Course Content

Below you will find the preliminary plan for what we will work on in our fourteen classes. 

In the column Reading, you find three pieces of information:

  1. Texts that we are going to talk about in class. It is a good idea to take a look at these texts before the class even if we will have some time during the class to read them.  
  2. Background literature on what we talk about in class. This is primarily meant for review after class.
  3. Slides used in class. Observe that these will not be complete in any sense and it won't be possible to review a missed class by only looking at the slides. 
# Date Meta-content

Content

Reading Events
1 Tu 30/8 Format and overview of the course requirements and assessment

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

  1. Download A cuneiform table
    Download A problem from the Rhind papyrus
    Sample Essay 1 Download Sample Essay 1, Sample Essay 2 Download Sample Essay 2
  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
2 Fr 2/9

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 Download here
    Any one of:
    a) Download Prop I.17 (Barrow)
    b) Download Prop I.17 (Byrne)
    c) Download Prop I.17 (Billingsley);

  2. Katz, Ch. 2-6 (read excerpts), in particular Ch. 3
    Stedall, Ch. I.2-3
    Fauvel-Gray, Ch. 3.A, 3.B.
    An online, browsable version of Euclid's Elements Links to an external site. by David Joyce
  3. Download Slides on Essay writing, Euclid's Elements Download Euclid's Elements
Start Essay 1
3 Tu 6/9

Approaches to a mathematical text;
questions to ask.

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

  1. Download Al-Jabr, 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. Slides on equation solving Download Slides on equation solving
Quiz 1 on Ancient and Greek mathematics
4 Fr 9/9

What is good and constructive peer review?
Critical reading of sources

Algebra vs Geometry. Units: the megalithic unit
Geometric algebra; Descartes, Viète

 

  1. Download megalithic unit, Download Thom's Statistical Examination,   Download Analytic, Download Descartes's analytic method, Download La Géométrie,
  2. Fauvel-Gray, 1.C (megalithic unit), 3.G (opinions on Greek algebra vs geometry)
    Katz, 14.2
    Stedall, Ch. 2.3
  3. Slides on geometric algebra Download Slides on geometric algebra
Submit Essay 1
Start Essay 2
5 Tu 13/9

 

 

 

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

  1.   Download Fermat
  2. 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
Quiz 2 on Arab and medieval mathematics, Equation solving and Algebra vs Geometry
6 Fr 16/9

Grading criteria for good peer review

 

The relations between mathematics, philosophy, religion, and the supernatural
  1. Plato, The Meno Links to an external site. dialog ( Download excerpt);
    Steiner, Mathematics and Occultism Links to an external site.( Download excerpt)
  2. The rest of the Meno dialog and Mathematics and Occultism, Katz, 2.2
  3. Slides on the beginnings of infinitesimal calculus Download Slides on the beginnings of infinitesimal calculus

Submit Essay 2

Start peer review

7 Tu 20/9

Dealing with peer review and rebuttals

The birth of calculus: infinitesimals, Newton, Leibniz
  1. Download Newton's letters, Download response by Hobbes
  2. Stedall, Ch. 3–4
    Katz, Ch. 15–16
    Fauvel-Gray, 12.C
  3. Slides on further developments of indivisibles Download further developments of indivisibles, Newton and Leibniz Download Newton and Leibniz
End peer review
Start rebuttal
8 Fr 23/9

 

The development of rigidity in mathematical arguments (with focus on calculus); logic
  1. Download Euler defending infinitesimals, Download Cauchy on continuity, Download A page from Principia
  2. Stedall, Ch. 10-11,16
    Katz, Ch. 22
  3. Slides: on rigor, Download on rigor, logic Download logic
End rebuttal
Start Essay 3
SF2725: topic selection
9 Tu 27/9

Analyzing a text with only partial understanding of the mathematics.

Formalism and intuitionism. Set theory, Cantor
  1. Download Hilbert 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. Slides: grundlagenkrise.pdf Download grundlagenkrise.pdf 
Quiz 3 on Calculus
10 Fr 30/9

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. Download Hacking on probability, Download Mishnah, 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
Submit Essay 3
Start peer review
Tu 4/10

lecture cancelled

End peer review
Start rebuttal
11 Fr 7/10

Analyzing a text with only partial understanding of the mathematics.

How to do research like a historian; Finding relevant sources

Equation solving part II: Abel, Galois, the birth of modern algebra.
Genius and genius cult.
Mathematics and politics, radicalism
  1. Download Letter by Galois, Download Lagrange on third order equations
  2. Stedall, Ch. 12.3, 13
    Katz, Ch. 21.2
  3. Slides on Galois Download Slides on Galois
End rebuttal
Start Essay 4
12 Tu 11/10

Mathematics arising from Fermat's Last Theorem.

The birth of abstract algebra.

Women in mathematics: Germaine, Noether.

  1. 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

Quiz 4 on modern algebra and probability theory

13 Fr 14/10

Mathematics and mathematical institutions in the 20th century
Popular reception of mathematics

The history of teaching mathematics

  1. Download AMS subject classificationEncyclopedia of Mathematics Education Links to an external site., Stephen Lerman, ed. Springer 2014, The Whetstone of Witte Links to an external site. ( Download Extraction of Roots), Klein's book ( Download Preface), Hej matematik Links to an external site. (in Swedish)
  2.  
Submit Essay 4