John F Turing's Books

What Can Be Computed?

A Practical Guide to the Theory of Computation

By: John MacCormick

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What Can Be Computed?

A Practical Guide to the Theory of Computation

By: John MacCormick

An accessible and rigorous textbook for introducing undergraduates to computer science theory What Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference. The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, and NP-completeness, including the Cook-Levin Theorem. But the book also provides a broader view of computer science and its historical development, with discussions of Turing's original 1936 computing machines, the connections between undecidability and Gödel's incompleteness theorem, and Karp's famous set of twenty-one NP-complete problems. Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book's examples and other content allow readers to view demonstrations of—and to experiment with—a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation. An accessible and rigorous introduction to the essential fundamentals of computer science theory, written specifically for undergraduates taking introduction to the theory of computation Features a practical, interactive approach using real computer programs (Python in the text, with forthcoming Java alternatives online) to enhance motivation and understanding Gives equal emphasis to computability and complexity Includes special topics that demonstrate the profound nature of key ideas in the theory of computation Lecture slides and Python programs are available at whatcanbecomputed.com

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405

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Princeton University Press

Published Date

ISBN 10

1400889847

ISBN 13

9781400889846

Alan M. Turing

By: Sara Turing,John F Turing,Lyn Irvine

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Alan M. Turing

By: Sara Turing,John F Turing,Lyn Irvine

So is described one of the greatest figures of the twentieth century, yet someone who was barely known beyond mathematical corridors till the revelations in the 1970s. It was then that Alan Turing's critical contributions to the breaking of the German Enigma code, along with the circumstances of his suicide at the height of his powers, became widely known. From the rather odd, precocious, gauche boy through an adolescence in which his mathematical ability began to blossom, to the achievements of his maturity, the story of Turing's life fascinates. In the years since his suicide, Turing's reputation has only grown, as his contributions to logic, mathematics, computing, artificial intelligence and computational biology have become better appreciated. To commemorate the centenary of Turing's birth, this republication of his mother's biography, unavailable for many years, is enriched by a new foreword by Martin Davis and a never-before published memoir by Alan's older brother, which sheds new light on Alan's relationship with his family, and on the man himself"--

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194

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ISBN 10

1139337084

ISBN 13

9781139337083

Logic from A to Z

The Routledge Encyclopedia of Philosophy Glossary of Logical and Mathematical Terms

By: John B. Bacon

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Logic from A to Z

The Routledge Encyclopedia of Philosophy Glossary of Logical and Mathematical Terms

By: John B. Bacon

First published in the most ambitious international philosophy project for a generation; the Routledge Encyclopedia of Philosophy. Logic from A to Z is a unique glossary of terms used in formal logic and the philosophy of mathematics. Over 500 entries include key terms found in the study of: * Logic: Argument, Turing Machine, Variable * Set and model theory: Isomorphism, Function * Computability theory: Algorithm, Turing Machine * Plus a table of logical symbols. Extensively cross-referenced to help comprehension and add detail, Logic from A to Z provides an indispensable reference source for students of all branches of logic.

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125

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Routledge

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ISBN 10

1134970978

ISBN 13

9781134970971

Complexity and Cryptography

An Introduction

By: John Talbot,D. J. A. Welsh

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Complexity and Cryptography

An Introduction

By: John Talbot,D. J. A. Welsh

Introductory textbook on Cryptography.

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310

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Cambridge University Press

Published Date

ISBN 10

0521617715

ISBN 13

9780521617710

Readings in Artificial Intelligence and Databases

By: John Mylopoulos,Michael L. Brodie

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Readings in Artificial Intelligence and Databases

By: John Mylopoulos,Michael L. Brodie

The interaction of database and AI technologies is crucial to such applications as data mining, active databases, and knowledge-based expert systems. This volume collects the primary readings on the interactions, actual and potential, between these two fields. The editors have chosen articles to balance significant early research and the best and most comprehensive articles from the 1980s. An in-depth introduction discusses basic research motivations, giving a survey of the history, concepts, and terminology of the interaction. Major themes, approaches and results, open issues and future directions are all discussed, including the results of a major survey conducted by the editors of current work in industry and research labs. Thirteen sections follow, each with a short introduction. Topics examined include semantic data models with emphasis on conceptual modeling techniques for databases and information systems and the integration of data model concepts in high-level data languages, definition and maintenance of integrity constraints in databases and knowledge bases, natural language front ends, object-oriented database management systems, implementation issues such as concurrency control and error recovery, and representation of time and knowledge incompleteness from the viewpoints of databases, logic programming, and AI.

