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Author : Robert E. Edwards (Mathematiker)
Publisher :
ISBN 13 : 9783540905134
Total Pages : 606 pages
Book Rating : 4.9/5 (51 download)
Download or read book A Formal Background to Mathematics written by Robert E. Edwards (Mathematiker) and published by . This book was released on 1979 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. E. Edwards
Publisher : Springer Science & Business Media
ISBN 13 : 1461299845
Total Pages : 968 pages
Book Rating : 4.4/5 (612 download)
Download or read book A Formal Background to Mathematics written by R. E. Edwards and published by Springer Science & Business Media. This book was released on 2013-12-18 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: §1 Faced by the questions mentioned in the Preface I was prompted to write this book on the assumption that a typical reader will have certain characteristics. He will presumably be familiar with conventional accounts of certain portions of mathematics and with many so-called mathematical statements, some of which (the theorems) he will know (either because he has himself studied and digested a proof or because he accepts the authority of others) to be true, and others of which he will know (by the same token) to be false. He will nevertheless be conscious of and perturbed by a lack of clarity in his own mind concerning the concepts of proof and truth in mathematics, though he will almost certainly feel that in mathematics these concepts have special meanings broadly similar in outward features to, yet different from, those in everyday life; and also that they are based on criteria different from the experimental ones used in science. He will be aware of statements which are as yet not known to be either true or false (unsolved problems). Quite possibly he will be surprised and dismayed by the possibility that there are statements which are "definite" (in the sense of involving no free variables) and which nevertheless can never (strictly on the basis of an agreed collection of axioms and an agreed concept of proof) be either proved or disproved (refuted).
Author : Robert E. Edwards
Publisher :
ISBN 13 :
Total Pages : 486 pages
Book Rating : 4.3/5 (91 download)
Download or read book A Formal Background to Mathematics written by Robert E. Edwards and published by . This book was released on 1979 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert E. Edwards
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (63 download)
Download or read book A Formal Background to Mathematics written by Robert E. Edwards and published by . This book was released on 1979 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Edmund Edwards
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (834 download)
Download or read book A Formal Background to Mathematics written by Robert Edmund Edwards and published by . This book was released on 1979 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. Edwards
Publisher :
ISBN 13 : 9783540904311
Total Pages : pages
Book Rating : 4.9/5 (43 download)
Download or read book Logic, Sets and Numbers written by R. Edwards and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert E. Edwards
Publisher :
ISBN 13 : 9781461380979
Total Pages : 0 pages
Book Rating : 4.3/5 (89 download)
Download or read book A formal background to mathematics written by Robert E. Edwards and published by . This book was released on 1979 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. E. Edwards
Publisher : Springer Science & Business Media
ISBN 13 : 1461380960
Total Pages : 651 pages
Book Rating : 4.4/5 (613 download)
Download or read book A Formal Background to Mathematics 2a written by R. E. Edwards and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 606 pages
Book Rating : 4.:/5 (926 download)
Download or read book A Formal Background to Mathematics written by and published by . This book was released on 1979 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. E. Edwards
Publisher : Springer
ISBN 13 : 9780387905136
Total Pages : 606 pages
Book Rating : 4.9/5 (51 download)
Download or read book A Formal Background to Mathematics 2a written by R. E. Edwards and published by Springer. This book was released on 1980-10-20 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. G. Hamilton
Publisher : Cambridge University Press
ISBN 13 : 9780521287616
Total Pages : 272 pages
Book Rating : 4.2/5 (876 download)
Download or read book Numbers, Sets and Axioms written by A. G. Hamilton and published by Cambridge University Press. This book was released on 1982 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.
