Alan Turing : His Work and Impact.

By: Cooper, S. BarryContributor(s): van Leeuwen, JPublisher: Saint Louis : Elsevier Science & Technology, 2013Copyright date: ©2013Description: 1 online resource (937 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9780123870124Subject(s): Turing, Alan MathisonGenre/Form: Electronic books. Additional physical formats: Print version:: Alan Turing : His Work and ImpactDDC classification: 510.92 B LOC classification: QA29.T8 -- C65 2013ebOnline resources: Click to View
Contents:
Front Cover -- Alan Turing: His Work and Impact -- Copyright -- List of Contributors -- Introduction -- Table of Contents -- Part I: How Do We Compute? What Can We Prove? -- Alan Mathison Turing by Max Newman -- A Comment on Newman's Biographical Memoir -- Alan Mathison Turing -- Scientific work -- 1. Mathematical logic -- '1. Computing machines -- 2. Three mathematical papers -- 3. Computing machines -- 4. Chemical theory of morphogenesis -- Bibliography -- On Computable Numbers, with an Application to the Entscheidungsproblem -- Alan and I -- On Computable Numbers, with an application to the entscheidungsproblem -- 1. Computing machines -- 2. Definitions -- Automatic machines -- Computing machines -- Circular and circle-free machines -- Computable sequences and numbers -- 3. Examples of computing machines -- 4. Abbreviated tables -- Further examples -- 5. Enumeration of computable sequences -- 6. The universal computing machine -- 7. Detailed description of the universal machine -- Subsidiary skeleton table -- 8. Application of the diagonal process -- 9. The extent of the computable numbers -- 10. Examples of large classes of numbers which are computable -- Computable convergence -- 11. Application to the Entscheidungsproblem -- Appendix -- Computability and effective calculability -- On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction -- Examining the Work and Its Later Impact -- The Importance of Universal Computation -- References -- Three Proofs of the Unsolvability of the Entscheidungsproblem -- The Entscheidungsproblem -- 1. Church's Proof -- 2. Turing's Proof -- 3. The should-have-been Gödel-Kleene Proof -- References -- Two Puzzles About Computation -- 1. Introduction -- 2. Why Do We Compute? -- Problem 1 -- Problem 2 -- 3. What Do We Compute? -- Why Does It Matter? -- References.
Turing Machines and Understanding Computational Complexity -- 1. Introduction -- 2. Formal definition of the Turing machine -- 2.1. Computable functions -- 2.2. Examples of computable functions -- 3. Computability thesis and the universal Turing machine -- 4. Undecidability of the halting problem -- 5. Complexity of computations -- 6. Importance of the Turing machine -- References -- From the Halting Problem to the Halting Probability -- Turing and the Art of Classical Computability -- 1. Mathematics as an art -- 2. Defining the effectively calculable functions -- 3. Why Turing and not Church? -- 4. Why Michelangelo and not Donatello? -- 5. Classical art and classical computability -- 5.1. Human scale -- 5.2. Composition and balance -- 6. Computability and recursion -- 7. The art of exposition -- 8. Conclusion -- References -- Turing Machines in Münster -- 1. Introduction -- 2. The object -- 2.1. Hardware layout -- 2.2. Examples -- 3. The papers -- 3.1. Universal Turing machines and Jones-Matiyasevich-masking -- 3.2. On the early history of register machines -- 4. Conclusion -- 5. State machine -- References -- Reflections on Wittgenstein's Debates with Turing During his Lectures on the Foundations of Mathematics -- References -- The Computational Power of Turing's Non-Terminating Circular a-Machines -- 1. Introduction -- 2. a-Machines and red-green Turing machines -- 2.1. a-Machines -- 2.2. Red-green Turing machines -- 2.3. Relation between a-machines and red-green Turing machines -- 3. Significance of the result -- 4. Conclusion -- Acknowledgements -- References -- Turing's Approach to Modelling States of Mind -- Acknowledgements -- References -- Conscious Cognition as a Discrete, Deterministic and Universal Turing Machine Process -- 1. Systems with states -- 2. The Turing machine: processes and computation -- 3. The neural Turing machine.
4. Conscious cognition: discrete temporal frames -- 5. Conscious cognition: mind states -- 6. Trained phenomenology -- 7. Conclusion -- References -- Virtual Machinery and Evolution of Mind (Part 1) -- 1. Virtual machines and causation -- 2. Virtuality -- 3. Causation and computation -- 4. Causation in RVMs -- 5. Implementable but irreducible -- 6. Implications -- References -- NOT -- References -- Halting and Non-Halting Turing Computations -- 1. Introduction -- 2. Turing machines -- 3. Resources -- 4. Halting time -- 5. Final comments -- Acknowledgements -- References -- Toward the Unknown Region: On Computing Infinite Numbers -- References -- On Computable Numbers, with an Application to the Entscheidungsproblem by A. M. Turing - Review by: Alonzo Church -- Church's Review of Computable Numbers -- Reference -- Computability and λ-Definability -- The Imperative and Functional Programming Paradigm -- 1. Models of computation -- 2. Functional programming -- 2.1. Features from lambda calculus -- 2.2. Features beyond lambda calculus -- 3. Types -- 4. Input/output -- 5. Current research -- 5.1. Parallelism -- 5.2. Certification -- 6. History and perspective -- References -- Computability and λ-Definability -- 1. Definition of λ-K-definability -- 2. Abbreviations -- 3. Mechanical conversion -- 4. Computability of λ-K-definable functions -- 5. Recursiveness of computable functions. -- The p-Function in λ-K Conversion -- Turing's Contributions to Lambda Calculus -- 1. Fixed point combinators in untyped lambda calculus -- 1.1. Lambda terms, reduction, and conversion -- 1.2. Fixed points -- 2. Weak normalisation of simply typed lambda calculus -- 2.1. Simply typed lambda terms and reduction -- 2.2. The proof of weak normalisation -- 2.3. Strong normalisation -- 3. Postscript -- References -- The p-Function in λ-K-Conversion.
