Extensions and Corollaries of Recent Work on Hilbert's Tenth Problem

Martin Davis

Franklin Classics Trade Press

One of the world's pioneers in the development of computer science offers a mesmerizing history of computers. Computers are everywhere today--at work, in the bank, in artist's studios, sometimes even in our pockets--yet they remain to many of us objects of irreducible mystery. How can today's computers perform such a bewildering variety of tasks if computing is just glorified arithmetic? The answer, as Martin Davis lucidly illustrates, lies in the fact that computers are essentially engines of logic. Their hardware and software embody concepts developed over centuries by logicians such as Leibniz, Boole, and Godel, culminating in the amazing insights of Alan Turing. The Universal Computer traces the development of these concepts by exploring with captivating detail the lives and work of the geniuses who first formulated them. Readers will come away with a revelatory understanding of how and why computers work and how the algorithms within them came to be.

The Universal Computer: The Road from Leibniz to Turing

Computers & Technology

Computer Science

W.W.Norton&Company

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

Applied Nonstandard Analysis (Dover Books on Mathematics)

Science & Math

Mathematics

Dover Publications

Every man his own landlord: A history of Coventry Building Society

[Coventry Building Society]

Broc Rhyfel

Literature & Fiction

Contemporary

Y Lolfa

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Books by Martin Davis