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697

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Morgan Kaufmann

Published Date

ISBN 10

0080886620

ISBN 13

9780080886626

A Concise History of Mathematics for Philosophers

By: John Stillwell

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A Concise History of Mathematics for Philosophers

By: John Stillwell

This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics.

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Cambridge University Press

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ISBN 10

1108456235

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9781108456234

Concise Guide to Numerical Algorithmics

The Foundations and Spirit of Scientific Computing

By: John Lawrence Nazareth

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Concise Guide to Numerical Algorithmics

The Foundations and Spirit of Scientific Computing

By: John Lawrence Nazareth

Numerical Algorithmic Science and Engineering (NAS&E), or more compactly, Numerical Algorithmics, is the theoretical and empirical study and the practical implementation and application of algorithms for solving finite-dimensional problems of a numeric nature. The variables of such problems are either discrete-valued, or continuous over the reals, or, and as is often the case, a combination of the two, and they may or may not have an underlying network/graph structure. This re-emerging discipline of numerical algorithmics within computer science is the counterpart of the now well-established discipline of numerical analysis within mathematics, where the latter’s emphasis is on infinite-dimensional, continuous numerical problems and their finite-dimensional, continuous approximates. A discussion of the underlying rationale for numerical algorithmics, its foundational models of computation, its organizational details, and its role, in conjunction with numerical analysis, in support of the modern modus operandi of scientific computing, or computational science & engineering, is the primary focus of this short monograph. It comprises six chapters, each with its own bibliography. Chapters 2, 3 and 6 present the book’s primary content. Chapters 1, 4, and 5 are briefer, and they provide contextual material for the three primary chapters and smooth the transition between them. Mathematical formalism has been kept to a minimum, and, whenever possible, visual and verbal forms of presentation are employed and the discussion enlivened through the use of motivating quotations and illustrative examples. The reader is expected to have a working knowledge of the basics of computer science, an exposure to basic linear algebra and calculus (and perhaps some real analysis), and an understanding of elementary mathematical concepts such as convexity of sets and functions, networks and graphs, and so on. Although this book is not suitable for use as the principal textbook for a course on numerical algorithmics (NAS&E), it will be of value as a supplementary reference for a variety of courses. It can also serve as the primary text for a research seminar. And it can be recommended for self-study of the foundations and organization of NAS&E to graduate and advanced undergraduate students with sufficient mathematical maturity and a background in computing. When departments of computer science were first created within universities worldwide during the middle of the twentieth century, numerical analysis was an important part of the curriculum. Its role within the discipline of computer science has greatly diminished over time, if not vanished altogether, and specialists in that area are now to be found mainly within other fields, in particular, mathematics and the physical sciences. A central concern of this monograph is the regrettable, downward trajectory of numerical analysis within computer science and how it can be arrested and suitably reconstituted. Resorting to a biblical metaphor, numerical algorithmics (NAS&E) as envisioned herein is neither old wine in new bottles, nor new wine in old bottles, but rather this re-emerging discipline is a decantation of an age-old vintage that can hopefully find its proper place within the larger arena of computer science, and at what appears now to be an opportune time.

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Springer Nature

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ISBN 10

3031217624

ISBN 13

9783031217623

Mathematics and Its History

By: John Stillwell

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Mathematics and Its History

By: John Stillwell

A concise, unified view of mathematics together with its historical development. Aiming at mathematicians who have mastered the basic topics but wish to gain a better grasp of mathematics as a whole, the author gives the reasons for the emergence of the main fields of modern mathematics, and explains the connections between them by tracing the course of a few mathematical themes from ancient times down to the 20th century. The emphasis here is on history as a method for unifying and motivating mathematics, rather than as an end in itself, and there is more mathematical detail than in other general histories. However, no historical expertise is assumed, and classical mathematics is rephrased in modern terms where needed. Nevertheless, there are copious references to original sources for readers wishing to explore the classics for themselves. In summary, readers will be able to add to their mathematical knowledge as well as gaining a new perspective on what they already know.

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381

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Springer Science & Business Media

Published Date

ISBN 10

1489900071

ISBN 13

9781489900074

Computability and Logic

By: George S. Boolos,John P. Burgess,Richard C. Jeffrey

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Computability and Logic

By: George S. Boolos,John P. Burgess,Richard C. Jeffrey

This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book has become a classic because of its accessibility to students without a mathematical background, and because it covers not simply the staple topics of an intermediate logic course such as Godel's Incompleteness Theorems, but also a large number of optional topics from Turing's theory of computability to Ramsey's theorem. John Burgess has now enhanced the book by adding a selection of problems at the end of each chapter, and by reorganising and rewriting chapters to make them more independent of each other and thus to increase the range of options available to instructors as to what to cover and what to defer.

