The thirtieth meeting was held January 25-26, 2013, at Northern Kentucky University (which, incidentally, marked the 15th anniversary of the ORESME Reading Group!).  We recognized the recent publication by Rob Bradley and Ed Sandifer, the co-founders of our sister seminar Arithmos, of Cauchy's Cours d'Analyse (Springer, 2009) by reading from their translation of these highly influential lecture notes by Augustin-Louis Cauchy (1789-1857) for a course that he never gave (!) at the École Polytechnique. It is in these lecture notes that Cauchy first introduced the concept of limits into the calculus. We read the following selections from the Cours d'Analyse:

  • Introduction - p.1-3
  • Preliminaries, p. 5-7, number and quantity, numerical value (i.e. absolute value) and the definition of the limit, which surprisingly is done in the didactic style - no epsilons!
  • Chapter 1 - p. 17-20 Functions. Note in section 1.2 that he describes an "algebra" of 11 basic functions. No "arbitrary rule" relating 2 sets. This is a practical notion of function.
  • Chapter 2 - p. 21 (definition of infinitely small) and p. 26-28 continuity of functions. Also: p. p. 38-41, the second epsilon proof in the book; follow this up with Theorem IV, which is a corollary and will be referred to below, on p. 92.
  • Chapter 5, p. 71-75; distributive functions and a theorem (Theorem 2) that he will use to sum the binomial series.
  • Chapter 6, p 85-90, convergence and divergence of series, Cauchy criterion, the famous false theorem, and p. 91-93, root, ratio and condensation tests.
  • Chapter 7 - p. 122-127, modulus and argument, p. 132-133, roots of unity.