Systems of Logic Based on Ordinals -- Turing's Thesis: Ordinal Logics and Oracle Computability -- 1. From Cambridge to Princeton -- 2. Turing in Princeton -- 3. The thesis: ordinal logics -- 4. Ordinal logics redux -- References -- Systems of Logic Based on Ordinals -- 1. The calculus of conversion. Gödel representations. -- 2. Effective calculability. Abbreviation of treatment. -- 3. Number-theoretic theorems. -- 4. A type of problem which is not number-theoretic. -- 5. Syntactical theorems as number-theoretic theorems. -- 6. Logic formulae. -- 7. Ordinals. -- 8. Ordinal logics. -- 9. Completeness questions. -- Definition of completeness of an ordinal logic -- Invariance of ordinal logics -- Incompleteness theorems. -- 10. The continuum hypothesis. A digression. -- 11. The purpose of ordinal logics. -- 12. Gentzen type ordinal logics. -- Index of definitions. -- Bibliography -- Examining the Work and Its Later Impact -- Turing's 'Oracle' in Proof Theory -- 1. Realisability -- 2. Heyting arithmetic in higher types -- 3. Realisability relative to an oracle -- References -- Truth and Turing -- References -- A Quantum Random Oracle -- 1. Turing's oracles -- 2. Value indefiniteness and the Kochen-Specker Theorem -- 3. An example of a quantum random oracle -- 4. A quantum random number generator certified by value indefiniteness -- 5. Hypercomputation via quantum random oracles -- References -- Practical Forms of Type Theory -- Preface -- Practical Forms of Type Theory -- 1. The nested-type system for a finite universe -- 2. Formal account of the nested-type system -- 3. Equivalence with Church's system -- 4. Relaxation of type notation -- The use of Dots as Brackets in Church's System -- Turing's dots -- The Use of Dots as Bracketsin Church's System -- General bracketing theory -- First form of rule -- Second form of rule -- Equivalence theorem.
Jutaxposition and omitted points -- Application to Church's system -- Discussion of the conventions -- Examples -- The Reform of Mathematical Notation and Phraseology -- Computation, Mathematical Notation and Linguistics -- References -- The Reform of Mathematical Notation and Phraseology -- Free and bound variables. Deduction theorem. Constants and parameters -- Theory of types and domains of definition -- Discussion of the system and application to normal mathematics -- Examining the Work and Its Later Impact -- Turing, Wittgenstein and Types: Philosophical Aspects of Turing's 'The Reform of Mathematical -- References -- Part II: Hiding and Unhiding Information: Cryptology, Complexity and Number Theory -- On the Gaussian error function -- Alan Turing and the Central Limit Theorem -- 1. Introduction -- 2. The central limit theorem -- 3. Turing's fellowship dissertation -- 3.1. Basic structure of the paper -- 3.2. The Quasi-necessary conditions -- 3.3. The sufficient conditions -- 3.4. One counterexample -- 4. Discussion -- References -- Turing's 'Preface' (1935) to 'On the Gaussian error function' -- Some Calculations of the Riemann Zeta function -- Alan Turing and the Riemann Zeta Function -- 1. Introduction -- 2. Recollection of some basics -- 3. On Turing's computations of the zeta function -- 4. On Turing's early work with zeta -- 5. A return to basics -- 6. Turing's skepticism about the RH -- References -- A Few Comments About Turing's Method -- References -- Some Calculations of The Riemann Zeta-Function -- Introduction -- Part I. General -- 1. The Θ notation -- 2. The approximate functional equation -- 3. Principles of the calculations -- 4. Evaluation of N(t) -- Part II. The Computations -- 1. Essentials of the Manchester computer -- 2. Outline of calculation method -- References -- On a Theorem of Littlewood -- 1. Introduction.
2. Outline of the method.
Summary: In this 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP, readers will find many of the most significant contributions from the four-volume set of the Collected Works of A. M. Turing. These contributions, together with commentaries from current experts in a wide spectrum of fields and backgrounds, provide insight on the significance and contemporary impact of Alan Turing's work. Offering a more modern perspective than anything currently available, Alan Turing: His Work and Impact gives wide coverage of the many ways in which Turing's scientific endeavors have impacted current research and understanding of the world. His pivotal writings on subjects including computing, artificial intelligence, cryptography, morphogenesis, and more display continued relevance and insight into today's scientific and technological landscape. This collection provides a great service to researchers, but is also an approachable entry point for readers with limited training in the science, but an urge to learn more about the details of Turing's work. 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP Named a 2013 Notable Computer Book in Computing Milieux by Computing Reviews Affordable, key collection of the most significant papers by A.M. Turing Commentary explaining the significance of each seminal paper by preeminent leaders in the field Additional resources available online.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Ebrary Ebrary Afghanistan
Available EBKAF00078931
Ebrary Ebrary Algeria
Available
Ebrary Ebrary Cyprus
Available
Ebrary Ebrary Egypt
Available
Ebrary Ebrary Libya
Available
Ebrary Ebrary Morocco
Available
Ebrary Ebrary Nepal
Available EBKNP00078931
Ebrary Ebrary Sudan

