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Tuesday, January 24, 2017

**Abstract:** In 1973 Abraham Robinson gave a talk about the nonstandard analysis (NSA) at the Institute for Advanced Study. After his talk Kurt G\"odel made a comment, in which he predicted that "...there are good reasons to believe that Non-Standard Analysis in some version or other will be the analysis of the future". One has to admit that during the fifty years since this prediction, it did not come true. One of the reasons is that the most part of researchers in NSA considered it as a tool of obtaining new results in standard mathematics, instead of consider it as a more appropriate language, in which the "book of nature is written". Nowadays, the investigation of DE's that simulate processes in science and economy are based on computer (discrete) simulations of these DE's.

In this talk I will try to justify the point of view that the language of NSA is more appropriate for investigation of the interaction between continuous models and their discrete simulations (or maybe vise versa - between discrete models and their continuous simulation, according to a popular among applied mathematicians point of view). The reason is that not well defined properties ("very big", "very small", "far enough of the boundaries of computer memory", etc.) can be introduced in the language of NSA on the level of rigor of Cantor's Set Theory. I will discuss some NSA theorems in algebra, calculus, ergodic theorem and quantum mechanics) concerning this problem that have intuitively clear sense and agree with computer experiments, while their formulation in the language of standard mathematics looks irrelevant and sometimes even unreadable.

Tuesday, January 31, 2017

Tuesday, February 7, 2017

Tuesday, February 21, 2017

Tuesday, February 28, 2017

Thursday, March 2, 2017

Tuesday, March 7, 2017

Tuesday, March 14, 2017

Thursday, March 16, 2017

Tuesday, March 28, 2017

Tuesday, April 4, 2017

Tuesday, April 25, 2017

Tuesday, August 29, 2017

Tuesday, September 5, 2017

Tuesday, September 12, 2017

Tuesday, September 19, 2017

Tuesday, September 26, 2017

Tuesday, October 3, 2017

Tuesday, October 31, 2017