David Pierce // Matematik (Mathematics) // M.S.G.S.Ü.

my other courses at the Nesin Matematik Köyü

Non-standard Analysis

A course given, summer 2009, at the Nesin Matematik Köyü. The abstract that I submitted was as follows:

Invented in the 17th century if not earlier, calculus can be understood in terms of “infinitesimals”: non-zero numbers whose absolute values are less than every fraction 1/n. In this understanding, the region bounded by a curve is the sum of rectangles of infinitesimal width; the slope of a curve at a point is a ratio of infinitesimals. But there are no infinitesimals on the so-called “real number line”. In the usual “rigorous” treatment of calculus, invented in the 19th century, infinitesimals do not appear: they are replaced with the notion of a “limit”. However, 20th-century logic shows that infinitesimals can be made just as “real” as the real numbers, so that the original intuitive approach to calculus is entirely justified.

Lecture notes

  1. Original version (distributed in Şirince):
  2. Corrected version:

Son değişiklik: Tuesday, 03 April 2012, 12:51:59 EEST