Course Content
Below you will find the plan of what we work on in each session. Subject to change.
| # | Date | Meta-content |
Content |
Reading | Events |
|---|---|---|---|---|---|
| 1 | Mo 27/8 | Format and overview of the course; requirements and assessment |
Prehistoric mathematics (Babylon and Egypt). |
Katz, Ch. 1 Slides: ishango.pdf Download ishango.pdf, multiplication-table-babylon.pdf Download multiplication-table-babylon.pdf, Egypt.pdf Download Egypt.pdf |
|
| 2 | Th 30/8 |
How to write an essay: content, structure, argumentation, etc.; |
Ancient Greek mathematics. |
On essay writing: here Links to an external site. and here Download here. Katz, Ch. 2-6 (read excerpts), in particular Ch. 3 Fauvel-Gray, Ch. 3.A, 3.B An online, browsable version of Euclid's Elements Links to an external site. by David Joyce Slides:essay-writing.pdf Download essay-writing.pdf, Elements.pdf Download Elements.pdf |
start essay 1 |
| 3 | Mo 3/9 |
Approaches to a mathematical text; |
equation solving. Mathematical competition, math as an art. |
On asking questions about a historical text: Wardhaugh Stedall, Ch. 1.4, 12.1 Katz, Ch. 9, 12.1-3 Slides: equations.pdf Download equations.pdf |
quiz on ancient and Greek mathematics |
| 4 | Th 6/9 |
what is good & constructive peer review? |
algebra vs geometry. Units: the megalithic unit |
Fauvel-Gray, 1.C (megalithic unit), 3.G (opinions on Greek algebra vs geometry) Katz, 14.2 Stedall, Ch. 2.3 |
turn in essay 1 start essay 2 |
| 5 | Mo 10/9 | Approaches to a mathematical text; questions to ask. |
the mathematical profession, motivations, careers: Fermat and friends; universities, monasteries |
Stedall, 6.1 Katz, 14.4 Slides: fermat.pdf Download fermat.pdf 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 |
quiz on Arab and medieval mathematics and equation solving |
| 6 | Th 13/9 |
grading criteria for good peer review |
The relations between mathematics, religion, and esoterics |
Plato, The Meno Links to an external site. dialog Steiner, Mathematics and Occultism Links to an external site. |
turn in essay 2 start peer review |
| 7 | Mo 17/9 |
dealing with peer review, rebuttals |
The birth of calculus: infinitesimals, Newton, Leibniz |
Stedall, Ch. 3–4 Katz, Ch. 15–16 Fauvel-Gray, 12.C Slides: towards-the-infinitesimally-small.pdf Download towards-the-infinitesimally-small.pdf, indivisibles-backlash.pdf Download indivisibles-backlash.pdf, Newton-Leibniz.pdf Download Newton-Leibniz.pdf |
end peer review start rebuttal |
| 8 | Th 20/9 |
analysis of sources wrt different aspects |
The development of rigidity in mathematical arguments (with focus on calculus) |
Stedall, Ch. 10-11,16 Katz, Ch. 22 Slides: rigor.pdf Download rigor.pdf |
end rebuttal start essay 3 SF2725: topic selection |
| 9 | Mo 24/9 |
Feedback on peer review and rebuttals. |
Probability theory: games, bets, odds, combinatorics. |
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 |
quiz on calculus |
| 10 | Th 27/9 |
analyzing a text with only partial understanding of the mathematics. |
Equation solving part II: Abel, Galois, the birth of modern algebra. Genius and genius cult. Mathematics and politics, radicalism |
Stedall, Ch. 12.3, 13 Katz, Ch. 21.2 Slides: galois.pdf Download galois.pdf |
turn in essay 3 start peer review |
| 11 | Mo 1/10 |
Mathematics arising from Fermat's Last Theorem. The birth of abstract algebra. Women in mathematics: Germaine, Noether. |
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 Slides: fermats-last-theorem.pdf Download fermats-last-theorem.pdf |
end peer review |
|
| 12 | Th 4/10 |
how to do research like a historian; finding relevant sources |
Mathematics, logic, and philosophy |
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) Slides: logic.pdf Download logic.pdf |
end rebuttal start essay 4 |
| 13 | Mo 8/10 | Mathematics and mathematical institutions in the 20th century Popular reception of mathematics |
Slides: 20-century.pdf Download 20-century.pdf (not including the movie clips) |
quiz on modern algebra and logic | |
| 14 | Th 11/10 | preparing for the exam; exam structure and past exams | The history of teaching mathematics |
Encyclopedia of Mathematics Education Links to an external site., Stephen Lerman, ed. Springer 2014 Slides: teaching.pdf Download teaching.pdf |
turn in essay 4 |