WISM103: History from Ellipse to Elliptic Curve 2018/19

Assignments

We will announce two assignments each lecture. Each pair selects three out of the six assignments to work on. We encourage you to explore the historical and social aspects of mathematics as well as to understand the mathematics at a more intuitive level than you have become accustomed to in regular mathematics courses.

Results are to be handed in in the form of one article-style paper. A (perhaps limited) level of integration of the individual assignments is preferred but this is not strictly necessary.

Several people have asked if it is ok to hand in by email, and indeed it is!

Anything handed in after the deadline will suffer a grade deduction of 1 point per working day or part thereof. We will consider the weekend as 1 working day.

Assignments and content of lectures

First lecture Fri 12 April

For your information and benefit: a digital copy of the Dictionary of Scientific Biography is available from the University Library and is accessible through WorldCat.

Second lecture Fri 26 April

• If you want more about the Bernoulli's and the paracentric isochrone then have a look at Bos, The lemiscate of Bernoulli, in: Lectures in the History of Mathematics, 1993, or Blåsjö, Transcendental Curves in the Leibnizian Calculus, 2016, par. 7.3 and 8.3. It is not my intention to lay too much stress on this topic, but it may give you a clear idea of the much more geometric way of thinking in the 17th century.
• As an original source (Learn from the Masters!) see Euler (site) e.g., paper E251 "De integratione aequationis differentialis mdx/√(1-x⁴)=ndy/√(1-y⁴)". There is an English translation and you can also see a scan of the original. You could also look around the site for other articles of Euler's under the subject "Elliptic functions".
• Fagnano's article Teorema da cui si deduce una nuova misura degli Archi Elittici... is available but much harder to read.
• Gauss: a very enjoyable article by David Cox: "The arithmetic-geometric mean of Gauss" in l'enseignement mathematiques, vol.30, 1984, p.275-330. It covers more than only Gauss and agM. Be sure to read section 3, Historical remarks. And yes, it's in English! Download it from their free site but if you want to print it then take this version with added whitespace.
• Reading Gauss himself is a bit steep because (a) mostly Latin (b) not finished, publishable work and (c) leaves a lot of work to the reader. But, if you like, follow any reference of your liking from the secondary literature (e.g., Cox) into the Gauss Werke.

Third lecture Friday 3 May

• Abel, first part of Recherches sur les fonctions elliptiques available in original French in Crelle's Journal and English translation at the MAA.
• Riemann, Grundlagen English translation is available in the math library (shelfnr RI 07(3)) and also somewhere in the net, but I can't link to it for (c)-reasons
• Legendre, Traite des fonctions elliptiques is available from the Gallica Site, which by the way gives access to many more (mainly French) material
• Gauss, Tagebuch
• Euler's work is available at the Euler archive
• Many journals (including old ones like Crelle) are available via the e-journal site of the UU, Goettinger Digitalisirungszentrum, Gallica and many other places

Friday 10 May