Course Content

Prehistoric mathematics (Babylon and Egypt).
Numbers and counting; zero; positional systems.
Scribes and mathematical training.

1. A cuneiform table Download A cuneiform table
   
   A problem from the Rhind papyrus Download A problem from the Rhind papyrus
2. Katz, Ch. 1
   Stedall, Ch. 1.1
   Fauvel-Gray: Ch. 1.D, 1.E
3. The Ishango bone Download The Ishango bone, Egypt Download Egypt, Babylon Download Babylon

How to write an essay: content, structure, argumentation, etc.;
grading criteria

Ancient Greek mathematics.
Reception of Babylonian & Egyptian mathematics.
Where this knowledge came from & what it was used for. Scholarship in Greece and the culture of commentaries. Proofs, definitions, and axioms. Euclid's elements.

1. Timeline of some Greek mathematicians Download Timeline of some Greek mathematicians
   On essay writing: here Links to an external site. and here Download here
   . (Sample_Essay_1,  Download Sample_Essay_1, 
   Sample_Essay_2 Download Sample_Essay_2
   )
2. Katz, Ch. 2-6 (read excerpts), in particular Ch. 3
   Stedall, Ch. I.2-3
   Fauvel-Gray, Ch. 3.A, 3.B
3. Slides on Essay writing Download Slides on Essay writing
   , Euclid's Elements Download Euclid's Elements

Approaches to a mathematical text;
questions to ask.

Euclid's elements. Equation solving. 

1. Any one of:
   a) Prop I.17 (Barrow) Download Prop I.17 (Barrow)
   
   b) Prop I.17 (Byrne) Download Prop I.17 (Byrne)
   
   c) Prop I.17 (Billingsley) Download Prop I.17 (Billingsley)
   ;
   Al-Jabr Download Al-Jabr
2. An online, browsable version of Euclid's Elements Links to an external site. by David Joyce
3. Slides on equation solving Download Slides on equation solving

What is good and constructive peer review?

Mathematical competition, math as an art.
conflict and stakes, claims and authorship.

1. Cossists bickering Download Cossists bickering
2. On asking questions about a historical text: Wardhaugh
   Stedall, Ch. 1.4, 12.1
   Katz, Ch. 9, 12.1-3
3. Notes from fourth class Download Notes from fourth class

Critical reading of sources

Approaches to a mathematical text;
questions to ask.

Algebra vs Geometry. Units: the megalithic unit
Euclid, Descartes etc.

The mathematical profession, motivations, careers: Fermat and friends; universities, monasteries

1. megalithic unit Download megalithic unit
   , Thom's Statistical Examination Download Thom's Statistical Examination
   ,  Analytic Download Analytic
   , Descartes's analytic method Download Descartes's analytic method
   , La Géométrie Download La Géométrie
   , Fermat Download Fermat
2. Fauvel-Gray, 1.C (megalithic unit), 3.G (opinions on Greek algebra vs geometry)
   Katz, 14.2
   Stedall, Ch. 2.3,
   Stedall, 6.1
   Katz, 14.4
   

   P. Tannery and C. Henry, Oeuvres de Fermat, Gauthier-Villars 1891

   M. S. Mahoney, The mathematical career of Pierre de Fermat, 1601–1665, Princeton University Press, 1994

3. Slides on Fermat Download Slides on Fermat,
   Notes from fifth clas Download Notes from fifth class

Grading criteria for good peer review

1. Plato, The Meno Links to an external site. dialog (excerpt Download excerpt
   );
   Steiner, Mathematics and Occultism Links to an external site.(excerpt Download excerpt
   )
2. The rest of the Meno dialog and Mathematics and Occultism, Katz, 2.2
3. Notes from sixth class Download Notes from sixth class

Submit Essay 2

Start peer review

Dealing with peer review and rebuttals

1. Newton's letters Download Newton's letters
   , response by Hobbes Download response by Hobbes
2. Stedall, Ch. 3–4
   Katz, Ch. 15–16
   Fauvel-Gray, 12.C
3. Slides on Indivisibles Download Indivisibles, further developments Download further developments, Newton and Leibniz; Download Newton and Leibniz; in-class notes Download in-class notes

Analysis of sources wrt different aspects
reading between the lines

1. Euler defending infinitesimals Download Euler defending infinitesimals
   , Cauchy on continuity Download Cauchy on continuity
    
2. Stedall, Ch. 10-11,16
   Katz, Ch. 22
3. Slides: on rigor Download on rigor

Feedback on peer review and rebuttals.
Critical reading of secondary sources.

Probability theory: games, bets, odds, combinatorics.
What is applied and what is pure mathematics?

1. Hacking on probability Download Hacking on probability
   , Mishnah Download Mishnah
   , Pascal to Fermat Download Pascal to Fermat
2. Stedall, Ch. 7
   Katz, Ch. 14.3, 18
   N. L. Rabinovitch, Probability and Statistical Inference in Ancient and Medieval Jewish Literature, University of Toronto Press, 1973
   G. Reith, The Age of Chance: Gambling in Western Culture, Routledge Studies in Social and Political Thought, 1999
3. Slides on probability Download Slides on probability

Analyzing a text with only partial understanding of the mathematics.

1. Letter by Galois Download Letter by Galois
   , Lagrange on third order equations Download Lagrange on third order equations
2. Stedall, Ch. 12.3, 13
   Katz, Ch. 21.2
3. Slides on Galois Download Slides on Galois

Mathematics arising from Fermat's Last Theorem.

The birth of abstract algebra.

Women in mathematics: Germaine, Noether.

1. Kummer on ideal numbers Download Kummer on ideal numbers
2. Stedall, Ch. 13.2
   Katz, Ch. 21
   Harold M. Edwards, Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory, Springer GTM 50, 1977
3. Slides on FLT and Noether Download Slides on FLT and Noether

End peer review
Start rebuttal

How to do research like a historian; Finding relevant sources

1. A page from Principia Download A page from Principia
   , Hilbert on foundations Download Hilbert on foundations
   , Weyl on foundations Download Weyl on foundations
2. Katz, Ch. 2.3, 21.3
   William Ewald, From Kant to Hilbert: A Source Book in the Foundations of Mathematics, Vol. II, 1996. Ch. 24 (David Hilbert), 25 (L.E.J. Brouwer)
3. Notes from twelvth class Download Notes from twelvth class

1. AMS subject classification Download AMS subject classification
2.  
3. Notes from Thirteenth Class Download Notes from Thirteenth Class

1. Encyclopedia of Mathematics Education Links to an external site., Stephen Lerman, ed. Springer 2014, The Whetstone of Witte Links to an external site. (Extraction of Roots Download Extraction of Roots
   ), Klein's book (Preface Download Preface
   ), Hej matematik Links to an external site. (in Swedish)
2.  
3. Notes from Fourteenth Class Download Notes from Fourteenth Class