The Elements of Mathematical Logic

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Author: Paul C. Rosenbloom

Publisher: Courier Corporation

ISBN: 0486446174

Category: Mathematics

Page: 214

View: 9360

This introduction to mathematical logic stresses the use of logical methods in attacking nontrivial problems. It covers the logic of classes, of propositions, of propositional functions, and the general syntax of language, with a brief introduction to so-called undecidability and incompleteness theorems; and much more. 1950 edition.

The Elements of Advanced Mathematics

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Author: Steven G. Krantz

Publisher: CRC Press

ISBN: 9780849384912

Category: Mathematics

Page: 176

View: 1703

Clearly written and easy to understand, The Elements of Advanced Mathematics covers logic, set theory, methods of proof, and axiomatic structures, providing an excellent grounding in analytical thinking. It facilitates the transition from elementary mathematics, generally characterized by problem-solving techniques, to advanced mathematics, characterized by theory, rigor, and proofs. This text clearly identifies and explains the components and methods of advanced mathematics. Each chapter contains exercises designed to assist the reader in understanding the material.

Direct and Converse Theorems

The Elements of Symbolic Logic

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Author: I. S. Gradshtein

Publisher: Elsevier

ISBN: 1483155072

Category: Mathematics

Page: 192

View: 8383

Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chapter explains several questions of mathematical logic–a science that is being developed in connection with the theory of mathematical proof. This edition is provided with a large number of problems and questions to help easily understand the material. The book is intended for students studying mathematics, specifically at intermediate colleges of various types. The text is also a useful reference for university students and teachers.

The Elements of Mathematical Semantics

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Author: Maurice V. Aldridge

Publisher: Walter de Gruyter

ISBN: 3110871432

Category: Language Arts & Disciplines

Page: 272

View: 3341

TRENDS IN LINGUISTICS is a series of books that open new perspectives in our understanding of language. The series publishes state-of-the-art work on core areas of linguistics across theoretical frameworks as well as studies that provide new insights by building bridges to neighbouring fields such as neuroscience and cognitive science. TRENDS IN LINGUISTICS considers itself a forum for cutting-edge research based on solid empirical data on language in its various manifestations, including sign languages. It regards linguistic variation in its synchronic and diachronic dimensions as well as in its social contexts as important sources of insight for a better understanding of the design of linguistic systems and the ecology and evolution of language. TRENDS IN LINGUISTICS publishes monographs and outstanding dissertations as well as edited volumes, which provide the opportunity to address controversial topics from different empirical and theoretical viewpoints. High quality standards are ensured through anonymous reviewing.

The Elements of Advanced Mathematics, Second Edition

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Author: Steven G. Krantz

Publisher: CRC Press

ISBN: 9781584883036

Category: Mathematics

Page: 232

View: 2449

The gap between the rote, calculational learning mode of calculus and ordinary differential equations and the more theoretical learning mode of analysis and abstract algebra grows ever wider and more distinct, and students' need for a well-guided transition grows with it. For more than six years, the bestselling first edition of this classic text has helped them cross the mathematical bridge to more advanced studies in topics such as topology, abstract algebra, and real analysis. Carefully revised, expanded, and brought thoroughly up to date, the Elements of Advanced Mathematics, Second Edition now does the job even better, building the background, tools, and skills students need to meet the challenges of mathematical rigor, axiomatics, and proofs. New in the Second Edition: Expanded explanations of propositional, predicate, and first-order logic, especially valuable in theoretical computer science A chapter that explores the deeper properties of the real numbers, including topological issues and the Cantor set Fuller treatment of proof techniques with expanded discussions on induction, counting arguments, enumeration, and dissection Streamlined treatment of non-Euclidean geometry Discussions on partial orderings, total ordering, and well orderings that fit naturally into the context of relations More thorough treatment of the Axiom of Choice and its equivalents Additional material on Russell's paradox and related ideas Expanded treatment of group theory that helps students grasp the axiomatic method A wealth of added exercises

A Concise Introduction to Mathematical Logic

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Author: Wolfgang Rautenberg

Publisher: Springer

ISBN: 9781441912213

Category: Mathematics

Page: 320

View: 1273

Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

Elements of the History of Mathematics

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Author: N. Bourbaki

Publisher: Springer Science & Business Media

ISBN: 3642616933

Category: Mathematics

Page: 301

View: 4599

Each volume of Nicolas Bourbakis well-known work, The Elements of Mathematics, contains a section or chapter devoted to the history of the subject. This book collects together those historical segments with an emphasis on the emergence, development, and interaction of the leading ideas of the mathematical theories presented in the Elements. In particular, the book provides a highly readable account of the evolution of algebra, geometry, infinitesimal calculus, and of the concepts of number and structure, from the Babylonian era through to the 20th century.

