Finite fields

Notes from a one-week course, January 18–24, 2016, given as part of a linear-algebra winter school at the Nesin Mathematics Village.

Geometries

Note added after the course: We covered projective geometry in the first week, hyperbolic in the second. I created a text version of the first week, with an introduction explaining the origins of the course and what might be added to it (92 pages, size A5, 12 point type, dated January 9, 2017):

Here is a corrected version of the Turkish Pappus text, dated September 26, 2016 (reminder to self: I get the table on the last page properly oriented in the pdf file by means of pdftk <filename>.pdf cat 1-63 64N output <newfilename>.pdf):

Thanks to the Village for printing the Pappus and Lobachevski texts exactly as desired: as a book of size A5, coil bound (helezon spiral) and not comb bound. Unfortunately there was one problem in the printing that I do not understand: in the figures, some dotted and dashed lines that appear on my computer screen just fine did not get printed. I do not know what to do about this in future, if not to make all lines solid.

We shall study projective geometry and hyperbolic geometry from their origins in the works of Pappus and Lobachevski respectively, September 12–25 (two weeks), 2016, at the Nesin Mathematics Village. // Nesin Matematik Köyü'nde 12–25 Eylül (iki hafta), 2016, arasında, Pappus'un ve Lobaçevski'nin eserlerinden ışınsal ve hiperbolik geometrileri öğreneceğiz.

I taught a similar course in fall 2015 // 2015 Güz döneminde benzer bir ders verdim.

The main texts // Ana metinleri:

Pappus of Alexandria, Collection, Book VII, Propositions 127–145 (Lemmas I–XIX to Euclid's Porisms)
- 2 Eylül 2016 tarihli Türkçe çevirim, 64 sayfa, A5 boyu // (Turkish translation by me, dated September 2, 2016):
  - pdf
  - ps
  - dvi
  - tex
- Greek and Latin, edited and translated by Hultsch (1 + 30 pages)
- Greek and English edited and translated by Alexander Jones (5 + 20 pages, no diagrams)
Lobachevski, “Geometrical Researches on the Theory of Parallels” (English translation by Halsted, 47 pages)