008), for a fourth-year undergraduate course.
- Ultraproducts and nonstandard analysis (notes from several courses in Şirince)
- Elementary Number Theory (196 pages), originally for a third-year undergraduate course.
- Elementary Number Theory II, given at METU in 2008 (153 pages, size A5, 12 point type, revised January 5, 2018)
Ordinal Analysis(48 pages, size A5, 12 point type, May 29, 2018):
- Undecidability of C(T0,
T1) (version of April 4, 2017; 14 pages, size
The text is based on work of Kim and Roush and formed part of my 1997 doctoral thesis, which otherwise produced Function fields and elementary equivalence
- Topics related to the Compactness Theorem
- Istanbul Model Theory Seminar
- Morley's Categoricity Theorem
- “Thales of Miletus: Sources and Interpretations” (over a hundred pages of notes, prepared originally for the talk “Thales Kanıt kavramının öncüsü olarak,” September 24, 2016, listed below
- Analytic Geometry, including
Thales and the Nine-point Conic(published in the De Morgan Gazette)
Conic Sections(as also above)
Abscissas and Ordinates(now published in the Journal of Humanistic Mathematics)
Analytic Geometry(part of which became
Abscissas and Ordinates)
- Geometry, including
Commensurability and Symmetry(now published as
On Commensurability and Symmetryin the Journal of Humanistic Mathematics
From Euclid to Descartes
Çarpma yöntemleri (Facebook'a koyduğum resimler) // Multiplication methods (pictures I put on Facebook)
Türkçede (in Turkish)
- Platonik Cisimler (Platonic Solids)
- Arşimet Cisimleri (Archimedean solids)
- Thales Kanıt kavramının öncüsü olarak (24 Eylül 2016 konuşma)
- Sonsuzküçük Analiz
- Matematik Paradoksları
- Koni kesitleri (conic sections)
- [Aksiyomatik] Kümeler kuramı (axiomatic set theory)
- Lineer Cebir
- Modeller kuramı (model theory)
- Önermeler mantığı (propositional logic)
- Posterler (posters)