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SPIRES-BOOKS: FIND KEYWORD LOGIC,SYMBOLIC AND MATHEMATICAL *END*INIT* use /tmp/qspiwww.webspi1/9808.66 QRY 131.225.70.96 . find keyword logic,symbolic and mathematical ( in books using www Cover
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Call number:SPRINGER-2014-9789462390249:ONLINE Show nearby items on shelf
Title:Recent Progress in General Topology III [electronic resource]
Author(s): K.P Hart
J van Mill
P Simon
Date:2014
Publisher:Paris : Atlantis Press : Imprint: Atlantis Press
Size:1 online resource
Note:The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland,1992 and 2002). The boo k was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in2002. The following areas experienced signifi cant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems
Contents:Topological Homogeneity
Some Recent Progress Concerning Topology of Fractals
A biased view of topology as a tool in functional analysis
Large scale versus small scale
Descriptive aspects of Rosenthal compacta
Minimality conditions in topological groups
Set
Theoretic update on Topology
Topics in Dimension Theory
Representations of dynamical systems on Banach spaces
Generalized metrizable spaces
Permanence in Coarse Geometry
Selections and Hyperspaces
Continuum Theory
Almost disjoint families and topology
Some Topics in Geometric Topology II
Topologic
ISBN:9789462390249
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Functional analysis , Logic, Symbolic and mathematical , Topology
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Call number:SPRINGER-2014-9789400775480:ONLINE Show nearby items on shelf
Title:Advances in Natural Deduction [electronic resource] : A Celebration of Dag Prawitz's Work
Author(s): Luiz Carlos Pereira
Edward Hermann Haeusler
Valeria de Paiva
Date:2014
Publisher:Dordrecht : Springer Netherlands : Imprint: Springer
Size:1 online resource
Note:This collection of papers celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour hisseminal research. Dag Prawit zs work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics andTheoretical Computer Science. The range of contributions includes ma terial on the extension of natural deduction with higher-order rules, as opposed to higher-order connectives, and a paper discussing the application of naturaldeduction rules to dealing with equality in predicate calculus. The volume continues with a key chapter summarizing work on the extension of the Curry-Howard isomorphism (itself a by-product of the work on natural deduction), viamethods of category theory that have been successfully applied to linear logic, as well as many other contributions from h ighly regarded authorities. With an illustrious group of contributors addressing a wealth of topics andapplications, this volume is a valuable addition to the libraries of academics in the multiple disciplines whose development has been given added scope by the methodologies supplied by natural deduction. The volume is representative ofthe rich and varied directions that Prawitz work has inspired in the area of natural deduction.
Contents:Chapter 1. Generalizaed elimination inferences Schroeder
Heister, Peter
Chapter 2. Revisiting Zucker's work on the Correspondence between Cut
Elimination and Normalisation Urban, Christian
Chapter 3. Proofs, Reasoning and the Metamorphosis of Logic Joinet, Jean
Baptiste
Chapter 4. Natural Deduction for Equality: The Missing Entity de Quieroz, Ruy J.G.B. and de Oliveira, Anjolina G
Chapter 5. Proof
theoretical Conception of Logic Legris, Javier
Chapter 6. On the Structure of Natural deduction Derivations for Generally Vana, Leonardo B., Veloso, Paulo A.S. , and Veloso, Sh
ISBN:9789400775480
Series:eBooks
Series:SpringerLink
Series:Trends in Logic, Studia Logica Library, 1572-6126 : v39
Series:Mathematics and Statistics (Springer-11649)
Keywords: Philosophy (General) , Logic , Computer science , Logic, Symbolic and mathematical
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Call number:SPRINGER-2014-9783764385040:ONLINE Show nearby items on shelf
Title:Kripkes Worlds [electronic resource] : An Introduction to Modal Logics via Tableaux
Author(s): Olivier Gasquet
Andreas Herzig
Bilal Said
Franois Schwarzentruber
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Possible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible worlds model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics(alethic, temporal, epis temic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, conditional, several paraconsistent and relevant logics). All these logics havebeen studied intensively in philosophical an d mathematical logic and in computer science, and have been applied increasingly in domains such as program semantics, artificial intelligence, and more recently in the semantic web.Additionally, all these logics were also studied proof theoretically. The proof systems for modal logics come in various styles: Hilbert style, natural deduction, sequents, and resolution. However, it is fair to say that the mostuniform and most successful such systems are tableaux systems. Given a logic and a formula, they al low one to check whether there is a model in that logic. This basically amounts to trying to build a model for the formula by building atree. This book follows a more general approach by trying to build a graph, the advantage being that a graph is closer to a Kripke model than a tree. It provides a step-by-step introduction to possible worlds semantics (and by that tomodal and other nonclassical logics) via the tableaux method. It is accompanied by a piece of software called LoTREC (www.irit.fr/Lotrec). L oTREC allows to check whether a given formula is true at a given world of a given model and tocheck whether a given formula is satisfiable in a given logic. The latter can be done immediately if the tableau system for that logic has already been implement ed in LoTREC. If this is not yet the case LoTREC offers the possibility toimplement a tableau system in a relatively easy way via a simple, graph-based, interactive language. >dy>
Contents:Preface
1 Modelling things with graphs
2 Talking about graphs
3 The basics of the model construction method
4 Logics with simple constraints on models
5 Logics with transitive accessibility relations
6 Model Checking
7 Modal logics with transitive closure
Bibliography
Index
ISBN:9783764385040
Series:eBooks
Series:SpringerLink
Series:Studies in Universal Logic
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical
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Call number:SPRINGER-2014-9783319067438:ONLINE Show nearby items on shelf
Title:Duality Theories for Boolean Algebras with Operators [electronic resource]
Author(s): Steven Givant
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:In this new text, Steven Givantthe author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarskidevelops three theories of duality for Boolean algebras with operators. Givant addressesthe two most recognized dualit ies (one algebraic and the other topological) and introduces a third duality, best understood as a hybrid of the first two. This text will be of interest to graduate students and researchers in the fieldsof mathematics, computer science, logic, and philos ophy who are interested in exploring special or general classes of Boolean algebras with operators. Readers should be familiar with the basic arithmetic and theory of Boolean algebras,as well as the fundamentals of point-set topology
Contents:1. Algebraic Duality
2. Topological Duality
3. Hybrid Duality
ISBN:9783319067438
Series:eBooks
Series:SpringerLink
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Logic, Symbolic and mathematical
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Call number:SPRINGER-2014-9783319067254:ONLINE Show nearby items on shelf
Title:Set Theory [electronic resource] : Exploring Independence and Truth
Author(s): Ralf Schindler
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of largecardinals, inner models, forcin g, and descriptive set theory. The following topics are covered: Forcing and constructability The Solovay-Shelah Theorem i.e. the equiconsistency of every set of reals is Lebesguemeasurable with one inaccessible cardinal Fine structure theory and a m odern approach to sharps Jensens Covering Lemma The equivalence of analytic determinacy with sharps The theory of extenders and iterationtrees A proof of projective determinacy from Woodin cardinals. Set Theory requires only a basic knowledge of math ematical logic and will be suitable for advanced students and researchers
Contents:Naive set theory
Axiomatic set theory
Ordinals
Cardinals
Constructability
Forcing
Descriptive set theory
Solovays model
The Raisonnier filter
Measurable cardinals
0# and Jensens Covering Lemma
Analytic and full determinacy
Projective determinacy
ISBN:9783319067254
Series:eBooks
Series:SpringerLink
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical
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Call number:SPRINGER-2014-9783319060804:ONLINE Show nearby items on shelf
Title:Recent Trends in Philosophical Logic [electronic resource]
Author(s): Roberto Ciuni
Heinrich Wansing
Caroline Willkommen
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This volume presents recent advances in philosophical logic with chapters focusing on non-classical logics, including paraconsistent logics, substructural logics, modal logics of agency and other modal logics. The authors coverthemes such as the know ability paradox, tableaux and sequent calculi, natural deduction, definite descriptions, identity, truth, dialetheism, and possible worlds semantics. The developments presented here focus on challengingproblems in the specification of fundamental philoso phical notions, as well as presenting new techniques and tools, thereby contributing to the development of the field. Each chapter contains a bibliography, to assist the reader inmaking connections in the specific areas covered. Thus this work provides bo th a starting point for further investigations into philosophical logic and an update on advances, techniques and applications in a dynamic field. Thechapters originate from papers presented during the Trends in Logic XI conference at the Ruhr University Bochum, June 2012
Contents:Chapter 1. Semantic Defectiveness: A Dissolution of Semantic Pathology Bradley Armour
Garb and James A. Woodbridge
Chapter 2. Emptiness and discharge in sequent calculus and natural deduction Michael Arndt and Luca Tranchini
Chapter 3. The Knowability Paradox in the light of a Logic for Pragmatics Massimiliano Carrara and Daniele Chi
Chapter 4. A Dialetheic Interpretation of Classical Logic Massimiliano Carrara and Enrico Martino
Chapter 5. Strongly semantic information as information about the truth Gustavo Cevolani
Chapter 6. Priest's Motorbike and Tolerant Identity Pabl
ISBN:9783319060804
Series:eBooks
Series:SpringerLink
Series:Trends in Logic, Studia Logica Library, 1572-6126 : v41
Series:Mathematics and Statistics (Springer-11649)
Keywords: Philosophy (General) , Genetic epistemology , Logic , Logic, Symbolic and mathematical
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Call number:SPRINGER-2014-9783319054469:ONLINE Show nearby items on shelf
Title:Perspectives in Computational Complexity [electronic resource] : The Somenath Biswas Anniversary Volume
Author(s): Manindra Agrawal
Vikraman Arvind
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Birkhuser
Size:1 online resource
Note:This book brings together contributions by leading researchers in computational complexity theory written in honor of Somenath Biswas on the occasion of his sixtieth birthday. They discuss current trends and exciting developmentsin this flourishing a rea of research and offer fresh perspectives on various aspects of complexity theory. The topics covered include arithmetic circuit complexity, lower bounds and polynomial identity testing, the isomorphismconjecture, space-bounded computation, graph isomo rphism, resolution and proof complexity, entropy and randomness. Several chapters have a tutorial flavor. The aim is to make recent research in these topics accessible to graduatestudents and senior undergraduates in computer science and mathematics. It c an also be useful as a resource for teaching advanced level courses in computational complexity
Contents:Preface
1. Complexity Theory Basics: NP and NL (Vikraman Arvind)
2. Investigations Concerning the Structure of Complete Sets (Eric Allender)
3. Space Complexity of the Directed Reachability Problem Over Surface
embedded Graphs (N.V. Vinodchandran)
4. Algebraic Complexity Classes (Meena Mahajan)
5. A Selection of Lower Bound Results for Arithmetic Circuits (Neeraj Kayal and Ramprasad Saptharishi)