Author : Angelo Margaris
Publisher : Courier Corporation
ISBN 13 : 9780486662695
Total Pages : 244 pages
Book Rating : 4.6/5 (626 download)
Download or read book First Order Mathematical Logic written by Angelo Margaris and published by Courier Corporation. This book was released on 1990-01-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Attractive and well-written introduction." — Journal of Symbolic Logic The logic that mathematicians use to prove their theorems is itself a part of mathematics, in the same way that algebra, analysis, and geometry are parts of mathematics. This attractive and well-written introduction to mathematical logic is aimed primarily at undergraduates with some background in college-level mathematics; however, little or no acquaintance with abstract mathematics is needed. Divided into three chapters, the book begins with a brief encounter of naïve set theory and logic for the beginner, and proceeds to set forth in elementary and intuitive form the themes developed formally and in detail later. In Chapter Two, the predicate calculus is developed as a formal axiomatic theory. The statement calculus, presented as a part of the predicate calculus, is treated in detail from the axiom schemes through the deduction theorem to the completeness theorem. Then the full predicate calculus is taken up again, and a smooth-running technique for proving theorem schemes is developed and exploited. Chapter Three is devoted to first-order theories, i.e., mathematical theories for which the predicate calculus serves as a base. Axioms and short developments are given for number theory and a few algebraic theories. Then the metamathematical notions of consistency, completeness, independence, categoricity, and decidability are discussed, The predicate calculus is proved to be complete. The book concludes with an outline of Godel's incompleteness theorem. Ideal for a one-semester course, this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. Carefully chosen exercises, with selected answers, help students test their grasp of the material. For any student of mathematics, logic, or the interrelationship of the two, this book represents a thought-provoking introduction to the logical underpinnings of mathematical theory. "An excellent text." — Mathematical Reviews
Author : Damir D. Dzhafarov
Publisher : Springer Nature
ISBN 13 : 3031113675
Total Pages : 498 pages
Book Rating : 4.0/5 (311 download)
Download or read book Reverse Mathematics written by Damir D. Dzhafarov and published by Springer Nature. This book was released on 2022-07-25 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reverse mathematics studies the complexity of proving mathematical theorems and solving mathematical problems. Typical questions include: Can we prove this result without first proving that one? Can a computer solve this problem? A highly active part of mathematical logic and computability theory, the subject offers beautiful results as well as significant foundational insights. This text provides a modern treatment of reverse mathematics that combines computability theoretic reductions and proofs in formal arithmetic to measure the complexity of theorems and problems from all areas of mathematics. It includes detailed introductions to techniques from computable mathematics, Weihrauch style analysis, and other parts of computability that have become integral to research in the field. Topics and features: Provides a complete introduction to reverse mathematics, including necessary background from computability theory, second order arithmetic, forcing, induction, and model construction Offers a comprehensive treatment of the reverse mathematics of combinatorics, including Ramsey's theorem, Hindman's theorem, and many other results Provides central results and methods from the past two decades, appearing in book form for the first time and including preservation techniques and applications of probabilistic arguments Includes a large number of exercises of varying levels of difficulty, supplementing each chapter The text will be accessible to students with a standard first year course in mathematical logic. It will also be a useful reference for researchers in reverse mathematics, computability theory, proof theory, and related areas. Damir D. Dzhafarov is an Associate Professor of Mathematics at the University of Connecticut, CT, USA. Carl Mummert is a Professor of Computer and Information Technology at Marshall University, WV, USA.
Author : Werner Balser
Publisher : Springer Science & Business Media
ISBN 13 : 0387225986
Total Pages : 314 pages
Book Rating : 4.3/5 (872 download)
Download or read book Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations written by Werner Balser and published by Springer Science & Business Media. This book was released on 2008-01-19 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.
Author : Egan J Chernoff
Publisher : IAP
ISBN 13 : 1681233037
Total Pages : 463 pages
Book Rating : 4.6/5 (812 download)
Download or read book Selected writings from the Journal of the British Columbia Association of Mathematics Teachers written by Egan J Chernoff and published by IAP. This book was released on 2016-06-01 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: The teaching and learning of mathematics in British Columbia has a long and storied history. An integral part of the past 50 years (1962-2012) of this history has been Vector: Journal of the British Columbia Association of Mathematics Teachers. This volume, which presents ten memorable articles from each of the past five decades, that is, 50 articles from the past 50 years of the journal, provides an opportunity to share this rich history with a wide range of individuals interested in the teaching and learning of mathematics and mathematics education. Each decade begins with an introduction, providing a historical context, and concludes with a commentary from a prominent member of the British Columbia mathematics education community. As a result, this monograph provides a historical account as well as a contemporary view of many of the trends and issues in the teaching and learning of mathematics. This volume is meant to serve as a resource for a variety of individuals including: teachers of mathematics, mathematics teacher educators, mathematics education researchers, historians, and undergraduate and graduate students. Most importantly, this volume is a celebratory retrospective on the work of the British Columbia Association of Mathematics Teachers.
Author : Roman Kossak
Publisher : Springer
ISBN 13 : 3319972987
Total Pages : 186 pages
Book Rating : 4.3/5 (199 download)
Download or read book Mathematical Logic written by Roman Kossak and published by Springer. This book was released on 2018-10-03 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.
Author : Hardy Grant
Publisher : Birkhäuser
ISBN 13 : 1493932640
Total Pages : 109 pages
Book Rating : 4.4/5 (939 download)
Download or read book Turning Points in the History of Mathematics written by Hardy Grant and published by Birkhäuser. This book was released on 2016-04-15 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation. Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the “wedding,” via analytic geometry, of algebra and geometry; the “taming” of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor’s creation of transfinite set theory. The origin of each turning point is discussed, along with the mathematicians involved and some of the mathematics that resulted. Problems and projects are included in each chapter to extend and increase understanding of the material. Substantial reference lists are also provided. Turning Points in the History of Mathematics will be a valuable resource for teachers of, and students in, courses in mathematics or its history. The book should also be of interest to anyone with a background in mathematics who wishes to learn more about the important moments in its development.