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374

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Cambridge University Press

Published Date

ISBN 10

0521007585

ISBN 13

9780521007580

Logic Colloquium 2005

By: Costas Dimitracopoulos,Ludomir Newelski,Dag Normann,John R. Steel

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Logic Colloquium 2005

By: Costas Dimitracopoulos,Ludomir Newelski,Dag Normann,John R. Steel

The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of developments, and the rest of the papers are chosen to complement the invited talks. This 2007 volume includes surveys, tutorials, and selected research papers from the 2005 meeting. Highlights include three papers on different aspects of connections between model theory and algebra; a survey of major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's philosophy of mathematics.

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272

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Cambridge University Press

Published Date

ISBN 10

1139467255

ISBN 13

9781139467254

The Facts on File Dictionary of Mathematics

By: John Daintith,Richard Rennie

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The Facts on File Dictionary of Mathematics

By: John Daintith,Richard Rennie

An illustrated dictionary of mathematical terms and concepts.

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273

Publisher

Infobase Publishing

Published Date

ISBN 10

1438109474

ISBN 13

9781438109473

Applied Analysis

By: John K Hunter,Bruno Nachtergaele

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Applied Analysis

By: John K Hunter,Bruno Nachtergaele

This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems, and is presented clearly and simply but without sacrificing mathematical rigor.The text is accessible to students from a wide variety of backgrounds, including undergraduate students entering applied mathematics from non-mathematical fields and graduate students in the sciences and engineering who want to learn analysis. A basic background in calculus, linear algebra and ordinary differential equations, as well as some familiarity with functions and sets, should be sufficient.

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455

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World Scientific Publishing Company

Published Date

ISBN 10

9813102772

ISBN 13

9789813102774

Superminds

People Harness Hypercomputation, and More

By: Selmer Bringsjord,Michael John Zenzen

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Superminds

People Harness Hypercomputation, and More

By: Selmer Bringsjord,Michael John Zenzen

This is the first book-length presentation and defense of a new theory of human and machine cognition, according to which human persons are superminds. Superminds are capable of processing information not only at and below the level of Turing machines (standard computers), but above that level (the "Turing Limit"), as information processing devices that have not yet been (and perhaps can never be) built, but have been mathematically specified; these devices are known as super-Turing machines or hypercomputers. Superminds, as explained herein, also have properties no machine, whether above or below the Turing Limit, can have. The present book is the third and pivotal volume in Bringsjord's supermind quartet; the first two books were What Robots Can and Can't Be (Kluwer) and AI and Literary Creativity (Lawrence Erlbaum). The final chapter of this book offers eight prescriptions for the concrete practice of AI and cognitive science in light of the fact that we are superminds.

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380

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402010958

ISBN 13

9781402010958

Growing Ideas of Number

By: John N Crossley

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Growing Ideas of Number

By: John N Crossley

Explores the notion of how ideas of number have grown throughout history. Illustrates some of the real problems and subtleties of number, including calculation, measuring, counting, and using machines.

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122

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ACER Press

Published Date

ISBN 10

1429454849

ISBN 13

9781429454841

An Introduction to Nonlinear Chemical Dynamics

Oscillations, Waves, Patterns, and Chaos

By: Irving R. Epstein,John A. Pojman

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An Introduction to Nonlinear Chemical Dynamics

Oscillations, Waves, Patterns, and Chaos

By: Irving R. Epstein,John A. Pojman

Just a few decades ago, chemical oscillations were thought to be exotic reactions of only theoretical interest. Now known to govern an array of physical and biological processes, including the regulation of the heart, these oscillations are being studied by a diverse group across the sciences. This book is the first introduction to nonlinear chemical dynamics written specifically for chemists. It covers oscillating reactions, chaos, and chemical pattern formation, and includes numerous practical suggestions on reactor design, data analysis, and computer simulations. Assuming only an undergraduate knowledge of chemistry, the book is an ideal starting point for research in the field. The book begins with a brief history of nonlinear chemical dynamics and a review of the basic mathematics and chemistry. The authors then provide an extensive overview of nonlinear dynamics, starting with the flow reactor and moving on to a detailed discussion of chemical oscillators. Throughout the authors emphasize the chemical mechanistic basis for self-organization. The overview is followed by a series of chapters on more advanced topics, including complex oscillations, biological systems, polymers, interactions between fields and waves, and Turing patterns. Underscoring the hands-on nature of the material, the book concludes with a series of classroom-tested demonstrations and experiments appropriate for an undergraduate laboratory.