6. Explicit Tensors (Markus Blser)
7. Progress on Polynomial Identity Testing (Nitin Saxena)
8. Malod and the Pascaline (Bruno Poizat)
9. A Tutorial in Time and Space Bound
ISBN:9783319054469
Series:eBooks
Series:SpringerLink
Series:Progress in Computer Science and Applied Logic : v26
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Logic, Symbolic and mathematical
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Call number:SPRINGER-2014-9783319048611:ONLINE Show nearby items on shelf
Title:Janus-Faced Probability [electronic resource]
Author(s): Paolo Rocchi
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The problem of probability interpretation was long overlooked before exploding in the 20th century, when the frequentist and subjectivist schools formalized two conflicting conceptions of probability. Beyond the radical followersof the two schools, a circle of pluralist thinkers tends to reconcile the opposing concepts. The author uses two theorems in order to prove that the various interpretations of probability do not come into opposition and can be used indifferent contexts. The goal here is to cl arify the multifold nature of probability by means of a purely mathematical approach and to show how philosophical arguments can only serve to deepen actual intellectual contrasts. The book canbe considered as one of the most important contributions in th e analysis of probability interpretation in the last 10-15 years
Contents:1 Interpretations of Probability
2 A Mathematical Approach to the Interpretation Problem
3 Probability Validation
4 About the Compatibility of Methods
5 Criticism on the Philosophical Pollution
6Some Remarks on the Argument of Probability
7Classical Modeling of the Probability Argument
8 Structural Modeling of the Probability Argument
9Mathematical Definitions of Probability on the Basis of the Structural Model
10 Exploring into the Essence of Events.
ISBN:9783319048611
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical , Distribution (Probability theory)
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Call number:SPRINGER-2014-9783319047478:ONLINE Show nearby items on shelf
Title:A Cp-Theory Problem Book [electronic resource] : Special Features of Function Spaces
Author(s): Vladimir V Tkachuk
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The books in Vladimir Tkachuks A Cp-Theory Problem Book series will be the go to texts for basic reference to Cp-theory. This second volume, Special Features of Function Spaces, gives a reasonably complete coverage ofCp-theory, systematically introdu cing each of the major topics and providing 500 carefully selected problems and exercises with complete solutions. Bonus results and open problems are also given. The text is designed to bring adedicated reader from basic topological principles to the fro ntiers of modern research covering a wide variety oftopics in Cp-theory and general topology at the professional level. The first volume, Topological and Function Spaces 2011, provided an introduction from scratch to Cp-theory and general topology, prepar ing the reader for a professional understanding of Cp-theory in the last section of its main text. This second volume continues from the first, andcan be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide fo r specialists working in Cp-theory and related topics. Additionally, the material can also be considered as an introductionto advanced set theory and descriptive set theory, presenting diverse topics of the theory of function spaces with the topology of p ointwise convergence, or Cp-theory which exists at the intersection of topological algebra, functionalanalysis and general topology. From the Reviews of Topological and Function Spaces: It is designed to bring a dedicated reader from the basic topological principles to the frontiers of modern research. Any reasonable course incalculus covers everything needed to understand this book. This volume can also be used as a reference for mathematicians working in or outside the field of topology (functional anal ysis) wanting to use results or methods ofCp-theory...On the whole, the book provides a useful addition to the literature on Cp-theory, especially at the instructional level. (Ma
Contents:Detailed Summary of Exercise Sections
Preface
Introduction
1. Duality Theorems and Properties of Function Spaces
2. Solutions of Problems 001
500
3. Bonus Results: Some Hidden statements
4. Open Problems
Bibliography
List of Special Symbols
Index
ISBN:9783319047478
Series:eBooks
Series:SpringerLink
Series:Problem Books in Mathematics, 0941-3502
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Logic, Symbolic and mathematical , Topology
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Call number:SPRINGER-2014-9783319015897:ONLINE Show nearby items on shelf
Title:Non-commutative Multiple-Valued Logic Algebras [electronic resource]
Author(s): Lavinia Corina Ciungu
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras a subject which has attracted much interest in the past few years because of its impact on informationscience, artificial intelli gence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices,pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebrasin thatalgebraic structures can be developed into fuzzy logics which connect quantum mechanics,mathematical logic, probability theory, algebra and soft computing. Written in a c lear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well asresearchers in mathematical logic and theoretical computer science
Contents:Pseudo
BCK algebras
Pseudo
hoops
Residuated lattices
Other non
commutative multiple
valued logic algebras
Classes of non
commutative residuated structures
States on multiple
valued logic algebras
Measures on pseudo
BCK algebras
Generalized states on residuated structures
Pseudo
hoops with internal states
ISBN:9783319015897
Series:eBooks
Series:SpringerLink
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Logic, Symbolic and mathematical , Distribution (Probability theory)
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Call number:SPRINGER-2014-9783319004822:ONLINE Show nearby items on shelf
Title:Leniewski's Systems of Logic and Foundations of Mathematics [electronic resource]
Author(s): Rafal Urbaniak
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw Leniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsawschool. The authors nuanced survey eschews secondary commentary, analyzing Leniewski's core philosophical views and evaluating the formulations that were to have such a profound influence on the evolution of mathematical logic. One of the undisputed leaders of the cohort of brillia nt logicians that congregated in Poland in the early twentieth century, Leniewski was a guide and mentor to a generation of celebrated analytical philosophers (Alfred Tarski washis PhD student). His primary achievement was a system of foundational mathema tical logic intended as an alternative to the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. Its three strandsprotothetic,ontology, and mereology, are detailed in discrete sections of this volume, alongside a wealth other chapters g rouped to provide the fullest possible coverage of Leniewskis academic output. With material on his earlyphilosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophys great pioneers
Contents:Chapter 1: Introduction
Chapter 2. Leniewski's early philosophical views
Chapter 3. Leniewski's Protothetic
Chapter 4. Leniewski's Ontology
Chapter 5. Leniewski's Mereology
Chapter 6. Leniewski and definitions
Chapter 7. Sets revisited
Chapter 8. Nominalism and higher
order quantification
ISBN:9783319004822
Series:eBooks
Series:SpringerLink
Series:Trends in Logic, Studia Logica Library, 1572-6126 : v37
Series:Mathematics and Statistics (Springer-11649)
Keywords: Philosophy (General) , Logic , Science Philosophy , Logic, Symbolic and mathematical
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Call number:SPRINGER-2014-9783034808316:ONLINE Show nearby items on shelf
Title:The Philosophy of Mathematics and Logic in the 1920s and 1930s in Poland [electronic resource]
Author(s): Roman Murawski
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period inthe history of Polish sc ience, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophicalreflection. We try to answer those questions by an alyzing both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polishscientists will be analyzed: Wacaw Sierpiski, Zygmunt Janiszewski, Stef an Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy ylisk and Leon Chwistek, Jan ukasiewicz, Zygmunt Zawirski, Stanisaw Leniewski, TadeuszKotarbiski, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyski, Stanisaw Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we considerin Chapter 1 some predecessors, in particular: Jan niadecki, Jzef Maria Hoene-Wroski, Samuel Dickstein and Edward Stamm
Contents:Introduction
Predecessors
The Polish School of Mathematics
Lvov
Warsaw School of Philosophy
Benedykt Bornstein
Cracow Centre
Conclusion
Biographical Notes
Bibliography
Index of Names
ISBN:9783034808316
Series:eBooks
Series:SpringerLink
Series:Science Networks. Historical Studies, 1421-6329 : v48
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Philosophy (General) , Logic , Logic, Symbolic and mathematical
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Call number:SPRINGER-2014-9783034807302:ONLINE Show nearby items on shelf
Title:Cardinal Invariants on Boolean Algebras [electronic resource] : Second Revised Edition
Author(s): J. Donald Monk
Date:2014
Edition:2nd ed. 2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its freesubalgebras, and cellularity , which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour ofthese functions under algebraic operations such as p roducts, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinitecombinatorics and forcing, the book reviews current knowledge about these f unctions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based onCardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) b y the same author, the present work is much larger than either of these. It contains solutions to many of the open problems of theearlier volumes. Among the new topics are continuum cardinals on Boolean algebras, with a lengthy treatment of the reaping nu mber. Diagrams at the end of the book summarize the relationships between the functions for many importantclasses of Boolean algebras, including interval algebras, tree algebras and superatomic algebras
Contents:Introduction
1. Special Operations on Boolean Algebras
2. Special Classes of Boolean Algebras
3. Cellularity
4. Depth
5. Topological Density
6. Pi
Weight
7. Length
8. Irredundance
9. Cardinality
10. Independence
11. Pi
Character
12. Tightness
13. Spread
14. Character
15. Hereditary Lindelf Degree
16. Hereditary Density
17. Incomparability
18. Hereditary Cofinality
19. Number of Ultrafilters
20. Number of Automorphisms
21. Number of Endomorphisms
22. Number of Ideals
23. Number of Subalgebras
24. Other Cardinal Functions
ISBN:9783034807302
Series:eBooks
Series:SpringerLink
Series:Progress in Mathematics, 0743-1643 : v142
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Logic, Symbolic and mathematical
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Call number:SPRINGER-2014-9781493914746:ONLINE Show nearby items on shelf
Title:Alfred Tarski [electronic resource] : Early Work in PolandGeometry and Teaching
Author(s): Andrew McFarland
Joanna McFarland
James T Smith
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Alfred Tarski (19011983) was a renowned Polish/American mathematician, a giant of the twentieth century, who helped establish the foundations of geometry, set theory, model theory, algebraic logic, and universal algebra.Throughout his career, he taug ht mathematics and logic at universities and sometimes in secondary schools. Many of his writings before 1939 were in Polish and remained inaccessible to most mathematicians and historians until now. Thisself-contained book focuses on Tarskis early contri butions to geometry and mathematics education, including the famous BanachTarski paradoxical decomposition of a sphere as well as high-school mathematical topics and pedagogy.These themes are significant since Tarskis later research on geometry and its fo undations stemmed in part from his early employment as a high-school mathematics teacher and teacher-trainer. The book contains careful translations andmuch newly uncovered social background of these works written during Tarskis years in Poland. Alfred Ta rski: Early Work in PolandGeometry and Teaching serves the mathematical, educational, philosophical, and historicalcommunities by publishing Tarskis early writings in a broadly accessible form, providing background from archival work in Poland, and updati ng Tarskis bibliography
