# 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):

#### 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

### Other

#### Logic

Ordinal Analysis

(48 pages, size A5, 12 point type, May 29, 2018): 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**(*T*_{0},*T*_{1}) (version of April 4, 2017; 14 pages, size A5):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 becameAbscissas and Ordinates

)

- Geometry, including
Commensurability and Symmetry

(now published asOn 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)

*Türkçede* (in Turkish)

- Thales Kanıt kavramının öncüsü olarak (24 Eylül 2016 konuşma)
- Sonsuzküçük Analiz
- Matematik Paradoksları
- Koni kesitleri (conic sections)
- [Aksiyomatik]
*Kümeler kuramı*(axiomatic set theory) *Modeller kuramı*(model theory)*Önermeler mantığı*(propositional logic)*Posterler*(posters)