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Undergraduate Topics in Computer Science

Proofs and Algorithms

An Introduction to Logic and Computability

Authors: Dowek, Gilles

  • Covers elementary topics such as proofs, models, recursive functions, and Church's theorem
  • Introduces more advanced topics, like rewriting, lambada-calculus, sequent calculus, and automated theorem proving
  • Written for students who have had no exposure to logic before
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eBook $29.99
price for USA
  • ISBN 978-0-85729-121-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Download immediately after purchase
Softcover $39.95
price for USA
  • ISBN 978-0-85729-120-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

Proofs and Algorithms: An Introduction to Logic and Computability

Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation.

Proofs and Algorithms: An Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself.

Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.

About the authors

Gilles Dowek is a Professor at École Polytechnique. He is also a Researcher at the Laboratoire d'Informatique de l'École Polytechnique and the Institut National de Recherche en Informatique et en Automatique (INRIA). His research concerns the formalization of mathematics and the mechanization of reasoning. His main contribution is a reformulation of the axiomatic method which provides a central role to the notion of computation.

Reviews

From the reviews:

“This work examines when the application of an algorithm can replace the construction of a proof. … focuses on establishing that provability is undecidable in predicate logic (Church’s theorem). The text generally consists of propositions followed by proofs, with commentary, examples, and exercises interspersed. … The book would be of interest to those with adequate background. Summing Up: Recommended. Graduate students and above.” (J. R. Burke, Choice, Vol. 49 (1), September, 2011)

“Mathematical logic is a challenging subject for many students. … this book, with its focus on the nature of proofs and algorithms and their relationship, appears to be targeted precisely for such an audience and should appeal to computer scientists and philosophers … . this book remains an introductory book on mathematical logic suited for a beginning graduate course in logic. … Its conciseness makes it well suited for a one-semester graduate course.” (Burkhard Englert, ACM Computing Reviews, February, 2012)


Table of contents (9 chapters)

Buy this book

eBook $29.99
price for USA
  • ISBN 978-0-85729-121-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Download immediately after purchase
Softcover $39.95
price for USA
  • ISBN 978-0-85729-120-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Proofs and Algorithms
Book Subtitle
An Introduction to Logic and Computability
Authors
Series Title
Undergraduate Topics in Computer Science
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-0-85729-121-9
DOI
10.1007/978-0-85729-121-9
Softcover ISBN
978-0-85729-120-2
Series ISSN
1863-7310
Edition Number
1
Number of Pages
XII, 156
Topics