Contents:1 Tarskis first paper
1.1 Introduction
1.2 Item 1 below (nearing completion)
2 Papers on equidecomposibility of polygons
2.1 Introduction
2.2 Item 2 below (nearing completion)
2.3 Item 6 below (old translation, needs redoing)
2.4 Item 8 below (old translation, needs redoing)
2.5 Exercise 31pc in item 11g below
3 Papers related to secondary teaching
3.1 Introduction
3.2 Item 4 below (meeting report)
3.3 Item 7 below (on circles, nearing completion)
3.4 Extract from Item 9 below (textbook)
3.5 Remainder of item 11 below (exercises)
4 Assorted cont
ISBN:9781493914746
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Logic, Symbolic and mathematical
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Call number:SPRINGER-2014-9781461488545:ONLINE Show nearby items on shelf
Title:Set Theory [electronic resource] : With an Introduction to Real Point Sets
Author(s): Abhijit Dasgupta
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbookpresents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins withthe DedekindPeano axioms and ends with the construction of the real numbers. The core CantorDedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundationalissues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theorysuch as the resolution of Lusin's problems on projective sets using determinacy of infinite ga mes and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable forstudents interested in any field of mathematics, not just for those planning to specialize in logic or foundations. The re is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semesteror one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a r elevant or adjacent area and beginners wanting to learn set theory via self-study
Contents:1 Preliminaries: Sets, Relations, and Functions
Part I Dedekind: Numbers
2 The DedekindPeano Axioms
3 Dedekinds Theory of the Continuum
4 Postscript I: What Exactly Are the Natural Numbers?
Part II Cantor: Cardinals, Order, and Ordinals
5 Cardinals: Finite, Countable, and Uncountable
6 Cardinal Arithmetic and the Cantor Set
7 Orders and Order Types
8 Dense and Complete Orders
9 Well
Orders and Ordinals
10 Alephs, Cofinality, and the Axiom of Choice
11 Posets, Zorns Lemma, Ranks, and Trees
12 Postscript II: Innitary Combinatorics
Part III Re
ISBN:9781461488545
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic , Algebra , Global analysis (Mathematics) , Logic, Symbolic and mathematical , Topology
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Call number:SPRINGER-2013-9783642331497:ONLINE Show nearby items on shelf
Title:Stochastic Calculus with Infinitesimals [electronic resource]
Author(s): Frederik Herzberg
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences(for instance in financia l mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts frommeasure theory and functional analysis or lack ful l mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's radically elementary theory of continuous-time stochastic processes, it is based on ademonstrably consistent use of infinitesimals and thus permits a radically s implified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of optionpricing and the Feynman path integral) are also discussed in the book
Note:Springer eBooks
Contents:1 Infinitesimal calculus, consistently and accessibly
2 Radically elementary probability theory
3 Radically elementary stochastic integrals
4 The radically elementary Girsanov theorem and the diffusion invariance principle
5 Excursion to nancial economics: A radically elementary approach to the fundamental theorems of asset pricing
6 Excursion to financial engineering: Volatility invariance in the Black
Scholes model
7 A radically elementary theory of It diffusions and associated partial differential equations
8 Excursion to mathematical physics: A radically elementary d
ISBN:9783642331497
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2067
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical , Distribution (Probability theory)
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Call number:SPRINGER-2013-9783540708568:ONLINE Show nearby items on shelf
Title:Ernst Zermelo - Collected Works/Gesammelte Werke II [electronic resource] : Volume II/Band II - Calculus of Variations, Applied Mathematics, and Physics/Variationsrechnung, Angewandte Mathematik und Physik
Author(s): Ernst Zermelo
Heinz-Dieter Ebbinghaus
Akihiro Kanamori
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Springer eBooks
ISBN:9783540708568
Series:e-books
Series:SpringerLink (Online service)
Series:Schriften der Mathematisch-naturwissenschaftlichen Klasse der Heidelberger Akademie der Wissenschaften : v23
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Science History , Philosophy (General) , Computer science , Logic, Symbolic and mathematical
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Call number:SPRINGER-2013-9783319015774:ONLINE Show nearby items on shelf
Title:The Real Numbers [electronic resource] An Introduction to Set Theory and Analysis
Author(s): John Stillwell
Date:2013
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
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Note:Springer 2013 e-book collections
Note:While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbersto model the line, an d to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theoryuncountability, the axiom of choice, and large cardinals. In fact, virtually all theconcepts of infinite set theory are needed fo r a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines adown-to-earth introduction to set theory with an exposition of the essen ce of analysisthe study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate studentsand professional mathematicians who, until now, have been content to assume the real numbers. I ts prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of realnumber and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich pr esentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will helpmotivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncoun table sets, countable ordinals, the continuum problem, the CantorSchrderBernsteintheorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions
Note:Springer eBooks
Contents:The Fundamental Questions
From Discrete to Continuous
Infinite Sets
Functions and Limits
Open Sets and Continuity
Ordinals
The Axiom of Choice
Borel Sets
Measure Theory
Reflections
Bibliography
Index
ISBN:9783319015774
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical
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Call number:SPRINGER-2013-9783319013336:ONLINE Show nearby items on shelf
Title:The Mathematics of Coordinated Inference [electronic resource] A Study of Generalized Hat Problems
Author(s): Christopher S Hardin
Alan D Taylor
Date:2013
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
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Note:Two prisoners are told that they will be brought to a room and seated so that each can see the other. Hats will be placed on their headseach hat is either red or green. The two prisoners must simultaneouslysubmit a guess oftheir own hat color, and th ey both go free if atleast one of them guesses correctly. While no communication is allowedonce the hats have been placed, they will, however, be allowed to havea strategy session before being broughtto the room. Is there astrategy ensuring their release? The answer turns out to be yes, and this is the simplest non-trivial example of a hat problem. This book deals with the question of how successfully one can predict thevalue of an arbitrary function at one or more points of its domainbased on some knowle dge of its values at other points. Topics rangefrom hat problems that are accessible to everyone willing to thinkhard, to some advanced topicsin set theory and infinitarycombinatorics. For example, there is a method of predicting the valuef(a) of a functi on f mapping the reals to the reals, based only onknowledge of f's values on the open interval (a 1, a), and foreverysuch function the prediction is incorrect only on a countable set that is nowhere dense. The monograph progresses from topics requiring f ewer prerequisites to those requiring more, with most of the text being accessible to anygraduate student in mathematics. The broad range of readership includes researchers, postdocs, and graduate students in the fields of set theory, mathematical logic, and combinatorics, The hope is that this book will bring togethermathematicians from different areas to think about set theory via a very broad array of coordinated inference problems
Note:Springer eBooks
Contents:1. Introduction
2. The Finite Setting
3. The Denumerable Setting: Full Visibility
4. The Denumerable Setting: One
Way Visibility
5. Dual Hat Problems and the Uncountable
6. Galvin's Setting: Neutral and Anonymous Predictors
7. The Topological Setting
8. Universality of the
Predictor
9. Generalizations and Galois
Tukey Connections
Bibliography
Index
ISBN:9783319013336
Series:e-books
Series:SpringerLink (Online service)
Series:Developments in Mathematics, 1389-2177 : v33
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical , Topology
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Call number:SPRINGER-2013-9783319009667:ONLINE Show nearby items on shelf
Title:Mathematics, Computer Science and Logic - A Never Ending Story [electronic resource] : The Bruno Buchberger Festschrift
Author(s): Peter Paule
Date:2013
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
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Note:This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of theseconcepts, the essays pla ce strong emphasis on developments still to come. The book originated in a 2002 symposium celebrating the work of Bruno Buchberger, Professor of Computer Mathematics at Johannes Kepler University, Linz, Austria,on the occasion of his 60th birthday. Among many other accomplishments, Professor Buchberger in 1985 was the founding editor of the Journal of Symbolic Computation the founder of the Research Institute for Symbolic Computation (RISC)and its chairman from 1987-2000 the founder in 1990 of the Softwar epark Hagenberg, Austria, and since then its director. More than a decade in the making, Mathematics, Computer Science and Logic - A Never Ending Story includes essaysby leading authorities, on such topics as mathematical foundations from the perspective of computer verification a symbolic-computational philosophy and methodology for mathematics the role of logic and algebra in softwareengineering and new directions in the foundations of mathematics. These inspiring essays invite general, mathematically i nterested readers to share state-of-the-art ideas which advance the never ending story of mathematics, computerscience and logic. Mathematics, Computer Science and Logic - A Never Ending Story is edited by Professor Peter Paule, Bruno Buchbergers successo r as director of the Research Institute for Symbolic Computation
Note:Springer eBooks
Contents:Preface
Henk Barendregt: Foundations of Mathematics from the Perspective of Computer Verification
Manfred Broy: On the Role of Logic and Algebra in Software Engineering
Stephen Wolfram: New Directions in the Foundations of Mathematics (2002)
Doron Zeilberger: Towards a Symbolic Computational Philosophy (and Methodology!) for Mathematics
ISBN:9783319009667
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Software engineering , Information theory , Algorithms , Computer software , Logic, Symbolic and mathematical
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Call number:SPRINGER-2013-9783319001197:ONLINE Show nearby items on shelf
Title:Logical Foundations of Mathematics and Computational Complexity [electronic resource] : A Gentle Introduction
Author(s): Pavel Pudlk
Date:2013
Publisher:Heidelberg : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
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Note:The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broadspectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areasare connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability.Emphasis is on explaining the essence of concepts and the ideas of p roofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to moredifficult ones. The notes after each section present some formal definitions, theorems a nd proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who areinterested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory
Note:Springer eBooks
Contents:Mathematicians world
Language, logic and computations
Set theory
Proofs of impossibility
The complexity of computations
Proof complexity
Consistency, Truth and Existence
References.
