
 Infinitesimal Analysis (Site not responding. Last check: ) 
  The concept of infinitesimal is one of the most important in mathematics; it was the concept that gave rise the calculus, and hence to analysis, and has been a driving force in fields such as differential geometry, differential topology, ergodic theory, financial mathematics, mathematical physics, perturbation theory, and stochastic analysis, to name only a few. 
  However, the existence of fields that extend the real numbers and include infinite and infinitesimal numbers was proved relatively recently, in the second half of the twentieth century, using constructions from formal logic. 
  Then we will study the techniques that are needed to use infinitesimal and infinite numbers using mathematical rigor, e.g., the Transfer Principle and the concepts of internal and external set. 
 www.math.utsa.edu /~iovino/teaching/fall05/infinitesimals.html (318 words) 