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407

Publisher

Oxford University Press

Published Date

ISBN 10

0198025661

ISBN 13

9780198025665

Population Ecology

First Principles - Second Edition

By: John H. Vandermeer,Deborah E. Goldberg

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Population Ecology

First Principles - Second Edition

By: John H. Vandermeer,Deborah E. Goldberg

The essential introduction to population ecology—now expanded and fully updated Ecology is capturing the popular imagination like never before, with issues such as climate change, species extinctions, and habitat destruction becoming ever more prominent. At the same time, the science of ecology has advanced dramatically, growing in mathematical and theoretical sophistication. Here, two leading experts present the fundamental quantitative principles of ecology in an accessible yet rigorous way, introducing students to the most basic of all ecological subjects, the structure and dynamics of populations. John Vandermeer and Deborah Goldberg show that populations are more than simply collections of individuals. Complex variables such as distribution and territory for expanding groups come into play when mathematical models are applied. Vandermeer and Goldberg build these models from the ground up, from first principles, using a broad range of empirical examples, from animals and viruses to plants and humans. They address a host of exciting topics along the way, including age-structured populations, spatially distributed populations, and metapopulations. This second edition of Population Ecology is fully updated and expanded, with additional exercises in virtually every chapter, making it the most up-to-date and comprehensive textbook of its kind. Provides an accessible mathematical foundation for the latest advances in ecology Features numerous exercises and examples throughout Introduces students to the key literature in the field The essential textbook for advanced undergraduates and graduate students An online illustration package is available to professors

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289

Publisher

Princeton University Press

Published Date

ISBN 10

1400848733

ISBN 13

9781400848737

A Primer on Determinism

By: John Earman

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A Primer on Determinism

By: John Earman

The title of this work is to be taken seriously: it is a small book for teaching students to read the language of determinism. Some prior knowledge of college-level mathematics and physics is presupposed, but otherwise the book is suitable for use in an advanced undergraduate or beginning graduate course in the philosophy of science. While writing I had in mind primarily a philosophical audience, but I hope that students and colleagues from the sciences will also find the treatment of scientific issues of interest. Though modest in not trying to reach beyond an introductory level of analysis, the work is decidedly immodest in trying to change a number of misimpressions that pervade the philosophical literature. For example, when told that classical physics is not the place to look for clean and unproblematic examples of determinism, most philosophers react with a mixture of disbelief and incomprehension. The misconcep tions on which that reaction is based can and must be changed.

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298

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Springer Science & Business Media

Published Date

ISBN 10

9027722404

ISBN 13

9789027722409

The Story of Proof

Logic and the History of Mathematics

By: John Stillwell

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The Story of Proof

Logic and the History of Mathematics

By: John Stillwell

How the concept of proof has enabled the creation of mathematical knowledge The Story of Proof investigates the evolution of the concept of proof—one of the most significant and defining features of mathematical thought—through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as “infinitesimal algebra,” and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved. Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field’s power and progress.

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457

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Princeton University Press

Published Date

ISBN 10

069123437X

ISBN 13

9780691234373

Cloud Computing

Implementation, Management, and Security

By: John W. Rittinghouse,James F. Ransome

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Cloud Computing

Implementation, Management, and Security

By: John W. Rittinghouse,James F. Ransome

Cloud Computing: Implementation, Management, and Security provides an understanding of what cloud computing really means, explores how disruptive it may become in the future, and examines its advantages and disadvantages. It gives business executives the knowledge necessary to make informed, educated decisions regarding cloud initiatives. The authors first discuss the evolution of computing from a historical perspective, focusing primarily on advances that led to the development of cloud computing. They then survey some of the critical components that are necessary to make the cloud computing paradigm feasible. They also present various standards based on the use and implementation issues surrounding cloud computing and describe the infrastructure management that is maintained by cloud computing service providers. After addressing significant legal and philosophical issues, the book concludes with a hard look at successful cloud computing vendors. Helping to overcome the lack of understanding currently preventing even faster adoption of cloud computing, this book arms readers with guidance essential to make smart, strategic decisions on cloud initiatives.