ISBN:9783319001197
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer software , Logic, Symbolic and mathematical
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Call number:SPRINGER-2013-9783034806091:ONLINE Show nearby items on shelf
Title:Towards a General Theory of Classifications [electronic resource]
Author(s): Daniel Parrochia
Pierre Neuville
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
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Note:This book is an essay on the epistemology of classifications. Its main purpose is not to provide an exposition of an actual mathematical theory of classifications, that is, a general theory which would be available to any kind ofthem: hierarchical or non-hierarchical, ordinary or fuzzy, overlapping or non-overlapping, finite or infinite, and so on, establishing a basis for all possible divisions of the real world. For the moment, such a theory remains nothingbut a dream. Instead, the authors essentia lly put forward a number of key questions. Their aim is rather to reveal the state of art of this dynamic field and the philosophy one may eventually adopt to go further. To this end theypresent some advances made in the course of the last century, discus s a few tricky problems that remain to be solved, and show the avenues open to those who no longer wish to stay on the wrong track. Researchers and professionalsinterested in the epistemology and philosophy of science, library science, logic and set theor y, order theory or cluster analysis will find this book a comprehensive, original and progressive introduction to the main questions in thisfield
Note:Springer eBooks
Contents:Foreword
1 Philosophical problems
2 Information data structures
3 Empirical Clustering and classic hierarchies
4 Algebra of trees
5 Generalized Classifications
6 Topology of generalized classifications
7 Meta
classification
8 For an axiomatic theory of classifications
9 Alternative theories and higher infinite
10 Postscript
Bibliography.
ISBN:9783034806091
Series:e-books
Series:SpringerLink (Online service)
Series:Studies in Universal Logic
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic , Information storage and retrieval systems , Algebra , Logic, Symbolic and mathematical
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Call number:SPRINGER-2013-9783034806008:ONLINE Show nearby items on shelf
Title:Visual Reasoning with Diagrams [electronic resource]
Author(s): Amirouche Moktefi
Sun-Joo Shin
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
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Note:Logic, the discipline that explores valid reasoning, does not need to be limited to a specific form of representation but should include any form as long as it allows us to draw sound conclusions from given information. The use ofdiagrams has a long but unequal history in logic: The golden age of diagrammatic logic of the 19th century thanks to Euler and Venn diagrams was followed by the early 20th century's symbolization of modern logic by Frege and Russell.Recently, we have been witnessing a reviva l of interest in diagrams from various disciplines - mathematics, logic, philosophy, cognitive science, and computer science. This book aims to provide a space for this newly debated topic -the logical status of diagrams - in order to advance the goal of universal logic by exploring common and/or unique features of visual reasoning
Note:Springer eBooks
Contents:Preface
1.What is a logical diagram? (Catherine Legg)
2.The geometry of diagrams and the logic of syllogisms (Richard Bosley)
3.A diagrammatic calculus of syllogisms (Ruggero Pagnan)
4.Beyond syllogisms: Carrolls (marked) quadriliteral diagram (Amirouche Moktefi)
5.A diagrammatic bridge between classical and fuzzy logics(Ferdinando Cavaliere)
6.Diagrammatic reasoning with Classes and relationships (Jrgen Fischer Nilsson)
7.On the completeness of spider diagrams augmented with constants (Gem Stapleton, John Howse, Simon Thompson, John Taylor and Peter C
ISBN:9783034806008
Series:e-books
Series:SpringerLink (Online service)
Series:Studies in Universal Logic
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic , Visualization , Logic, Symbolic and mathematical
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Call number:SPRINGER-2013-9781461472544:ONLINE Show nearby items on shelf
Title:The Mathematics of Paul Erds II [electronic resource]
Author(s): Ronald L Graham
Jaroslav Neetil
Steve Butler
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
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Note:This is the most comprehensive survey of the mathematical life of the legendary Paul Erds (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erds'research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 1000 pages, arranged into two volumes. These volumes contain both high level research articles aswell as key articles that survey some of the cornerst ones of Erds' work, each written by a leading world specialist in the field. A special chapter Early Days, rare photographs, and art related to Erds complement this strikingcollection. A unique contribution is the bibliography on Erds' publications: the m ost comprehensive ever published. This new edition, dedicated to the 100th anniversary of Paul Erds' birth, contains updates on many of the articlesfrom the two volumes of the first edition, several new articles from prominent mathematicians, a new introd uction, and more biographical information about Paul Erds with an updated list of publications. The second volume containschapters on graph theory and combinatorics, extremal and Ramsey theory, and a section on infinity that covers Erds' research on set t heory. All of these chapters are essentially updated, particularly the extremal theory chapter thatcontains a survey of flag algebras, a new technique for solving extremal problems
Note:Springer eBooks
Contents:VOLUME II
Part I Combinatorics and Graph Theory
Introduction
Reconstruction Problems for Digraphs
Neighborly Families of Boxes and Bipartite Coverings
On the Isolation of a Common Secret
Properties of Graded Posets Preserved by Some Operations
The Dimension of Random Graph Orders
Hereditary and Monotone Properties of Graphs
Cycles and Paths in Triangle
Free Graphs
Problems in Graph Theory from Memphis
Some Remarks on the Cycle Plus Triangles Problem
Intersection Representations of the Complete Bipartite Graph
Reflections on a Problem of Erds and Hajnal
ISBN:9781461472544
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Combinatorics , Logic, Symbolic and mathematical
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Call number:SPRINGER-2013-9781461466369:ONLINE Show nearby items on shelf
Title:An Invitation to Abstract Mathematics [electronic resource]
Author(s): Bla Bajnok
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:This undergraduate textbook is intended primarily for a transition course into higher mathematics, although it is written with a broader audience in mind. The heart and soul of this book is problem solving, where each problemis carefully chosen to cl arify a concept, demonstrate a technique, or to enthuse. The exercises require relatively extensive arguments, creative approaches, or both, thus providing motivation for the reader. With a unified approachto a diverse collection of topics, this text poin ts out connections, similarities, and differences among subjects whenever possible. This book shows students that mathematics is a vibrant and dynamic human enterprise by includinghistorical perspectives and notes on the giants of mathematics, by mentioni ng current activity in the mathematical community, and by discussing many famous and less well-known questions that remain open for future mathematicians.Ideally, this text should be used for a two semester course, where the first course has no prerequisi tes and the second is a more challenging course for math majors yet, the flexible structure of the book allows it to be used in avariety of settings, including as a source of various independent-study and research projects
Note:Springer eBooks
Contents:Preface to Instructors
Preface to Students
Acknowledgments
I What's Mathematics
1 Let's Play a Game!
2 What's the Name of the Game?
3 How to Make a Statement?
4 What's True in Mathematics?
5 Famous Classical Theorems
6 Recent Progress in Mathematics
II How to Solve It?
