Nonstandard Analysis (Dover Books on Mathematics)

Book Details:

• Author: Alain M. Robert

• Publisher: Dover

• Binding: Paperback

• Number of Pages: 176

• ISBN-13: 0800759432790

• Languages: English

• Dimensions: 9.0 x 5.9 x 0.5 inches

About The Book:
Nonstandard Analysis by Alain M. Robert is a brilliant and concise introduction to the world of nonstandard analysis (NSA). Written with clarity and wit, this book is designed to bring a complete change in how NSA is taught, making it both accessible and engaging. The author succeeds in presenting complex mathematical concepts in a way that is simple, deep, and insightful—qualities that are rarely seen in educational literature. As praised by J.-M. Lévy-Leblond in the European Journal of Physics, this book represents mathematics teaching at its best.

This book introduces NSA through the axiomatic IST (internal set theory) approach, presenting the theory in a structured, rigorous manner. The two-part treatment begins with a clear exposition of theoretical topics such as:

• Idealization, standardization, and transfer

• Real numbers and numerical functions

• Continuity, differentiability, and integration

The second part covers practical applications, including:

• Invariant means

• Approximation of functions

• Differential equations

• Perturbation of a Green function

• An invariant subspaces problem

Exercises at the end of each chapter, along with hints and full solutions, allow readers to deepen their understanding of the material. Whether you are a student or a professional, Nonstandard Analysis equips you with a solid foundation in this advanced area of mathematics, making it a valuable resource for learning and teaching NSA.