[FOM] Book announcement

S B Cooper pmt6sbc at maths.leeds.ac.uk
Sat Feb 23 03:13:42 EST 2008

Book Announcement:


Cooper, S. Barry; Loewe, Benedikt; Sorbi, Andrea (Eds.)
2008, Springer Mathematics of Computing series XIII,
560 pp. 19 illus., Hardcover
ISBN: 978-0-387-36033-1

In recent years, classical computability has expanded beyond its original
scope to address issues related to computability and complexity in algebra,
analysis, and physics. The deep interconnection between "computation" and
"proof" has originated much of the most significant work in constructive
mathematics, theoretical computer science and mathematical logic of the last
70 years. Moreover, the increasingly compelling necessity to deal with
computability in the real world (such as computing on continuous data,
biological computing, and physical models) has brought focus to new
paradigms of computation that are based on biological and physical models.
These models address questions of efficiency in a radically new way and even
threaten to move the so-called Turing barrier, i.e. the line between the
decidable and the undecidable.

This book examines new developments in the theory and practice of
computation from a mathematical perspective, with topics ranging from
classical computability to complexity, from biocomputing to quantum
computing. The book opens with an introduction by Andrew Hodges, the Turing
biographer, who analyzes the pioneering work that anticipated recent
developments concerning computation's allegedly new paradigms. The remaining
material covers traditional topics in computability theory such as relative
computability, theory of numberings, and domain theory, in addition to
topics on the relationships between proof theory, computability, and
complexity theory. New paradigms of computation arising from biology and
quantum physics are also discussed, as well as the computability of the real
numbers and its related issues.

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