7 Let's be Logical!
8 Setting Examples
9 Quantifier Mechanics
10 Mathematical Structures
11 Working in the Fields (and Other Structures)
12 Universal Proofs
13 The Domino Effect
14 More Domino Games
15 Existential Proofs
16 A Cornucopia of Famous Problems
III Advanced
ISBN:9781461466369
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical
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Call number:SPRINGER-2013-9781461457466:ONLINE Show nearby items on shelf
Title:A Course on Mathematical Logic [electronic resource]
Author(s): Shashi Mohan Srivastava
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted withlogic and would like to learn Gdels incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related tofoundations and computability, such as logic, axiomati c set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this newedition is toprovide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types tomodel theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new editionalso introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, hom ogeneous structures, definability, and many more. Review from the first edition: All results includedin the book are very carefully selected and proved. The authors manner of writing is excellent, which will surely make this book useful to many categories of readers. --Marius Tarnauceanu, Zentralblatt MATH
Note:Springer eBooks
Contents:Preface
1 Syntax of First
Order Logic
2 Semantics of First
Order Languages
3 Propositional Logic
4 Completeness Theorem for First
Order Logic
5 Model Theory
6 Recursive Functions and Arithmetization of Theories
7 Incompleteness Theorems and Recursion Theory
References
Index
ISBN:9781461457466
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Algebra , Logic, Symbolic and mathematical
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Call number:SPRINGER-2013-9781461436317:ONLINE Show nearby items on shelf
Title:A Logical Introduction to Proof [electronic resource]
Author(s): Daniel W Cunningham
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
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Note:A Logical Introduction to Proof is a unique textbook that uses a logic-first approach to train and guide undergraduates through a transition or bridge course between calculus and advanced mathematics courses. Theauthors approach prepares the student for the rigors required in future mathematics courses and is appropriate for majors in mathematics, computer science, engineering, as well as other applied mathematical sciences. It may alsobe beneficial as a supplement for students at the graduate level who need guidance or reference for writing proofs. Core topics covered are logic, sets, relations, functions, and induction, where logic is the instrument foranalyzing the structure of mathematical assertions and is a tool for composing mathematical proof s. Exercises are given at the end of each section within a chapter. Chapter 1 focuses on propositional logic while Chapter 2 is devoted tothe logic of quantifiers. Chapter 3 methodically presents the key strategies that are used in mathematical proofs eac h presented as a proof diagram. Every proof strategy is carefully illustrated by a variety of mathematical theoremsconcerning the natural, rational, and real numbers. Chapter 4 focuses on mathematical induction and concludes with a proof of the fundamenta l theorem of arithmetic. Chapters 5 through 7 introduce students to the essential concepts thatappear in all branches of mathematics. Chapter 8 introduces the basic structures of abstract algebra: groups, rings, quotient groups, and quotient rings. Finall y, Chapter 9 presents proof strategies that explicitly show students how todeal with the fundamental definitions that they will encounter in real analysis, followed by numerous examples of proofs that use these strategies. The appendix provides a useful s ummary of strategies for dealing with proofs
Note:Springer eBooks
Contents:Preface
The Greek Alphabet
1. Propositional Logic
2. Predicate Logic
3. Proof Strategies and Diagrams
4. Mathematical Induction
5. Set Theory
6. Functions
7. Relations
8. Core Concepts in Abstract Algebra
9. Core Concepts in Real Analysis
A Summary of Strategies
References
List of Symbols. Index
ISBN:9781461436317
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical
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Call number:SPRINGER-2013-9781447146162:ONLINE Show nearby items on shelf
Title:L.E.J. Brouwer Topologist, Intuitionist, Philosopher [electronic resource] : How Mathematics Is Rooted in Life
Author(s): Dirk Dalen
Date:2013
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
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Note:Dirk van Dalens biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius complex and often controversial andgiftedwith a deep intuition, he ha d an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famousBrouwer fixed point theorem. Brouwers main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name intuitionism. This made him one of themain protagonists in the foundation crisis of mathematics. As a confirmed internation alist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during thetwentieth century was turbulent nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role.The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and any body interested in the history of mathematics in the first half of the twentieth century
Note:Springer eBooks
Contents:Child and Student
Mathematics and Mysticism
The Dissertation
Cantor
Schoenflies Topology
The New Topology
Making a Career
The War Years
Mathematics after the War
Politics and Mathematics
The Breakthrough
The Fathers of Dimension
Progress, Recognition, and Frictions
From Berlin to Vienna
The Three Battles
The Thirties
War and Occupation
Post
War Events
The Restless Emeritus
ISBN:9781447146162
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical , Topology
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Call number:SPRINGER-2013-9781447145585:ONLINE Show nearby items on shelf
Title:Logic and Structure [electronic resource]
Author(s): Dirk Dalen
Date:2013
Edition:5th ed. 2013
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Dirk van Dalens popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gdels famous incompletenesstheorem. Propositional and predicat e logic are presented in an easy-to-read style using Gentzens natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness,Skolem-Lwenheim, non-standard models and quantifier elimination. The discuss ion of classical logic is concluded with a concise exposition of second-order logic. In view of the growing recognition of constructive methods andprinciples, intuitionistic logic and Kripke semantics is carefully explored. A number of specific constructi ve features, such as apartness and equality, the Gdel translation, the disjunction and existence property are also included.The last chapter on Gdel's first incompleteness theorem is self-contained and provides a systematic exposition of the necessary rec ursion theory. This new edition has been properly revised and contains a new section onultra-products
Note:Springer eBooks
Contents:Introduction
Propositional Logic
Predicate Logic
Completeness and Applications
Second Order Logic
Intuitionistic Logic
Normalization
Gdel's theorem
ISBN:9781447145585
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical
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Call number:SPRINGER-2012-9788847026100:ONLINE Show nearby items on shelf
Title:Non solo calcoli [electronic resource] : Domande e risposte sui perch della matematica
Author(s): Vinicio Villani
Claudio Bernardi
Sergio Zoccante
Roberto Porcaro
Date:2012
Publisher:Milano : Springer Milan : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Nell'infanzia si pongono i classici interrogativi con tanti perch?. Purtroppo poi, nel corso dell'educazione matematica, la curiosit diminuisce e spesso ci si accontenta di chiedere come si fa?. Questo libro dedicato ai perch della logica e teoria de gli insiemi, dell'analisi matematica, della probabilit e statistica. Si completano cos gli argomenti di matematica insegnati a scuola, dopo i precedenti testi di V. Villani sui perchdellalgebra e geometria. Il titolo contiene un messaggio. In logica si af fronta il calcolo delle proposizioni, lanalisi matematica nota anche col nome di calcolo, la probabilit detta calcolo delle probabilit. In tutti etre i casi si potrebbe focalizzare lattenzione sulla parola calcolo. Ma questo riduttivo: il calcolo una componente importante, ma altrettanto importante la comprensione critica di tutto ci che sta alla base dei calcoli.Il libro rivolto a chi insegna matematica e a tutte le persone che hanno conservato una genuina curiosit scientifica.
