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Books > Computing & IT > General theory of computing > Mathematical theory of computation
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The Foundations of Computability Theory (Hardcover, 1st ed. 2015)
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The Foundations of Computability Theory (Hardcover, 1st ed. 2015)
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This book offers an original and informative view of the
development of fundamental concepts of computability theory. The
treatment is put into historical context, emphasizing the
motivation for ideas as well as their logical and formal
development. In Part I the author introduces computability theory,
with chapters on the foundational crisis of mathematics in the
early twentieth century, and formalism; in Part II he explains
classical computability theory, with chapters on the quest for
formalization, the Turing Machine, and early successes such as
defining incomputable problems, c.e. (computably enumerable) sets,
and developing methods for proving incomputability; in Part III he
explains relative computability, with chapters on computation with
external help, degrees of unsolvability, the Turing hierarchy of
unsolvability, the class of degrees of unsolvability, c.e. degrees
and the priority method, and the arithmetical hierarchy. This is a
gentle introduction from the origins of computability theory up to
current research, and it will be of value as a textbook and guide
for advanced undergraduate and graduate students and researchers in
the domains of computability theory and theoretical computer
science.
General
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