Elements of Intuitionism

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Author: Michael A. E. Dummett

Publisher: Oxford University Press

ISBN: 9780198505242

Category: Mathematics

Page: 331

View: 5450

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.

Theory of Sets

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Author: N. Bourbaki

Publisher: Springer Science & Business Media

ISBN: 9783540225256

Category: Mathematics

Page: 414

View: 5579

This is a softcover reprint of the English translation of 1968 of N. Bourbaki's, Théorie des Ensembles (1970).

Elements of Mathematical Logic

(Model Theory)

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Author: Georg Kreisel,Jean Louis Krivine

Publisher: Elsevier

ISBN: 9780444534125

Category: Electronic books

Page: 222

View: 467

Handbook of Mathematical Logic

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Author: J. Barwise

Publisher: Elsevier

ISBN: 9780080933641

Category: Mathematics

Page: 1164

View: 1073

The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.

Handbook of Logic and Proof Techniques for Computer Science

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Author: Steven G. Krantz

Publisher: Springer Science & Business Media

ISBN: 1461201152

Category: Computers

Page: 245

View: 9725

Logic is, and should be, the core subject area of modern mathemat ics. The blueprint for twentieth century mathematical thought, thanks to Hilbert and Bourbaki, is the axiomatic development of the subject. As a result, logic plays a central conceptual role. At the same time, mathematical logic has grown into one of the most recondite areas of mathematics. Most of modern logic is inaccessible to all but the special ist. Yet there is a need for many mathematical scientists-not just those engaged in mathematical research-to become conversant with the key ideas of logic. The Handbook of Mathematical Logic, edited by Jon Bar wise, is in point of fact a handbook written by logicians for other mathe maticians. It was, at the time of its writing, encyclopedic, authoritative, and up-to-the-moment. But it was, and remains, a comprehensive and authoritative book for the cognoscenti. The encyclopedic Handbook of Logic in Computer Science by Abramsky, Gabbay, and Maibaum is a wonderful resource for the professional. But it is overwhelming for the casual user. There is need for a book that introduces important logic terminology and concepts to the working mathematical scientist who has only a passing acquaintance with logic. Thus the present work has a different target audience. The intent of this handbook is to present the elements of modern logic, including many current topics, to the reader having only basic mathe matical literacy.

Handbook of Set Theory

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Author: Matthew Foreman,Akihiro Kanamori

Publisher: Springer Science & Business Media

ISBN: 1402057644

Category: Mathematics

Page: 2230

View: 1275

Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.

A Profile of Mathematical Logic

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Author: Howard DeLong

Publisher: Courier Corporation

ISBN: 0486139158

Category: Mathematics

Page: 320

View: 1112

This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.

The Elements of Euclid

With Select Theorems Out of Archimedes by the Learned Andrew Tacquet. To which are Added, Practical Corollaries, Shewing the Uses of Many of the Propositions ...

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Author: Euclid

Publisher: N.A

ISBN: N.A

Category: Geometry

Page: 308

View: 6307

The Elements of Creativity and Giftedness in Mathematics

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Author: B. Sriraman,Kyeong Hwa Lee

Publisher: Springer Science & Business Media

ISBN: 946091439X

Category: Education

Page: 240

View: 8024

The Elements of Creativity and Giftedness in Mathematics edited by Bharath Sriraman and KyeongHwa Lee covers recent advances in mathematics education pertaining to the development of creativity and giftedness. The book is international in scope in the “sense” that it includes numerous studies on mathematical creativity and giftedness conducted in the U.S.A, China, Korea, Turkey, Israel, Sweden, and Norway in addition to cross-national perspectives from Canada and Russia. The topics include problem -posing, problem-solving and mathematical creativity; the development of mathematical creativity with students, pre and in-service teachers; cross-cultural views of creativity and giftedness; the unpacking of notions and labels such as high achieving, inclusion, and potential; as well as the theoretical state of the art on the constructs of mathematical creativity and giftedness. The book also includes some contributions from the first joint meeting of the American Mathematical Society and the Korean Mathematical Society in Seoul, 2009. Topics covered in the book are essential reading for graduate students and researchers interested in researching issues and topics within the domain of mathematical creativity and mathematical giftedness. It is also accessible to pre-service and practicing teachers interested in developing creativity in their classrooms, in addition to professional development specialists, mathematics educators, gifted educators, and psychologists.