Q-1 said:I am looking for for some good books on non-standard analysis. Hoping for something simple and not too complex.
George Jones said:You might like to look at Keisler's book on first-year calculus from the point of view of non-standard analysis, and Keisler's background book "Foundations of Infinitesimal Calculus". These are freely available from the links at
https://www.math.wisc.edu/~keisler/
Non-standard analysis is a mathematical framework that extends the traditional real number system to include infinitesimal and infinite numbers. It was developed in the 1960s by Abraham Robinson to provide a rigorous foundation for calculus and other areas of mathematics.
Books on non-standard analysis can be useful for understanding the foundations of calculus and other mathematical concepts. They can also provide insight into alternative approaches to traditional mathematics and help expand one's understanding of mathematical concepts.
Books on non-standard analysis are typically aimed at advanced undergraduate and graduate students in mathematics and related fields. However, anyone with a strong background in mathematics can benefit from reading these books.
Some highly recommended books on non-standard analysis include "Nonstandard Analysis" by Martin Davis, "Nonstandard Analysis: A Practical Guide with Applications" by Alain Robert, and "Nonstandard Analysis: Axiomatically" by Vieri Benci and Bruno Finetti.
Yes, non-standard analysis has found applications in various areas such as mathematical physics, probability theory, and economics. It has also been used to provide new insights and solutions to long-standing problems in mathematics.