Access a wide range of magazines and books using Pressreader and Ebook central.

Enjoy your reading, British Council Sudan.

Available
Ebrary Ebrary Tunisia
Available
Total holds: 0

Front Cover -- Alan Turing: His Work and Impact -- Copyright -- List of Contributors -- Introduction -- Table of Contents -- Part I: How Do We Compute? What Can We Prove? -- Alan Mathison Turing by Max Newman -- A Comment on Newman's Biographical Memoir -- Alan Mathison Turing -- Scientific work -- 1. Mathematical logic -- '1. Computing machines -- 2. Three mathematical papers -- 3. Computing machines -- 4. Chemical theory of morphogenesis -- Bibliography -- On Computable Numbers, with an Application to the Entscheidungsproblem -- Alan and I -- On Computable Numbers, with an application to the entscheidungsproblem -- 1. Computing machines -- 2. Definitions -- Automatic machines -- Computing machines -- Circular and circle-free machines -- Computable sequences and numbers -- 3. Examples of computing machines -- 4. Abbreviated tables -- Further examples -- 5. Enumeration of computable sequences -- 6. The universal computing machine -- 7. Detailed description of the universal machine -- Subsidiary skeleton table -- 8. Application of the diagonal process -- 9. The extent of the computable numbers -- 10. Examples of large classes of numbers which are computable -- Computable convergence -- 11. Application to the Entscheidungsproblem -- Appendix -- Computability and effective calculability -- On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction -- Examining the Work and Its Later Impact -- The Importance of Universal Computation -- References -- Three Proofs of the Unsolvability of the Entscheidungsproblem -- The Entscheidungsproblem -- 1. Church's Proof -- 2. Turing's Proof -- 3. The should-have-been Gödel-Kleene Proof -- References -- Two Puzzles About Computation -- 1. Introduction -- 2. Why Do We Compute? -- Problem 1 -- Problem 2 -- 3. What Do We Compute? -- Why Does It Matter? -- References.

