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  1. The Mathematical Experience: Study Edition.Philip J. Davis - 1981 - Birkhäuser.
    Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...
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  2. Reasoning by Mathematical Induction in Children's Arithmetic.Leslie Smith - 2002 - Elsevier.
    The central argument that Leslie Smith makes in this study is that reasoning by mathematical induction develops during childhood. The basis for this claim is a study conducted with children aged five to seven years in school years one and two.
  3. Learning to Reason: An Introduction to Logic, Sets, and Relations.Nancy Rodgers - 2000 - Wiley.
    Learn how to develop your reasoning skills and how to write well-reasoned proofs Learning to Reason shows you how to use the basic elements of mathematical language to develop highly sophisticated, logical reasoning skills. You'll get clear, concise, easy-to-follow instructions on the process of writing proofs, including the necessary reasoning techniques and syntax for constructing well-written arguments. Through in-depth coverage of logic, sets, and relations, Learning to Reason offers a meaningful, integrated view of modern mathematics, cuts through confusing terms and (...)
  4. Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century.Paolo Mancosu (ed.) - 1996 - Oxford, England: Oxford University Press.
    The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...)
  5. Simple Logic.Daniel Bonevac - 1998 - Oxford and New York: Oup Usa.
    Simple Logic succeeds in conveying the standard topics in introductory logic with easy-to-understand explanations of rules and methods, whilst featuring a multitude of interesting and relevant examples drawn from both literary texts and contemporary culture.
  6. Symbolic Logic and Mechanical Theorem Proving.Chin-Liang Chang - 1973 - New York, NY, USA: Academic Press.
    This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4–9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
  7. Logic Minimization Algorithms for Vlsi Synthesis.Robert K. Brayton, Gary D. Hachtel, C. McMullen & Alberto Sangiovanni-Vincentelli - 1984 - Springer Verlag.
    The roots of the project which culminates with the writing of this book can be traced to the work on logic synthesis started in 1979 at the IBM Watson Research Center and at University of California, Berkeley. During the preliminary phases of these projects, the impor tance of logic minimization for the synthesis of area and performance effective circuits clearly emerged. In 1980, Richard Newton stirred our interest by pointing out new heuristic algorithms for two-level logic minimization and the potential (...)
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  8. Symbolic Logic.Dale Jacquette - 2001 - Wadsworth Publishing Company.
    This comprehensive intro text covers central topics of elementary and symbolic logic. It contains many problems and exercises and provides a solid foundation for continued study of advanced topics in logic.
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  9. IB Course Companion: Mathematical Studies.Stephen Bedding, Mal Coad, Jane Forrest, Beryl Fussey & Paula Waldman de Tokman - 2007 - Oxford University Press.
    This book has been designed specifically to support the student through the IB Diploma Programme in Mathematical Studies. It includes worked examples and numerous opportunities for practice. In addition the book will provide students with features integrated with study and learning approaches, TOK and the IB learner profile. Examples and activities drawn from around the world will encourage students to develop an international perspective.
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  10. Mathematical Studies.Stephen Bedding, Mal Coad, Jane Forrest, Beryl Fussey & Paula Waldman de Tokman - 2007 - Oxford University Press.
    This book has been designed specifically to support the student through the IB Diploma Programme in Mathematical Studies. It includes worked examples and numerous opportunities for practice. In addition the book will provide students with features integrated with study and learning approaches, TOK and the IB learner profile. Examples and activities drawn from around the world will encourage students to develop an international perspective.
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  11. The Combinatory Programme.Erwin Engeler (ed.) - 1994 - Birkhäuser.
    Combinatory logic started as a programme in the foundation of mathematics and in an historical context at a time when such endeavours attracted the most gifted among the mathematicians. This small volume arose under quite differ ent circumstances, namely within the context of reworking the mathematical foundations of computer science. I have been very lucky in finding gifted students who agreed to work with me and chose, for their Ph. D. theses, subjects that arose from my own attempts 1 to (...)
  12. Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education.Sal Restivo, Jean Paul Van Bendegem & Roland Fischer (eds.) - 1993 - State University of New York Press.
