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Q-1

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I am looking for for some good books on non-standard analysis. Hoping for something simple and not too complex.

Any tips on good books appreciated.

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In summary, Some recommended books on non-standard analysis include Keisler's "First-Year Calculus" and "Foundations of Infinitesimal Calculus", which are available for free online. Other similar level books include "Nonstandard Analysis" by A. Robinson and "The Non-Standard Analysis" by A. Loeb.

- #1

Q-1

- 29

- 5

I am looking for for some good books on non-standard analysis. Hoping for something simple and not too complex.

Any tips on good books appreciated.

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George Jones

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Q-1 said:I am looking for for some good books on non-standard analysis. Hoping for something simple and not too complex.

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/

- #3

Q-1

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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/

Thank you. That helps a lot.

- #4

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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.

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