Notes (Notlar)

Türkçe'deki notlarım aşağıdadır (my notes in Turkish are below).

The word 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, Model-theory of vector-spaces over unspecified fields, as an example. I have also drafted a 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)

Course notes

Algebra

• 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.

Geometry

• Conic Sections (31 pages, size A5, March 21, 2015): for use in a course of analytic geometry
• See also my courses in projective and hyperbolic geometry (based on Pappus and Lobachevski):
  • Mimar Sinan, 2015
  • Şirince, 2016
  • Şirince, 2017

Logic

• Logical Paradoxes (8 pages, size A5, September 23, 2013)
• 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)

Number theory

• 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)

History

• Math history course logbook

Other

Logic

• Ordinal Analysis (48 pages, size A5, 12 point type, May 29, 2018):
  • pdf
  • ps
  • dvi
  • tex
  This is a philosophy of mathematics and the teaching of it, originating as a preface in English to the Turkish set-theory text listed below.
• Undecidability of C(T₀, T₁) (version of April 4, 2017; 14 pages, size A5):
  • pdf
  • ps
  • dvi
  • tex

  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
• Descartes as Model Theorist
• Istanbul Model Theory Seminar
• Morley's Categoricity Theorem
• Ultraproducts

Geometry

• “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 Symmetry in the Journal of Humanistic Mathematics
  • From Euclid to Descartes

Çarpma yöntemleri (Facebook'a koyduğum resimler) // Multiplication methods (pictures I put on Facebook)

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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)