    An international group of distinguished scholars brings a variety of resources to bear on the major issues in the study and teaching of mathematics, and on the problem of understanding mathematics as a cultural and social phenomenon. All are guided by the notion that our understanding of mathematical knowledge must be grounded in and reflect the realities of mathematical practice. Chapters on the philosophy of mathematics illustrate the growing influence of a pragmatic view in a field traditionally dominated by platonic (...)
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  13. The Logic of History.Charles Morazé - 1976 - Mouton.
  14. Non-Standard Logics for Automated Reasoning.Philippe Smets (ed.) - 1988 - Academic Press.
    Although there are a few books available that give brief surveys of a variety of nonstandard logics, there is a growing need for a critical presentation providing both a greater depth and breadth of insight into these logics. This book assembles a wider and deeper view of the many potentially applicable logics. Three appendixes provide short tutorials on classical logic and modal logics, and give a brief introduction to the existing literature on the logical aspects of probability theory. These tutorials (...)
  15. The Laboratory of the Mind: Thought Experiments in the Natural Sciences.James Robert Brown - 1991 - Routledge.
    Newton's bucket, Einstein's elevator, Schrödinger's cat – these are some of the best-known examples of thought experiments in the natural sciences. But what function do these experiments perform? Are they really experiments at all? Can they help us gain a greater understanding of the natural world? How is it possible that we can learn new things just by thinking? In this revised and updated new edition of his classic text _The Laboratory of the Mind_, James Robert Brown continues to defend (...)
  16. Computer Science Logic: 6th Workshop, Csl'92, San Miniato, Italy, September 28 - October 2, 1992. Selected Papers.Egon Börger, Gerhard Jäger, Hans Kleine Büning, Simone Martini & Michael M. Richter - 1993 - Springer Verlag.
    This workshop on stochastic theory and adaptive control assembled many of the leading researchers on stochastic control and stochastic adaptive control to increase scientific exchange and cooperative research between these two subfields of stochastic analysis. The papers included in the proceedings include survey and research. They describe both theoretical results and applications of adaptive control. There are theoretical results in identification, filtering, control, adaptive control and various other related topics. Some applications to manufacturing systems, queues, networks, medicine and other topics (...)
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  17. Uncertain Inference.Henry E. Kyburg Jr, Jr. Kyburg & Choh Man Teng - 2001 - Cambridge University Press.
    Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. For example, it is a vital element in developing artificial intelligence that will not be undermined by its own rigidities. There have been many approaches to the problem of uncertain inference, ranging from probability to inductive logic to nonmonotonic logic. Thisbook seeks to provide a clear exposition of these approaches within a unified framework. The principal market for the book (...)
  18. Computer Science Logic 5th Workshop, Csl '91, Berne, Switzerland, October 7-11, 1991 : Proceedings'.Egon Börger, Gerhard Jäger, Hans Kleine Büning & Michael M. Richter - 1992 - Springer.
    This volume presents the proceedings of the workshop CSL '91 held at the University of Berne, Switzerland, October 7-11, 1991. This was the fifth in a series of annual workshops on computer sciencelogic. The volume contains 33 invited and selected papers on a variety of logical topics in computer science, including abstract datatypes, bounded theories, complexity results, cut elimination, denotational semantics, infinitary queries, Kleene algebra with recursion, minimal proofs, normal forms in infinite-valued logic, ordinal processes, persistent Petri nets, plausibility logic, (...)
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  19. Conversations on Mind, Matter, and Mathematics.Jean-Pierre Changeux & Alain Connes - 1998 - Princeton University Press.
    "This wonderfully eloquent and playful colloquy of two brilliant minds gives new life to the old notion of Dialogue, a sadly forgotten form now.... I "love" this book!
  20. Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences.Ivor Grattan-Guinness (ed.) - 1993 - Routledge.
    The Companion Encyclopedia is the first comprehensive work to cover all the principal lines and themes of the history and philosophy of mathematics from ancient times up to the twentieth century. In 176 articles contributed by 160 authors of 18 nationalities, the work describes and analyzes the variety of theories, proofs, techniques, and cultural and practical applications of mathematics. The work's aim is to recover our mathematical heritage and show the importance of mathematics today by treating its interactions with the (...)
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  21. History and Philosophy of Modern Mathematics.William Aspray & Philip Kitcher - 1988 - U of Minnesota Press.
