Page count: 144 pages
Category: Math, Informatics and Science
The book contains the material of a one-semester course on nonstandard analysis. After a brief introduction to the necessary background in logic, it starts by discussing nonstandard versions of the basic notions of elementary calculus, as e.g. convergence, continuity, derivative, and Riemann integral. Subsequent chapters cover gradually more advanced subjects. Nonstandard method is used to prove several fundamental and important theorems in topological and metric spaces, real, and complex analysis.
The book can be used by engineers, physicists, mathematicians, but first of all, university students, who want to understand what the infinitesimals are, how the nonstandard method works, and what are its advantages and disadvantages. By providing nonstandard proofs for significant, interesting and deep mathematical theorems, it examplifies that the nonstandard method is not a toy, but could be a handy research tool.
The author is the head of the Computer and Statistics Center of the Central European University, Budapest, and researcher at the Eotvos Lorand University. His personal web page is at www.renyi.hu/~csirmaz.