Turing Machines and Understanding Computational Complexity -- 1. Introduction -- 2. Formal definition of the Turing machine -- 2.1. Computable functions -- 2.2. Examples of computable functions -- 3. Computability thesis and the universal Turing machine -- 4. Undecidability of the halting problem -- 5. Complexity of computations -- 6. Importance of the Turing machine -- References -- From the Halting Problem to the Halting Probability -- Turing and the Art of Classical Computability -- 1. Mathematics as an art -- 2. Defining the effectively calculable functions -- 3. Why Turing and not Church? -- 4. Why Michelangelo and not Donatello? -- 5. Classical art and classical computability -- 5.1. Human scale -- 5.2. Composition and balance -- 6. Computability and recursion -- 7. The art of exposition -- 8. Conclusion -- References -- Turing Machines in Münster -- 1. Introduction -- 2. The object -- 2.1. Hardware layout -- 2.2. Examples -- 3. The papers -- 3.1. Universal Turing machines and Jones-Matiyasevich-masking -- 3.2. On the early history of register machines -- 4. Conclusion -- 5. State machine -- References -- Reflections on Wittgenstein's Debates with Turing During his Lectures on the Foundations of Mathematics -- References -- The Computational Power of Turing's Non-Terminating Circular a-Machines -- 1. Introduction -- 2. a-Machines and red-green Turing machines -- 2.1. a-Machines -- 2.2. Red-green Turing machines -- 2.3. Relation between a-machines and red-green Turing machines -- 3. Significance of the result -- 4. Conclusion -- Acknowledgements -- References -- Turing's Approach to Modelling States of Mind -- Acknowledgements -- References -- Conscious Cognition as a Discrete, Deterministic and Universal Turing Machine Process -- 1. Systems with states -- 2. The Turing machine: processes and computation -- 3. The neural Turing machine.

4. Conscious cognition: discrete temporal frames -- 5. Conscious cognition: mind states -- 6. Trained phenomenology -- 7. Conclusion -- References -- Virtual Machinery and Evolution of Mind (Part 1) -- 1. Virtual machines and causation -- 2. Virtuality -- 3. Causation and computation -- 4. Causation in RVMs -- 5. Implementable but irreducible -- 6. Implications -- References -- NOT -- References -- Halting and Non-Halting Turing Computations -- 1. Introduction -- 2. Turing machines -- 3. Resources -- 4. Halting time -- 5. Final comments -- Acknowledgements -- References -- Toward the Unknown Region: On Computing Infinite Numbers -- References -- On Computable Numbers, with an Application to the Entscheidungsproblem by A. M. Turing - Review by: Alonzo Church -- Church's Review of Computable Numbers -- Reference -- Computability and λ-Definability -- The Imperative and Functional Programming Paradigm -- 1. Models of computation -- 2. Functional programming -- 2.1. Features from lambda calculus -- 2.2. Features beyond lambda calculus -- 3. Types -- 4. Input/output -- 5. Current research -- 5.1. Parallelism -- 5.2. Certification -- 6. History and perspective -- References -- Computability and λ-Definability -- 1. Definition of λ-K-definability -- 2. Abbreviations -- 3. Mechanical conversion -- 4. Computability of λ-K-definable functions -- 5. Recursiveness of computable functions. -- The p-Function in λ-K Conversion -- Turing's Contributions to Lambda Calculus -- 1. Fixed point combinators in untyped lambda calculus -- 1.1. Lambda terms, reduction, and conversion -- 1.2. Fixed points -- 2. Weak normalisation of simply typed lambda calculus -- 2.1. Simply typed lambda terms and reduction -- 2.2. The proof of weak normalisation -- 2.3. Strong normalisation -- 3. Postscript -- References -- The p-Function in λ-K-Conversion.