Note:Springer eBooks
Contents:Logica e Teoria degli insiemi
Analisi matematica
Probabilit e Statistica
ISBN:9788847026100
Series:e-books
Series:SpringerLink (Online service)
Series:Convergenze
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Logic, Symbolic and mathematical , Statistics
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Call number:SPRINGER-2012-9788847023611:ONLINE Show nearby items on shelf
Title:Logic: A Brief Course [electronic resource]
Author(s): Daniele Mundici
Date:2012
Publisher:Milano : Springer Milan : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This short book, geared towards undergraduate students of computer science and mathematics, is specifically designed for a first course in mathematical logic. A proof of Gdel's completeness theorem and its main consequences isgiven using Robinson's c ompleteness theorem and Gdel's compactness theorem for propositional logic. The reader will familiarize himself with many basic ideas and artifacts of mathematical logic: a non-ambiguous syntax, logicalequivalence and consequence relation, the Davis-Putna m procedure, Tarski semantics, Herbrand models, the axioms of identity, Skolem normal forms, nonstandard models and, interestingly enough, proofs and refutations viewed as graphicobjects. The mathematical prerequisites are minimal: the book is accessible to anybody having some familiarity with proofs by induction. Many exercises on the relationship between natural language and formal proofs make the book alsointeresting to a wide range of students of philosophy and linguistics
Note:Springer eBooks
Contents:Introduction
Fundamental Logical Notions
The Resolution Method
Robinson Completeness Theorem
Fast Classes for DPP
Godel Compactness Theorem
Propositional Logic: Syntax
Propositional Logic: Semantics
Normal Forms
Recap: Expressivity and Efficiency
The Quantifiers There Exists and For All
Syntax of Predicate Logic
The Meaning of Clauses
Godel Completeness Theorem for the Logic of Clauses
Equality Axioms
The Predicate Logic L
ISBN:9788847023611
Series:e-books
Series:SpringerLink (Online service)
Series:UNITEXT, 2038-5714
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Logic, Symbolic and mathematical , Semantics
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Call number:SPRINGER-2012-9783642278754:ONLINE Show nearby items on shelf
Title:Sparsity [electronic resource] : Graphs, Structures, and Algorithms
Author(s): Jaroslav Neetil
Patrice Ossona de Mendez
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authorsdevised an unifying clas sification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremalcombinatorial invariants. This study of sparse str uctures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphismpreservation,fixed parameter tractability and constraint satisfaction prob lems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Neetil is a professor atCharles University, Prague Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010
Note:Springer eBooks
Contents:Part I Presentation: 1. Introduction
2. A Few Problems
3. Commented Contents
Part II. The Theory: 4. Prolegomena
5. Measuring Sparsity
6. Classes and their Classification
7. Bounded Height Trees and Tree
Depth
8. Decomposition
9. Independence
10. First
Order Constraint Satisfaction Problems and Homomorphism Dualities
11. Restricted Homomorphism Dualities
12. Counting
13. Back to Classes
Part III Applications: 14. Classes with Bounded Expansion Examples
15. Property Testing, Hyperfiniteness and Separators
16. Algorithmic Applications
17. Other
ISBN:9783642278754
Series:e-books
Series:SpringerLink (Online service)
Series:Algorithms and Combinatorics, 0937-5511 : v28
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer software , Computational complexity , Combinatorics , Discrete groups , Logic, Symbolic and mathematical
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Call number:SPRINGER-2012-9783642109324:ONLINE Show nearby items on shelf
Title:Teoria algebrica dei meccanismi automatici [electronic resource]
Author(s): R Righi
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:H. Soubies-Camy: Lalgbre logique applique aux techniques binaires, I parte: lezioni.- H. Soubies-Camy: Lalgbre logique applique aux techniques binaires, II parte: disegni.- J. Piesch: Switching Algebra.- J.P. Roth: Unateoria per la progettazione logi ca dei Meccanismi Automatici
Note:Springer eBooks
Contents:H. Soubies
Camy: Lalgbre logique applique aux techniques binaires, I parte: lezioni
H. Soubies
Camy: Lalgbre logique applique aux techniques binaires, II parte: disegni
J. Piesch: Switching Algebra
J.P. Roth: Una teoria per la progettazione logica dei Meccanismi Automatici
ISBN:9783642109324
Series:e-books
Series:SpringerLink (Online service)
Series:C.I.M.E. Summer Schools : v19
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Visualization , Logic, Symbolic and mathematical
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Call number:SPRINGER-2012-9783034803793:ONLINE Show nearby items on shelf
Title:Around and Beyond the Square of Opposition [electronic resource]
Author(s): Jean-Yves Bziau
Dale Jacquette
Date:2012
Publisher:Basel : Springer Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various fields: epistemology,linguistics, mathemati cs, sociology, physics. The square can also be generalized in other two-dimensional or multi-dimensional objects extending in breadth and depth the original Aristotelian theory. The square of opposition is a veryattractive theme which has been going throu gh centuries without evaporating. Since 10 years there is a new growing interest for the square due to recent discoveries and challenging interpretations. This book presents a collection ofpreviously unpublished papers by high level specialists of the squ are from all over the world
Note:Springer eBooks
Contents:1 Historical and Critical Aspects of the Square
2 Philosophical Discussions around the Square of Opposition
3 The Square of Opposition and Non
Classical Logics
4 Constructions Generalizing the Square of Opposition
5 Applications of the Square of Opposition
ISBN:9783034803793
Series:e-books
Series:SpringerLink (Online service)
Series:Studies in Universal Logic
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic , Logic, Symbolic and mathematical
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Call number:SPRINGER-2012-9781461442653:ONLINE Show nearby items on shelf
Title:Introduction to Mathematical Structures and Proofs [electronic resource]
Author(s): Larry J Gerstein
Date:2012
Edition:2nd ed. 2012
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a bridge course can help ensure a smooth transition.Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuitionand rigorand the flexible thinkingrequired to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader. The new material in this second edition includes a section on graphtheory, several new sections on number theory (including primitive roots, with an appli cation to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers). Froma review of the first edition: ...Gerstein wantsvery gentlyto teach his students to think. He wants to show t hem how to wrestle with a problem (one that is more sophisticated than plug and chug), how to build a solution,and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I th ink students will find appealing. ...I am confident that a student who works throughGerstein's book will really come away with (i) some mathematical technique, and (ii) some mathematical knowledge. Gersteins book states quite plainly that the text is desi gned for use in a transitions course. Nothing benefits atextbook author more than having his goals clearly in mind, and Gersteins book achieves its goals. I would be happy to use it in a transitions course. Steven Krantz, American Mathematical Monthly
Note:Springer eBooks
Contents:Preface to the Second Edition
Preface to the First Edition
1. Logic
2. Sets
3. Functions
4. Finite and Infinite Sets
5. Combinatorics
6. Number Theory
7. Complex Numbers
Hints and Partial Solutions to Selected Odd
Numbered Exercises
Index
ISBN:9781461442653
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Combinatorics , Logic, Symbolic and mathematical , Number theory
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Call number:SPRINGER-2012-9781461440420:ONLINE Show nearby items on shelf
Title:Lecture Notes on O-Minimal Structures and Real Analytic Geometry [electronic resource]
Author(s): Chris Miller
Jean-Philippe Rolin
Patrick Speissegger
Date:2012
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes fromgraduate courses assoc iated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields Chris Miller on o-minimality and Hardy fields Jean-Philippe Rolin on the construction ofo-minimal structures from quasianalytic classes Fer nando Sanz on non-oscillatory trajectories of vector fields and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is anadaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such asresearch papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or imagesthereof, of definable systems of differential equations
Note:Springer eBooks
Contents:Preface
Blowings
up of Vector Fields (F. Cano)
Basics of o
Minimality and Hardy Fields (C. Miller)
Construction of o
Minimal Structures from Quasianalytic Classes (J
P. Rolin)
Course on Non
Oscillatory Trajectories
F.S. Snchez)
Pfaffian Sets and o
Minimality (P. Speissegger)
Theorems of the Complement (A. Fornasiero, T. Servi)
ISBN:9781461440420
Series:e-books
Series:SpringerLink (Online service)
Series:Fields Institute Communications, 1069-5265 : v62
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Logic, Symbolic and mathematical
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Call number:SPRINGER-2012-9781447121732:ONLINE Show nearby items on shelf
Title:Combinatorial Set Theory [electronic resource] : With a Gentle Introduction to Forcing
Author(s): Lorenz J Halbeisen
Date:2012
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lieson the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like thecontinuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of eachchapter put the results in a historical context, and the numerou s related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in thefoundations of mathematics, but will be of particular use to graduates in this field
Note:Springer eBooks
Contents:The Setting
Overture: Ramsey's Theorem
The Axioms of Zermelo
Fraenkel Set Theory
Cardinal Relations in ZF only
The Axiom of Choice
How to Make Two Balls from One
Models of Set Theory with Atoms
Twelve Cardinals and their Relations
The Shattering Number Revisited
Happy Families and their Relatives
Coda: A Dual Form of Ramsey's Theorem
The Idea of Forcing
Martin's Axiom
The Notion of Forcing
Models of Finite Fragments of Set Theory
Proving Unprovability
Models in which AC Fails
Combining Forcing Notions
Models in which p = c
Properties of
ISBN:9781447121732
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical
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Call number:SPRINGER-2012-9780817683191:ONLINE Show nearby items on shelf
Title:A Beginner's Guide to Finite Mathematics [electronic resource] For Business, Management, and the Social Sciences
Author(s): W.D Wallis
Date:2012
Edition:2nd ed. 2012
