Dover Publications Applied nonstandard analysis, paperback/martin davis

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Geared toward upper-level undergraduates and graduate students, this text explores the applications of nonstandard analysis without assuming any knowledge of mathematical logic.

It develops the key techniques of nonstandard analysis at the outset from a single, powerful construction; then, beginning with a nonstandard construction of the real number system, it leads students through a nonstandard treatment of the basic topics of elementary real analysis, topological spaces, and Hilbert space.

Important topics include nonstandard treatments of equicontinuity, nonmeasurable sets, and the existence of Haar measure.

The focus on compact operators on a Hilbert space includes the Bernstein-Robinson theorem on invariant subspaces, which was first proved with nonstandard methods.

Ever mindful of the needs of readers with little background in these subjects, the text offers a straightforward treatment that provides a strong foundation for advanced studies of analysis About the Author: Martin Davis: Computer Science Pioneer Dover's publishing relationship with Martin Davis, now retired from NYU and living in Berkeley, goes back to 1985 when we reprinted his classic 1958 book Computability and Unsolvability, widely regarded as a classic of theoretical computer science.

A graduate of New York's City College, Davis received his Ph D from Princeton in the late 1940s and became one of the first computer programmers in the early 1950s, working on the ORDVAC computer at The University of Illinois.

He later settled at NYU where he helped found the Computer Science Department.

Not many books from the infancy of computer science are still alive after several decades, but Computability and Unsolvability is the exception.

And The Undecidable is an anthology of fundamental papers on undecidability and unsolvability by major figures in the field including Godel, Church, Turing, Kleene, and Post.

Critical Acclaim for Computability and Unsolvability This book gives an expository account of the.