Nonstandard Analysis by Jaap Ponstein
About this book :-
"Nonstandard Analysis" by "Jaap Ponstein" offers an intuitive and accessible introduction to "nonstandard analysis", focusing on the use of "infinitesimals" and infinitely large numbers as legitimate mathematical objects. Rather than relying heavily on formal logic or model theory, the book adopts a more direct and concept-driven approach, making the subject easier to grasp for readers with a background in calculus or real analysis.
The text carefully explains how nonstandard numbers extend the real number system and how familiar concepts such as limits, continuity, and derivatives can be reinterpreted using infinitesimal methods. Ponstein emphasizes clarity and conceptual understanding, showing how classical results in "analysis" can be obtained through nonstandard reasoning. This approach highlights the intuitive power of infinitesimals while still respecting mathematical rigor.
Originally published as a tribute to Ponstein’s work, the book is well suited for students, educators, and mathematicians interested in alternative foundations of calculus. It serves as a gentle bridge between traditional analysis and "nonstandard methods", offering a fresh perspective on the foundations of mathematics and the logical structure behind calculus.
The text is accessible to students from a wide variety of backgrounds, including undergraduate students entering applied mathematics from non-mathematical fields and graduate students in the sciences and engineering who want to learn analysis. A basic background in calculus, linear algebra and ordinary differential equations, as well as some familiarity with functions and sets, should be sufficient.
Book Detail :-
Title:
Nonstandard Analysis by Jaap Ponstein
Publisher:
University of Groningen
Year:
2001
Pages:
465
Type:
PDF
Language:
English
ISBN-10 #:
B0006BNKKA
ISBN-13 #:
N\A
License:
University Educational Resource
Amazon:
Amazon
About Author :-
The author
Jaap Ponstein
was a Dutch mathematician associated with the University of Groningen, known for his interest in the "foundations of calculus" and alternative approaches to mathematical analysis. Later in his career, he focused on developing intuitive ways to understand "infinitesimals" beyond traditional limit-based methods. His posthumously published work reflects a clear and concept-driven style, aiming to make "nonstandard analysis" accessible without heavy reliance on formal logic. Ponstein’s contributions offer valuable insight into "mathematical foundations" and provide readers with a fresh perspective on classical analysis.
Book Contents :-
1. Generalities
2. Basic theory
3. Some applications
4. Some special topics
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