Foundations Of Mathematics

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The Foundations of Mathematics

Kenneth Kunen
The Foundations of Mathematics Book PDF

Author : Kenneth Kunen
Publisher : Unknown
Page : 251 pages
File Size : 50,9 Mb
Release : 2009
Category : Mathematics
ISBN : 1904987141

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The Foundations of Mathematics by Kenneth Kunen Pdf

Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.

Reflections on the Foundations of Mathematics

Stefania Centrone,Deborah Kant,Deniz Sarikaya
Reflections on the Foundations of Mathematics Book PDF

Author : Stefania Centrone,Deborah Kant,Deniz Sarikaya
Publisher : Springer Nature
Page : 511 pages
File Size : 45,5 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9783030156558

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Reflections on the Foundations of Mathematics by Stefania Centrone,Deborah Kant,Deniz Sarikaya Pdf

This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.

Foundations of Mathematics 9 S Tudent Edition

McGraw-Hill Ryerson, Limited
Foundations of Mathematics 9 S Tudent Edition Book PDF

Author : McGraw-Hill Ryerson, Limited
Publisher : Unknown
Page : 460 pages
File Size : 48,7 Mb
Release : 2013-04-23
Category : Mathematics
ISBN : 1259077411

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Foundations of Mathematics 9 S Tudent Edition by McGraw-Hill Ryerson, Limited Pdf

"A new resource written specifically for the Foundations of Mathematics 9 (MFM 1P) course. The McGraw-Hill Ryerson Foundations of Mathematics 9 program is a carefully blended mix of print and digital resources designed to meet all teaching and learning needs."--Publ. website.

Introduction to the Foundations of Mathematics

Raymond L. Wilder
Introduction to the Foundations of Mathematics Book PDF

Author : Raymond L. Wilder
Publisher : Courier Corporation
Page : 352 pages
File Size : 47,9 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780486276205

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Introduction to the Foundations of Mathematics by Raymond L. Wilder Pdf

Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.

The Foundations of Mathematics in the Theory of Sets

John P. Mayberry
The Foundations of Mathematics in the Theory of Sets Book PDF

Author : John P. Mayberry
Publisher : Cambridge University Press
Page : 454 pages
File Size : 52,8 Mb
Release : 2000
Category : Mathematics
ISBN : 0521770343

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The Foundations of Mathematics in the Theory of Sets by John P. Mayberry Pdf

This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.

The Logical Foundations of Mathematics

William S. Hatcher
The Logical Foundations of Mathematics Book PDF

Author : William S. Hatcher
Publisher : Elsevier
Page : 330 pages
File Size : 49,9 Mb
Release : 2014-05-09
Category : Mathematics
ISBN : 9781483189635

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The Logical Foundations of Mathematics by William S. Hatcher Pdf

The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems. The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory. Comprised of eight chapters, this book begins with an introduction to first-order logic. In particular, two complete systems of axioms and rules for the first-order predicate calculus are given, one for efficiency in proving metatheorems, and the other, in a "natural deduction" style, for presenting detailed formal proofs. A somewhat novel feature of this framework is a full semantic and syntactic treatment of variable-binding term operators as primitive symbols of logic. Subsequent chapters focus on the origin of modern foundational studies; Gottlob Frege's formal system intended to serve as a foundation for mathematics and its paradoxes; the theory of types; and the Zermelo-Fraenkel set theory. David Hilbert's program and Kurt Gödel's incompleteness theorems are also examined, along with the foundational systems of W. V. Quine and the relevance of categorical algebra for foundations. This monograph will be of interest to students, teachers, practitioners, and researchers in mathematics.

Foundations of Mathematics

Philip Brown
Foundations of Mathematics Book PDF

Author : Philip Brown
Publisher : Mercury Learning and Information
Page : 382 pages
File Size : 44,7 Mb
Release : 2016-03-14
Category : Mathematics
ISBN : 9781944534417

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Foundations of Mathematics by Philip Brown Pdf

Foundations of Mathematics offers the university student or interested reader a unique reference book by covering the basics of algebra, trigonometry, geometry, and calculus. There are many instances in the book to demonstrate the interplay and interconnectedness of these topics. The book presents definitions and examples throughout for clear, easy learning. Numerous exercises are included at the ends of the chapters, and readers are encouraged to complete all of them as an essential part of working through the book. It offers a unique experience for readers to understand different areas of mathematics in one clear, concise text. Instructors’ resources are available upon adoption. Features: •Covers the basics of algebra, trigonometry, geometry, and calculus •Includes all of the mathematics needed to learn calculus •Demonstrates the interplay and interconnectedness of these topics •Uses numerous examples and exercises to reinforce concepts

Conceptions of Set and the Foundations of Mathematics

Luca Incurvati
Conceptions of Set and the Foundations of Mathematics Book PDF

Author : Luca Incurvati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 41,9 Mb
Release : 2020-01-23
Category : History
ISBN : 9781108497824

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Conceptions of Set and the Foundations of Mathematics by Luca Incurvati Pdf

Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.