    History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In (...)
  22. EPSA Philosophical Issues in the Sciences · Launch of the European Philosophy of Science Association.Mauricio Suárez, Mauro Dorato & Miklós Rédei (eds.) - 2009 - Dordrecht, Netherland: Springer.
    This volume collects papers presented at the Founding Conference of the European Philosophy of Science Association meeting, held November 2007. It provides an excellent overview of the state of the art in philosophy of science in different European countries.
  23. Sweet Reason: A Field Guide to Modern Logic.James M. Henle, Jay L. Garfield, Thomas Tymoczko & Emily Altreuter - 1995 - New York and Oxford: Wiley-Blackwell.
    _Sweet Reason: A Field Guide to Modern Logic, 2nd Edition_ offers an innovative, friendly, and effective introduction to logic. It integrates formal first order, modal, and non-classical logic with natural language reasoning, analytical writing, critical thinking, set theory, and the philosophy of logic and mathematics. An innovative introduction to the field of logic designed to entertain as it informs Integrates formal first order, modal, and non-classical logic with natural language reasoning, analytical writing, critical thinking, set theory, and the philosophy of (...)
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  24. Foundations: Logic, Language, and Mathematics.Hugues Leblanc, Elliott Mendelson & A. Orenstein - 1984 - Dordrecht, Netherland: Springer.
  25. Mathematics, a Concise History and Philosophy.W. S. Anglin - 1994 - Springer.
    This is a concise introductory textbook for a one semester course in the history and philosophy of mathematics. It is written for mathematics majors, philosophy students, history of science students and secondary school mathematics teachers. The only prerequisite is a solid command of pre-calculus mathematics. It is shorter than the standard textbooks in that area and thus more accessible to students who have trouble coping with vast amounts of reading. Furthermore, there are many detailed explanations of the important mathematical procedures (...)
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  26. Notes on Logic and Set Theory.P. T. Johnstone - 1987 - Cambridge University Press.
    A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed (...)
  27. Descartes' Dream: The World According to Mathematics.Philip J. Davis - 1986 - Dover Publications.
    Philosopher Rene Descartes visualized a world unified by mathematics, in which all intellectual issues could be resolved rationally by local computation. This series of provocative essays takes a modern look at the seventeenth-century thinker’s dream, examining the physical and intellectual influences of mathematics on society, particularly in light of technological advances. They survey the conditions that elicit the application of mathematic principles; the effectiveness of these applications; and how applied mathematics constrain lives and transform perceptions of reality. Highly suitable for (...)
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  28. Mathematical Reasoning: Analogies, Metaphors, and Images.Lyn D. English (ed.) - 1997 - L. Erlbaum Associates.
    Presents the latest research on how reasoning with analogies, metaphors, metonymies, and images can facilitate mathematical understanding. For math education, educational psychology, and cognitive science scholars.
  29. Godel's Theorem in Focus.S. G. Shanker (ed.) - 1987 - Routledge.
    A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.
  30. Instantiation Theory on the Foundations of Automated Deduction.James G. Williams - 1991 - Springer Verlag.
    This monograph presents a new, general algorithm for use in building theorem provers and logic programming systems. The algorithm is based on a theory that may be developed into a general theory of logics. Appropriate applications of the algorithm and its underlying theory are given.
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  31. The Reality of Numbers: A Physicalist's Philosophy of Mathematics.John Bigelow - 1988 - Oxford, England: Oxford University Press.
    Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.
  32. The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford, England: Oxford University Press.
    This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...
  33. Mathematics in a Postmodern Age a Christian Perspective.Russell W. Howell & James Bradley - 2001 - Eerdmans Publishing Company.
    The discipline of mathematics has not been spared the sweeping critique of postmodernism. Is mathematical theory true for all time, or are mathematical constructs in fact fallible? This fascinating book examines the tensions that have arisen between modern and postmodern views of mathematics, explores alternative theories of mathematical truth, explains why the issues are important, and shows how a Christian perspective makes a difference. Contributors: W. James Bradley William Dembski Russell W. Howell Calvin Jongsma David Klanderman Christopher Menzel Glen VanBrummelen (...)
  34. What is Mathematics, Really.Reuben Hersh - 1997 - Oxford, England: Oxford University Press.
    Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist (...)