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The present textbook gives a concise introduction to finite mathematics. It covers the topics counting, discrete probability, graph theory, linear equations, and linear programmingThe mathematical level seems higher thanthe average US textbook on thi s topic. It is well written and easy to read, with many examples and applications. Internationale Mathematische Nachrichten (Review of First Edition) This book is designed for an elementaryone-semester course in finite mathematics and applications. Finite mathematics here means applicable discrete mathematics used by students in business, management and social sciencesA number of worked examples, called sampleproblems, are included in the body of each section. Every chapter is closed with a lot of exercis es complete solutions are provided at the end of the bookI would recommend this book [to] everyone who wants to have a first look atapplied discrete mathematics. Simulation News (Review of First Edition) This second edition of A Beginners Guide to Finite Mathematics: For Business, Management, and the Social Sciencestakes a distinctly applied approachto finite mathematics at the freshman and sophomore level. Topics are presented sequentially: the book opens with a brief review of sets and numbers, followed by an introduction to data sets, histograms, means and medians. Countingtechniques and the Binomial Theorem are covered, which provide the foundation for elementary probability theory this, in turn, leads to basic statistics. This new edition includes ch apters on game theory and financial mathematics.Graph theory is defined, with particular emphasis on its use in mathematical modeling. Matrices and vectors are discussed, along with several elementary commercial applications, including linear programming, the theory of games, andfinancial mathematics. Ample examples and illustrations are provided throughout each section contains two sets of problems, with solutio
Note:Springer eBooks
Contents:Preface
Numbers and Sets
Counting
Probability
Graph Theory
Linear Equations and Matrices
Linear Programming
Theory of Games
Financial Mathematics
Your Turn Solutions
Answers to Exercises A
Index
ISBN:9780817683191
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Combinatorics , Logic, Symbolic and mathematical , Distribution (Probability theory)
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Call number:SPRINGER-2012-9780817682958:ONLINE Show nearby items on shelf
Title:The Mathematical Experience, Study Edition [electronic resource]
Author(s): Philip J Davis
Reuben Hersh
Elena Anne Marchisotto
Date:2012
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Winner of the 1983National Book Award, The Mathematical Experience presented a highlyinsightful overview of mathematics that effectively conveyed its power and beauty to a largeaudience of mathematicians andnon-mathematicians alike. The study edition of the work followed about a decade later, supplementing the original material of the book with exercises to provide a self-contained treatment usable for the classroom. This softcoverversion reproduces the study edition andincludes epilogues by the thre e original authors to reflect on the book's content 15 years after its publication, and to demonstrate its continued applicability to the classroom.Moreover,The Companion Guide to the Mathematical Experienceoriginally published and sold separatelyis freel y available online to instructors who use the work, further enhancingits pedagogicalvalue and making itanexceptionally usefuland accessible resource for a wide range oflower-level courses inmathematics and mathematics education. A wealth of customizable o nline course materials for the bookcan be obtainedfrom Elena AnneMarchisotto (elena.marchisotto@csun.edu) upon request. Reviews [The authors] have tried to provide a book usable in a course for liberal arts students and for future secondary teachers. They have done much more! This course shouldbe required of every undergraduate major employing the mathematical sciences. It differs from the mathematics appreciation coursescourses that are merely a collection of amusing puzzles and toy problems giving an il lusion ofa mathematical encounterpresently found in many institutions. Students of this course are introduced to the context in which mathematics exists and the incredible magnitude of words devoted to communicating mathematics (hundredsof thousands of th eorems each year). How much mathematics can there be? they are asked. Instructors in a Mathematical Experience course must be prepared t
Note:Springer eBooks
Contents:Preface
Preface to the Study Edition
Acknowledgements
Introduction
Overture
1. The Mathematical Landscape
2. Varieties of Mathematical Experience
3. Outer Issues
4. Inner Issues
5. Selected Topics in Mathematics
6. Teaching and Learning
7. From Certainty to Fallibility
8. Mathematical Reality
Glossary
Bibliography
Index
Epilogue
ISBN:9780817682958
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Education Philosophy , Science Philosophy , Logic, Symbolic and mathematical
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Call number:SPRINGER-2012-9780817682866:ONLINE Show nearby items on shelf
Title:A Beginner's Guide to Discrete Mathematics [electronic resource]
Author(s): W.D Wallis
Date:2012
Edition:Second Edition
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Wallis's book on discrete mathematics is a resource for an introductory course in a subject fundamental to both mathematics and computer science, a course that is expected not only to cover certain specific topics but also tointroduce students to imp ortant modes of thought specific to each discipline . . . Lower-division undergraduates through graduate students. Choice (Review of the First Edition) Very appropriately entitled as a 'beginner's guide',this textbook presents itself as the first exposure to discrete mathematics and rigorous proof for the mathematics or computer science student. Zentralblatt MATH (Review of the First Edition) This second edition of A BeginnersGuide to Discrete Mathematicspresents a detailedguide to discrete mathematicsand its relationship to other mathematical subjects includingset theory, probability, cryptography, graph theory, and number theory.Thistextbookhas a distinctly applied orientation and explores a variety of applications. Key features of the second edition: * Includesa new chapter on the theory of voting as well asnumerous new examples and exercises throughout thebook * Introduces functions, vectors, matrices, number systems, scientific notations, and the representation of numbers in computers * Provides exam ples, which then lead into easy practice problems throughout the text, and fullexercises at the end of each chapter *Full solutions for practice problems are provided at the end of the book This text is intended for undergraduates in mathematics and compu ter science, however, featured special topics andapplications may also interest graduate students
Note:Springer eBooks
Contents:Properties of Numbers
Sets and Data Structures
Boolean Algebras and Circuits
Relations and Functions
The Theory of Counting
Probability
Graph Theory
Matrices
Number Theory and Cryptography
The Theory of Voting
Solutions to Practic Exercises
Answers to Selected Exercises
Index
ISBN:9780817682866
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computational complexity , Combinatorics , Logic, Symbolic and mathematical , Mathematical statistics
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Call number:SPRINGER-2012-9780817682682:ONLINE Show nearby items on shelf
Title:Excursions in the History of Mathematics [electronic resource]
Author(s): Israel Kleiner
Date:2012
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Partfive provides biographie s of five mathematicians who played major roles in the historical events described in the first four parts of the work. Each of the first three partson number theory, calculus/analysis, and proofbeginswith a survey of the respective subject and is followe d in more depth by specialized themes. Among the specialized themes are: Fermat as the founder of modern number theory, Fermats Last Theorem from Fermat to Wiles, the historyof the function concept, paradoxes, the principle of continuity, and an historica l perspective on recent debates about proof. The fourth part contains essays describing mathematics courses inspired by history. The essays deal withnumbers as a source of ideas in teaching, with famous problems, and with the stories behind various great quotations. The last part gives an account of five mathematiciansDedekind, Euler, Gauss, Hilbert, and Weierstrasswhoselives and work we hope readers will find inspiring. Key features of the work include: * A preface describing in some detail the author's ideas on teaching mathematics courses, in particular, the role of history in such courses *Explicit comments and suggestions for teachers on how history can affect the teaching of mathematics * A description of a course in the history of mathematics taugh t in an In-Service Master's Program for high school teachers *Inclusion of issues in the philosophy of mathematics * An extensive list of relevant references at the end of each chapter. Excursions in the History of Mathematics was written with several goa ls in mind: to arouse mathematicsteachers interest in the history of their subject to encourage mathematics teachers with at least some knowledge of the history of mathe
Note:Springer eBooks
Contents:A. Number Theory
1. Highlights in the History of Number Theory: 1700 BC
2008
2. Fermat: The Founder of Modern Number Theory
3. Fermat's Last Theorem: From Fermat to Wiles
B. Calculus/Analysis
4. A History of the Infinitely Small and the Infinitely Large in Calculus, with Remarks for the Teacher
5. A Brief History of the Function Concept
6. More on the History of Functions, Including Remarks on Teaching
C. Proof
7. Highlights in the Practice of Proof: 1600 BC
2009
8. Paradoxes: What are they Good for?
9. Principle of Continuity: 16th
19th centuries
10
ISBN:9780817682682
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Logic, Symbolic and mathematical , Number theory
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Call number:SPRINGER-2012-9780817682538:ONLINE Show nearby items on shelf
Title:Mathematical Olympiad Treasures [electronic resource]
Author(s): Titu Andreescu
Bogdan Enescu
Date:2012
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
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Note:I took great pleasure in reading Mathematical Olympiad Treasures, by Titu Andreescu and Bogdan Enescu. This book is the fruit of the prodigious activity of two well-known creators of mathematics problems in various mathematicaljournals.... In all the chapters, the reader can find numerous challenging problems. All featured solutions are interesting, given in increasing level of difficulty some of them are real gems that will give great satisfaction to anymath lover attempting to solve the problemsor even extend them. I believe strongly that Mathematical Olympiad Treasures will reveal the beauty of mathematics to all students, teachers, and all math lovers. MAA Online (Reviewof the First Edition) ...this is one of a long recent series of challenging s econdary math books, coauthored by Dr. Titu Andreescu and published by Birkhuser, a series that has definitely enriched the literature on secondarymathematicsa credit to the coauthor and to the wisdom of the editor. Zentralblatt MATH (Review of the First Edition) This second edition of Mathematical Olympiad Treasures contains a stimulating collection of problems ingeometry and trigonometry, algebra, number theory, and combinatorics. It encourages readers to think creatively about techniques and strategies for solving real-world problems, with new sections, revisions, and many more Olympiad-likeproblems at various levels of difficulty. The problems are clustered by topic into three self-contained chapters. The book begins with elementary facts, followed by carefully selected problems and detailed, step-by-step solutions,which then lead to more complicated, challenging problems and their solutions. Reflecting the vast experience of two professors andMathematical Olympiad coaches, the text will be invaluable to teachers, students, and puzzleenthusiasts. The advanced reader is challenged to find alternative solutions and extensions of the proposed problems
Note:Springer eBooks
Contents:I Problems
1 Algebra
2 Geometry and Trigonometry
3 Number Theory and Combinatorics
II Solutions
4 Algebra
5 Geometry and Trigonometry
6 Number Theory and Combinatorics
ISBN:9780817682538
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Combinatorics , Logic, Symbolic and mathematical , Number theory
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Call number:SPRINGER-2011-9789400708402:ONLINE Show nearby items on shelf
Title:Advanced ukasiewicz calculus and MV-algebras [electronic resource]
Author(s): D Mundici
Date:2011
Publisher:Dordrecht : Springer Netherlands