New Foundations in Mathematics

Garret Sobczyk
New Foundations in Mathematics Book PDF

Author : Garret Sobczyk
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 41,6 Mb
Release : 2012-10-26
Category : Mathematics
ISBN : 9780817683856

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New Foundations in Mathematics by Garret Sobczyk Pdf

The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.

Foundations of Constructive Mathematics

M.J. Beeson
Foundations of Constructive Mathematics Book PDF

Author : M.J. Beeson
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642689529

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Foundations of Constructive Mathematics by M.J. Beeson Pdf

This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connec tions with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Con structive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind.

Practical Foundations of Mathematics

Paul Taylor
Practical Foundations of Mathematics Book PDF

Author : Paul Taylor
Publisher : Cambridge University Press
Page : 590 pages
File Size : 55,8 Mb
Release : 1999-05-13
Category : Mathematics
ISBN : 0521631076

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Practical Foundations of Mathematics by Paul Taylor Pdf

This book is about the basis of mathematical reasoning both in pure mathematics itself (particularly algebra and topology) and in computer science (how and what it means to prove correctness of programs). It contains original material and original developments of standard material, so it is also for professional researchers, but as it deliberately transcends disciplinary boundaries and challenges many established attitudes to the foundations of mathematics, the reader is expected to be open minded about these things.

Foundations of Logic and Mathematics

Yves Nievergelt
Foundations of Logic and Mathematics Book PDF

Author : Yves Nievergelt
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201250

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Foundations of Logic and Mathematics by Yves Nievergelt Pdf

This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.

Foundations of Mathematics and Physics One Century After Hilbert

Joseph Kouneiher
Foundations of Mathematics and Physics One Century After Hilbert Book PDF

Author : Joseph Kouneiher
Publisher : Springer
Page : 441 pages
File Size : 52,6 Mb
Release : 2018-05-26
Category : Science
ISBN : 9783319648132

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Foundations of Mathematics and Physics One Century After Hilbert by Joseph Kouneiher Pdf

This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating. All those who want to benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too.

Cultural Foundations of Mathematics

C. K. Raju
Cultural Foundations of Mathematics Book PDF

Author : C. K. Raju
Publisher : Pearson Education India
Page : 536 pages
File Size : 50,8 Mb
Release : 2007
Category : Calculus
ISBN : 8131708713

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Cultural Foundations of Mathematics by C. K. Raju Pdf

The Volume Examines, In Depth, The Implications Of Indian History And Philosophy For Contemporary Mathematics And Science. The Conclusions Challenge Current Formal Mathematics And Its Basis In The Western Dogma That Deduction Is Infallible (Or That It Is Less Fallible Than Induction). The Development Of The Calculus In India, Over A Thousand Years, Is Exhaustively Documented In This Volume, Along With Novel Insights, And Is Related To The Key Sources Of Wealth-Monsoon-Dependent Agriculture And Navigation Required For Overseas Trade - And The Corresponding Requirement Of Timekeeping. Refecting The Usual Double Standard Of Evidence Used To Construct Eurocentric History, A Single, New Standard Of Evidence For Transmissions Is Proposed. Using This, It Is Pointed Out That Jesuits In Cochin, Following The Toledo Model Of Translation, Had Long-Term Opportunity To Transmit Indian Calculus Texts To Europe. The European Navigational Problem Of Determining Latitude, Longitude, And Loxodromes, And The 1582 Gregorian Calendar-Reform, Provided Ample Motivation. The Mathematics In These Earlier Indian Texts Suddenly Starts Appearing In European Works From The Mid-16Th Century Onwards, Providing Compelling Circumstantial Evidence. While The Calculus In India Had Valid Pramana, This Differed From Western Notions Of Proof, And The Indian (Algorismus) Notion Of Number Differed From The European (Abacus) Notion. Hence, Like Their Earlier Difficulties With The Algorismus, Europeans Had Difficulties In Understanding The Calculus, Which, Like Computer Technology, Enhanced The Ability To Calculate, Albeit In A Way Regarded As Epistemologically Insecure. Present-Day Difficulties In Learning Mathematics Are Related, Via Phylogeny Is Ontogeny , To These Historical Difficulties In Assimilating Imported Mathematics. An Appendix Takes Up Further Contemporary Implications Of The New Philosophy Of Mathematics For The Extension Of The Calculus, Which Is Needed To Handle The Infinities Arising In The Study Of Shock Waves And The Renormalization Problem Of Quantum Field Theory.

Foundations of Mathematical Analysis

Richard Johnsonbaugh,W.E. Pfaffenberger
Foundations of Mathematical Analysis Book PDF

Author : Richard Johnsonbaugh,W.E. Pfaffenberger
Publisher : Courier Corporation
Page : 450 pages
File Size : 46,9 Mb
Release : 2012-09-11
Category : Mathematics
ISBN : 9780486134772

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Foundations of Mathematical Analysis by Richard Johnsonbaugh,W.E. Pfaffenberger Pdf

Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.