  35. The Foundations of Arithmetic: A Logico-Mathematical Enquiry Into the Concept of Number.J. L. Austin (ed.) - 1950 - New York, NY, USA: Northwestern University Press.
    _The Foundations of Arithmetic_ is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics and in general ontology.
  36. Non-Standard Analysis.Abraham Robinson - 1961 - North-Holland Publishing Co..
    Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested (...)
  37. Mathematics Without Numbers: Towards a Modal-Structural Interpretation.Geoffrey Hellman - 1989 - Oxford, England: Oxford University Press.
    Develops a structuralist understanding of mathematics, as an alternative to set- or type-theoretic foundations, that respects classical mathematical truth while ...
  38. Hyperproof: For Macintosh.Jon Barwise & John Etchemendy - 1994 - Center for the Study of Language and Inf.
    Hyperproof is a system for learning the principles of analytical reasoning and proof construction, consisting of a text and a Macintosh software program. Unlike traditional treatments of first-order logic, Hyperproof combines graphical and sentential information, presenting a set of logical rules for integrating these different forms of information. This strategy allows students to focus on the information content of proofs, rather than the syntactic structure of sentences. Using Hyperproof the student learns to construct proofs of both consequence and nonconsequence using (...)
  39. An Accompaniment to Higher Mathematics.George R. Exner - 1997 - Springer.
    This text prepares undergraduate mathematics students to meet two challenges in the study of mathematics, namely, to read mathematics independently and to understand and write proofs. The book begins by teaching how to read mathematics actively, constructing examples, extreme cases, and non-examples to aid in understanding an unfamiliar theorem or definition (a technique famililar to any mathematician, but rarely taught); it provides practice by indicating explicitly where work with pencil and paper must interrupt reading. The book then turns to proofs, (...)
  40. Where Mathematics Comes From How the Embodied Mind Brings Mathematics Into Being.George Lakoff & Rafael E. Núñez - 2000
  41. The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
    Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...)
  42. Tarski's World Version 4.0 for Ms Windows.Jon Barwise & John Etchemendy - 1993
  43. Principles of Mathematics.Bertrand Russell - 1937 - Routledge.
    Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...)
  44. A Computational Logic Handbook.Robert S. Boyer, Robert S. Boyer & J. Strother Moore - 1988
  45. Logic for Information Technology.Antony Galton - 1990
    The value of logic techniques in circuit design has been well-known for many years, but a thorough grounding in mathematical logic is needed for all stages of software development, especially program specification, verification and program transformation. In all these stages, logic underpins the theory, bearing out the dictum that Logic is the calculus of computer science. This book presents the subject of mathematical logic in order to provide a grounding for students in computer science.
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  46. Science in the Looking Glass: What Do Scientists Really Know?E. Brian Davies - 2003 - Oxford University Press UK.
    How do scientific conjectures become laws? Why does proof mean different things in different sciences? Do numbers exist, or were they invented? Why do some laws turn out to be wrong? In this wide-ranging book, Brian Davies discusses the basis for scientists' claims to knowledge about the world. He looks at science historically, emphasizing not only the achievements of scientists from Galileo onwards, but also their mistakes. He rejects the claim that all scientific knowledge is provisional, by citing examples from (...)
  47. First Logic.Michael F. Goodman - 1992 - Lanham, MD, USA: Upa.
    This third edition includes expanded exercise sets for all chapters, updated examples, and extended discussion of concepts such as inductive reasoning, truth trees, and natural deduction. This text will be helpful to all those who are interested in learning about the discipline of logic.
  48. Converging Realities: Toward a Common Philosophy of Physics and Mathematics.Roland Omnès - 2004 - Princeton University Press.
    The philosophical relationship between mathematics and the natural sciences is the subject of Converging Realities, the latest work by one of the leading thinkers on the subject.
  49. Realism in Mathematics.Penelope Maddy - 1990 - Oxford, England and New York, NY, USA: Oxford University Prress.
    Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...)
  50. Understanding the Infinite.Shaughan Lavine - 1994 - Cambridge, MA and London: Harvard University Press.
    An engaging account of the origins of the modern mathematical theory of the infinite, his book is also a spirited defense against the attacks and misconceptions ...
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