Systems of Logic Based on Ordinals -- Turing's Thesis: Ordinal Logics and Oracle Computability -- 1. From Cambridge to Princeton -- 2. Turing in Princeton -- 3. The thesis: ordinal logics -- 4. Ordinal logics redux -- References -- Systems of Logic Based on Ordinals -- 1. The calculus of conversion. Gödel representations. -- 2. Effective calculability. Abbreviation of treatment. -- 3. Number-theoretic theorems. -- 4. A type of problem which is not number-theoretic. -- 5. Syntactical theorems as number-theoretic theorems. -- 6. Logic formulae. -- 7. Ordinals. -- 8. Ordinal logics. -- 9. Completeness questions. -- Definition of completeness of an ordinal logic -- Invariance of ordinal logics -- Incompleteness theorems. -- 10. The continuum hypothesis. A digression. -- 11. The purpose of ordinal logics. -- 12. Gentzen type ordinal logics. -- Index of definitions. -- Bibliography -- Examining the Work and Its Later Impact -- Turing's 'Oracle' in Proof Theory -- 1. Realisability -- 2. Heyting arithmetic in higher types -- 3. Realisability relative to an oracle -- References -- Truth and Turing -- References -- A Quantum Random Oracle -- 1. Turing's oracles -- 2. Value indefiniteness and the Kochen-Specker Theorem -- 3. An example of a quantum random oracle -- 4. A quantum random number generator certified by value indefiniteness -- 5. Hypercomputation via quantum random oracles -- References -- Practical Forms of Type Theory -- Preface -- Practical Forms of Type Theory -- 1. The nested-type system for a finite universe -- 2. Formal account of the nested-type system -- 3. Equivalence with Church's system -- 4. Relaxation of type notation -- The use of Dots as Brackets in Church's System -- Turing's dots -- The Use of Dots as Bracketsin Church's System -- General bracketing theory -- First form of rule -- Second form of rule -- Equivalence theorem.

Jutaxposition and omitted points -- Application to Church's system -- Discussion of the conventions -- Examples -- The Reform of Mathematical Notation and Phraseology -- Computation, Mathematical Notation and Linguistics -- References -- The Reform of Mathematical Notation and Phraseology -- Free and bound variables. Deduction theorem. Constants and parameters -- Theory of types and domains of definition -- Discussion of the system and application to normal mathematics -- Examining the Work and Its Later Impact -- Turing, Wittgenstein and Types: Philosophical Aspects of Turing's 'The Reform of Mathematical -- References -- Part II: Hiding and Unhiding Information: Cryptology, Complexity and Number Theory -- On the Gaussian error function -- Alan Turing and the Central Limit Theorem -- 1. Introduction -- 2. The central limit theorem -- 3. Turing's fellowship dissertation -- 3.1. Basic structure of the paper -- 3.2. The Quasi-necessary conditions -- 3.3. The sufficient conditions -- 3.4. One counterexample -- 4. Discussion -- References -- Turing's 'Preface' (1935) to 'On the Gaussian error function' -- Some Calculations of the Riemann Zeta function -- Alan Turing and the Riemann Zeta Function -- 1. Introduction -- 2. Recollection of some basics -- 3. On Turing's computations of the zeta function -- 4. On Turing's early work with zeta -- 5. A return to basics -- 6. Turing's skepticism about the RH -- References -- A Few Comments About Turing's Method -- References -- Some Calculations of The Riemann Zeta-Function -- Introduction -- Part I. General -- 1. The Θ notation -- 2. The approximate functional equation -- 3. Principles of the calculations -- 4. Evaluation of N(t) -- Part II. The Computations -- 1. Essentials of the Manchester computer -- 2. Outline of calculation method -- References -- On a Theorem of Littlewood -- 1. Introduction.

2. Outline of the method.

In this 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP, readers will find many of the most significant contributions from the four-volume set of the Collected Works of A. M. Turing. These contributions, together with commentaries from current experts in a wide spectrum of fields and backgrounds, provide insight on the significance and contemporary impact of Alan Turing's work. Offering a more modern perspective than anything currently available, Alan Turing: His Work and Impact gives wide coverage of the many ways in which Turing's scientific endeavors have impacted current research and understanding of the world. His pivotal writings on subjects including computing, artificial intelligence, cryptography, morphogenesis, and more display continued relevance and insight into today's scientific and technological landscape. This collection provides a great service to researchers, but is also an approachable entry point for readers with limited training in the science, but an urge to learn more about the details of Turing's work. 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP Named a 2013 Notable Computer Book in Computing Milieux by Computing Reviews Affordable, key collection of the most significant papers by A.M. Turing Commentary explaining the significance of each seminal paper by preeminent leaders in the field Additional resources available online.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

There are no comments on this title.

to post a comment.