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341

Publisher

CRC Press

Published Date

ISBN 10

1439806810

ISBN 13

9781439806814

Higher-Order Computability

By: John Longley,Dag Normann

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Higher-Order Computability

By: John Longley,Dag Normann

This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations. The subject originated in the 1950s with the work of Kleene, Kreisel and others, and has since expanded in many different directions under the influence of workers from both mathematical logic and computer science. The ideas of higher-order computability have proved valuable both for elucidating the constructive content of logical systems, and for investigating the expressive power of various higher-order programming languages. In contrast to the well-known situation for first-order functions, it turns out that at higher types there are several different notions of computability competing for our attention, and each of these has given rise to its own strand of research. In this book, the authors offer an integrated treatment that draws together many of these strands within a unifying framework, revealing not only the range of possible computability concepts but the relationships between them. The book will serve as an ideal introduction to the field for beginning graduate students, as well as a reference for advanced researchers

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587

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Springer

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ISBN 10

3662479923

ISBN 13

9783662479926

Classical Econophysics

By: Allin F. Cottrell,Paul Cockshott,Gregory John Michaelson,Ian P. Wright,Victor Yakovenko

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Classical Econophysics

By: Allin F. Cottrell,Paul Cockshott,Gregory John Michaelson,Ian P. Wright,Victor Yakovenko

This book sets out to address some basic questions drawing from classical political economy and information theory and using an econophysics methodology: What is information? Why is it valuable? What is the relationship between money and information?

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385

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Routledge

Published Date

ISBN 10

1134020767

ISBN 13

9781134020768

Godel

A Life Of Logic, The Mind, And Mathematics

By: John L. Casti,Werner DePauli,L Casti

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Godel

A Life Of Logic, The Mind, And Mathematics

By: John L. Casti,Werner DePauli,L Casti

Kurt Gödel was an intellectual giant. His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Shattering hopes that logic would, in the end, allow us a complete understanding of the universe, Gödel's theorem also raised many provocative questions: What are the limits of rational thought? Can we ever fully understand the machines we build? Or the inner workings of our own minds? How should mathematicians proceed in the absence of complete certainty about their results? Equally legendary were Gödel's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first book for a general audience on this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life.

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222

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ISBN 10

0786747609

ISBN 13

9780786747603

Dynamics in One Complex Variable

(AM-160) - Third Edition

By: John Milnor

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Dynamics in One Complex Variable

(AM-160) - Third Edition

By: John Milnor

This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.

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313

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Princeton University Press

Published Date

ISBN 10

1400835534

ISBN 13

9781400835539

Beyond Belief

Randomness, Prediction and Explanation in Science

By: John L. Casti

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Beyond Belief

Randomness, Prediction and Explanation in Science

By: John L. Casti

How can we predict and explain the phenomena of nature? What are the limits to this knowledge process? The central issues of prediction, explanation, and mathematical modeling, which underlie all scientific activity, were the focus of a conference organized by the Swedish Council for the Planning and Coordination of Research, held at the Abisko Research Station in May of 1989. At this forum, a select group of internationally known scientists in physics, chemistry, biology, economics, sociology and mathematics discussed and debated the ways in which prediction and explanation interact with mathematical modeling in their respective areas of expertise. Beyond Belief is the result of this forum, consisting of 11 chapters written specifically for this volume. The multiple themes of randomness, uncertainty, prediction and explanation are presented using (as vehicles) several topical areas from modern science, such as morphogenetic fields, Boscovich covariance, and atmospheric variability. This multidisciplinary examination of the foundational issues of modern scientific thought and methodology will offer stimulating reading for a very broad scientific audience.

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458

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CRC Press

Published Date

ISBN 10

1351086995

ISBN 13

9781351086998

Classical Topology and Combinatorial Group Theory

By: John Stillwell

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Classical Topology and Combinatorial Group Theory

By: John Stillwell

This introduction to topology stresses geometric aspects, focusing on historical background and visual interpretation of results. The 2nd edition offers 300 illustrations, numerous exercises, challenging open problems and a new chapter on unsolvable problems.

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360

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Springer Science & Business Media

Published Date

ISBN 10

0387979700

ISBN 13

9780387979700

Reverse Mathematics

Proofs from the Inside Out

By: John Stillwell

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Reverse Mathematics

Proofs from the Inside Out

By: John Stillwell

This volume presents reverse mathematics to a general mathematical audience for the first time. Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. to logic.

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198

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Princeton University Press

Published Date

ISBN 10

0691196419

ISBN 13

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Book's by John F Turing

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