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:In recent years, the discovery of the relationships between formulas in ukasiewicz logic and rational polyhedra, Chang MV-algebras and lattice-ordered abelian roups, MV-algebraic states and coherent de Finettis assessmentsof continuous events, has ch anged the study and practice of many-valued logic. This book is intended as an up-to-date monograph on innite-valued ukasiewicz logic and MV-algebras. Each chapter features a combination of classicaland recent results, well beyond the traditional domain o f algebraic logic: among others, a comprehensive account is given of many eective procedures that have been recently developed for the algebraic and geometric objectsrepresented by formulas in ukasiewicz logic. The book embodies the viewpoint that modern ukasiewicz logic and MV-algebras provide a benchmark for the study of several deep mathematical problems, such as Rnyi conditionals ofcontinuously valued events, the many-valued generalization of Carathodory algebraic probability theory, morphisms and inv ariant measures of rational polyhedra, bases and Schauder bases as jointly renable partitions of unity, andrst-order logic with [0,1]-valued identity on Hilbert space. Complete versions are given of a compact body of recent results and techniques, proving virtually everything that is used throughout, so that the book can be used both forindividual study and as a source of reference for the more advanced reader
Note:Springer eBooks
Contents:Preface
Chapter 1. Prologue: de Finetti coherence criterion and ukasiewicz logic
Chapter 2. Rational polyhedra, Interpolation, Amalgamation
Chapter 3. The Galois connection (Mod, Th) in 21
Chapter 4. The spectral and the maximal spectral space
Chapter 5. De Concini
Procesi theorem and Schauder bases
Chapter 6. Bases and nitely presented MV
algebras
Chapter 7. The free product of MV
algebras
The construction of free products
Chapter 8. Direct limits, conuence and multisets
Chapter 9. Tensors
Chapter 10. States and the Kroupa
Panti Theorem
Chap
ISBN:9789400708402
Series:e-books
Series:SpringerLink (Online service)
Series:Trends in Logic : v35
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical
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Call number:SPRINGER-2011-9789400703209:ONLINE Show nearby items on shelf
Title:Methods of Cut-Elimination [electronic resource]
Author(s): Alexander Leitsch
Matthias Baaz
Date:2011
Publisher:Dordrecht : Springer Netherlands
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book on methods of cut-elimination contains a thorough and rigorous analysis of reductive cut-elimination methods and an in-depth presentation of the recent method CERES developed by the authors. It includes a detailedcomplexity analysis and com parison of CERES and of reductive methods. It presents several applications of CERESto interpolation, fast cut-elimination, generalization of proofs and to the analysis of mathematical proofs. Finally, itprovides an extension of CERES to non-classical log ics, in particular to finitely-valued logics and to Gdel logic
Note:Springer eBooks
Contents:1 Preface
2 Introduction
3 Preliminaries
4 Complexity of Cut
Elimination
5 Reduction and Elimination
6 Cut
Elimination by Resolution
7 Extensions of CERES
8 Applications of CERES
9 CERES in Nonclassical Logics
10 Related Research
ISBN:9789400703209
Series:e-books
Series:SpringerLink (Online service)
Series:Trends in Logic : v34
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Logic, Symbolic and mathematical
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Call number:SPRINGER-2011-9789400700055:ONLINE Show nearby items on shelf
Title:Dual Tableaux: Foundations, Methodology, Case Studies [electronic resource]
Author(s): Ewa Orlowska
Joanna Goliska Pilarek
Date:2011
Publisher:Dordrecht : Springer Netherlands : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The book presents logical foundations of dual tableaux together with a number of their applications both to logics traditionally dealt with in mathematics and philosophy (such as modal, intuitionistic, relevant, and many-valuedlogics) and to various applied theories of computational logic (such as temporal reasoning, spatial reasoning, fuzzy-set-based reasoning, rough-set-based reasoning, order-of magnitude reasoning, reasoning about programs, thresholdlogics, logics of conditional decisions). The di stinguishing feature of most of these applications is that the corresponding dual tableaux are built in a relational language which provides useful means of presentation of the theories.In this way modularity of dual tableaux is ensured. We do not need to develop and implement each dual tableau from scratch, we should only extend the relational core common to many theories with the rules specific for a particulartheory
Note:Springer eBooks
Contents:1. Dual Tableau for Classical First
Order Logic
2. Dual Tableaux for Logics of Classical Algebras of Binary
3. Theories of Point Relations and Relational Model Checking
4. Dual Tableaux for Peirce Algebras
5. Dual Tableaux for Fork Algebras
6. Dual Tableaux for Relational Databases
Part III. Relational Reasoning in Traditional Non
classical Logics
7. Dual Tableaux for Classical Modal Logics
8. Dual Tableaux for Some Logics Based on Intuitionism
9. Dual Tableaux for Relevant Logics
10. Dual Tableaux for Many
valued Logics
Part IV. Relational Reasoning in Logi
ISBN:9789400700055
Series:e-books
Series:SpringerLink (Online service)
Series:Trends in Logic, 1572-6126 : v33
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic , Computer science , Logic, Symbolic and mathematical
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Call number:SPRINGER-2011-9789400700024:ONLINE Show nearby items on shelf
Title:Hybrid Logic and its Proof-Theory [electronic resource]
Author(s): Torben Braner
Date:2011
Publisher:Dordrecht : Springer Netherlands
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times,possible worlds, stat es in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There islittle consensus about proof-theory for ord inary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book wedemonstrate that hybrid-logical proof-theory remedies these defic iencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics(propositional, first-order, intensional first-order, and intuitionistic)
Note:Springer eBooks
Contents:Preface,
1 Introduction to Hybrid Logic
2 Proof
Theory of Propositional Hybrid Logic
3 Tableaus and Decision Procedures for Hybrid Logic
4 Comparison to Seligmans Natural Deduction System
5 Functional Completeness for a Hybrid Logic
6 First
Order Hybrid
7 Intensional First
Order Hybrid Logic
8 Intuitionistic Hybrid Logic
9 Labelled Versus Internalized Natural Deduction
10 Why does the Proof
Theory of Hybrid Logic Behave soWell?
References
Index
ISBN:9789400700024
Series:e-books
Series:SpringerLink (Online service)
Series:Applied Logic Series, 1386-2790 : v37
Series:Mathematics and Statistics (Springer-11649)
Keywords: Philosophy (General) , Logic , Computer science , Logic, Symbolic and mathematical
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Call number:SPRINGER-2011-9788847018846:ONLINE Show nearby items on shelf
Title:Logica: Metodo Breve [electronic resource]
Author(s): Daniele Mundici
Date:2011
Publisher:Milano : Springer Milan : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Senza richiedere prerequisiti il testo si propone di fornire una dimostrazione dei fondamentali teoremi della logica matematica (compattezza, completezza di Gdel, Lwenheim-Skolem) introducendo i concetti sintattici e semanticiin modo progressivo, dal la logica booleana a quella predicativa. Per facilitare la lettura attiva, il testo contiene numerosi esercizi
Note:Springer eBooks
ISBN:9788847018846
Series:e-books
Series:SpringerLink (Online service)
Series:UNITEXT, 2038-5714 : v1
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Logic, Symbolic and mathematical , Semantics
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Call number:SPRINGER-2011-9788847018365:ONLINE Show nearby items on shelf
Title:Giuseppe Peano between Mathematics and Logic [electronic resource] : Proceeding of the International Conference in honour of Giuseppe Peano on the 150th anniversary of his birth and the centennial of the FormularioMathematico, Turin (Italy), October 23,2008 / edited by Fulvia Skof
Author(s): Fulvia Skof
Date:2011
Publisher:Milano : Springer Milan
Size:1 online resource
Note:Springer e-book platform
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Note:This book contains the papers developing out the presentations given at the International Conference organized by the Torino Academy of Sciences and the Department of Mathematics Giuseppe Peano of the Torino University tocelebrate the 150th anniversa ry of G. Peano's birth - one of the greatest figures in modern mathematics and logic and the most important mathematical logician in Italy - a century after the publication of Formulario Mathematico, agreat attempt to systematise Mathematics in symbolic f orm
Note:Springer eBooks
Contents:Giuseppe Peano and Mathematical Analysis in Italy
Some Contributions of Peano to Analysis in the Light of the Work of Belgian Mathematicians
Peano, his School andNumerical Analysis
Geometric Calculus and Geometry Foundations in Peano
The Formulario between Mathematics and History
Giuseppe Peano: a Revolutionary in Symbolic Logic?
At the Origins of Metalogic
Foundations of Geometry in the School of Peano
ISBN:9788847018365
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Science Philosophy , Logic, Symbolic and mathematical
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Call number:SPRINGER-2011-9788847017443:ONLINE Show nearby items on shelf
Title:Un mondo di idee [electronic resource] : La matematica ovunque
Author(s): Ciro Ciliberto
Roberto Lucchetti
Date:2011
Publisher:Milano : Springer Milan
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:La variet e linteresse dei contributi alla Lettera Matematica Pristem hanno spinto i curatori, daccordo con il comitato di redazione, a proporre in questa raccolta alcuni articoli apparsi sulla rivista dalla suafondazione ad oggi. atica Pristem una rivista, edita dalla Springer-Verlag Italia, che affronta temi legati alla ricerca matematica, ai fondamenti di questa disciplina, alla sua storia e alle sue applicazioni negli ambiti pi vari.La sfida quella di interessare e divertire il lettore, riuscen do allo stesso tempo a convincerlo che la matematica, di solito ritenuta affare di pochi iniziati, lontana dagli interessi della gente comune, arido esercizio di astrusicalcoli, invece fondamentale nella nostra vita quotidiana, ed davvero dappertutto at torno a noi: nelle carte di credito, nella posta elettronica, in internet, nellarte, nei giochi, nelle scelte (anche di tipo etico) chefacciamo in situazioni conflittuali, e perfino in politica
Note:Springer eBooks
ISBN:9788847017443
Series:e-books
Series:SpringerLink (Online service)
Series:I blu, pagine di scienza
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical , Number theory
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Call number:SPRINGER-2011-9783642217746:ONLINE Show nearby items on shelf
Title:From Objects to Diagrams for Ranges of Functors [electronic resource]
Author(s): Pierre Gillibert
Friedrich Wehrung
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This work introduces tools from the field of category theory that make it possible to tackle a number of representation problems that have remained unsolvable to date (e.g. the determination of the range of a given functor). Thebasic idea is: if a fu nctor lifts many objects, then it also lifts many (poset-indexed) diagrams
Note:Springer eBooks
Contents:1 Background
2 Boolean Algebras Scaled with Respect to a Poset
3 The Condensate Lifting Lemma (CLL)
4 Larders from First
order Structures
5 Congruence
Preserving Extensions
6 Larders from von Neumann Regular Rings
7 Discussion
ISBN:9783642217746
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2029
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , K-theory , Logic, Symbolic and mathematical
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