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30 produkter

Del 123 - Graduate Texts in Mathematics
Numbers
AvHeinz-Dieter Ebbinghaus,Hans Hermesm. fl.
Häftad, Engelska, 1990
869 kr
Skickas inom 5-8 vardagar
A book about numbers sounds rather dull. This one is not. Instead it is a lively story about one thread of mathematics-the concept of "number" told by eight authors and organized into a historical narrative that leads the reader from ancient Egypt to the late twentieth century. It is a story that begins with some of the simplest ideas of mathematics and ends with some of the most complex. It is a story that mathematicians, both amateur and professional, ought to know. Why write about numbers? Mathematicians have always found it diffi cult to develop broad perspective about their subject. While we each view our specialty as having roots in the past, and sometimes having connec tions to other specialties in the present, we seldom see the panorama of mathematical development over thousands of years. Numbers attempts to give that broad perspective, from hieroglyphs to K-theory, from Dedekind cuts to nonstandard analysis.
Numbers
AvReinhold Remmert,Alexander Prestelm. fl.
E-bok
PDF, Engelska, 2012
1 026 kr
Läs direkt efter köp
A book about numbers sounds rather dull. This one is not. Instead it is a lively story about one thread of mathematics-the concept of "number" told by eight authors and organized into a historical narrative that leads the reader from ancient Egypt to the late twentieth century. It is a story that begins with some of the simplest ideas of mathematics and ends with some of the most complex. It is a story that mathematicians, both amateur and professional, ought to know. Why write about numbers? Mathematicians have always found it diffi cult to develop broad perspective about their subject. While we each view our specialty as having roots in the past, and sometimes having connec tions to other specialties in the present, we seldom see the panorama of mathematical development over thousands of years. Numbers attempts to give that broad perspective, from hieroglyphs to K-theory, from Dedekind cuts to nonstandard analysis.
Del 291 - Graduate Texts in Mathematics
Mathematical Logic
AvHeinz-Dieter Ebbinghaus,Jörg Flumm. fl.
Inbunden, Engelska, 2021
761 kr
Skickas inom 10-15 vardagar
This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science.The chapters are carefully organized, featuring complete proofs and numerous examples throughout. Beginning with motivating examples, the book goes on to present the syntax and semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type proof of the completeness theorem is given. These introductory chapters prepare the reader for the advanced topics that follow, such as Gödel's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindström's theorems on the maximality of first-order logic, and results linking logic with automata theory. This new edition features many modernizations, as well as two additional important results: The decidability of Presburger arithmetic, and the decidability of the weak monadic theory of the successor function.Mathematical Logic is ideal for students beginning their studies in logic and the foundations of mathematics. Although the primary audience for this textbook will be graduate students or advanced undergraduates in mathematics or computer science, in fact the book has few formal prerequisites. It demands of the reader only mathematical maturity and experience with basic abstract structures, such as those encountered in discrete mathematics or algebra.
Mathematical Logic
AvWolfgang Thomas,Jorg Flumm. fl.
E-bok
PDF, Engelska, 2021
710 kr
Läs direkt efter köp
This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science.
The chapters are carefully organized, featuring complete proofs and numerous examples throughout. Beginning with motivating examples, the book goes on to present the syntax and semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type proof of the completeness theorem is given. These introductory chapters prepare the reader for the advanced topics that follow, such as Gödel''s Incompleteness Theorems, Trakhtenbrot''s undecidability theorem, Lindström''s theorems on the maximality of first-order logic, and results linking logic with automata theory. This new edition features many modernizations, as well as two additional important results: The decidability of Presburger arithmetic, and the decidability of the weak monadic theory of the successor function.
Mathematical Logic is ideal for students beginning their studies in logic and the foundations of mathematics. Although the primary audience for this textbook will be graduate students or advanced undergraduates in mathematics or computer science, in fact the book has few formal prerequisites. It demands of the reader only mathematical maturity and experience with basic abstract structures, such as those encountered in discrete mathematics or algebra.
Del 291 - Graduate Texts in Mathematics
Mathematical Logic
AvHeinz-Dieter Ebbinghaus,Jörg Flumm. fl.
Häftad, Engelska, 2022
546 kr
Skickas inom 10-15 vardagar
This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science.The chapters are carefully organized, featuring complete proofs and numerous examples throughout. Beginning with motivating examples, the book goes on to present the syntax and semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type proof of the completeness theorem is given. These introductory chapters prepare the reader for the advanced topics that follow, such as Gödel's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindström's theorems on the maximality of first-order logic, and results linking logic with automata theory. This new edition features many modernizations, as well as two additional important results: The decidability of Presburger arithmetic, and the decidability of the weak monadic theory of the successor function.Mathematical Logic is ideal for students beginning their studies in logic and the foundations of mathematics. Although the primary audience for this textbook will be graduate students or advanced undergraduates in mathematics or computer science, in fact the book has few formal prerequisites. It demands of the reader only mathematical maturity and experience with basic abstract structures, such as those encountered in discrete mathematics or algebra.
Del 1141 - Lecture Notes in Mathematics
Recursion Theory Week
Proceedings of a Conference held in Oberwolfach, West Germany, April 15-21, 1984
AvHeinz-Dieter Ebbinghaus,Gert H. Müllerm. fl.
Häftad, Engelska, 1985
545 kr
Skickas inom 10-15 vardagar
Finite Model Theory
Second Edition
AvHeinz-Dieter Ebbinghaus,Jörg Flum
Inbunden, Engelska, 2005
1 947 kr
Skickas inom 10-15 vardagar
Finite model theory, the model theory of finite structures, has roots in clas sical model theory; however, its systematic development was strongly influ enced by research and questions of complexity theory and of database theory. Model theory or the theory of models, as it was first named by Tarski in 1954, may be considered as the part of the semantics of formalized languages that is concerned with the interplay between the syntactic structure of an axiom system on the one hand and (algebraic, settheoretic, . . . ) properties of its models on the other hand. As it turned out, first-order language (we mostly speak of first-order logic) became the most prominent language in this respect, the reason being that it obeys some fundamental principles such as the compactness theorem and the completeness theorem. These principles are valuable modeltheoretic tools and, at the same time, reflect the expressive weakness of first-order logic. This weakness is the breeding ground for the freedomwhich modeltheoretic methods rest upon. By compactness, any first-order axiom system either has only finite models of limited cardinality or has infinite models. The first case is trivial because finitely many finite structures can explicitly be described by a first-order sentence. As model theory usually considers all models of an axiom system, modeltheorists were thus led to the second case, that is, to infinite structures. In fact, classical model theory of first-order logic and its generalizations to stronger languages live in the realm of the infinite.
Finite Model Theory
Second Edition
AvJorg Flum,Heinz-Dieter Ebbinghaus
E-bok
PDF, Engelska, 2005
2 517 kr
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Finite model theory, the model theory of finite structures, has roots in clas sical model theory; however, its systematic development was strongly influ enced by research and questions of complexity theory and of database theory. Model theory or the theory of models, as it was first named by Tarski in 1954, may be considered as the part of the semantics of formalized languages that is concerned with the interplay between the syntactic structure of an axiom system on the one hand and (algebraic, settheoretic, . . . ) properties of its models on the other hand. As it turned out, first-order language (we mostly speak of first-order logic) became the most prominent language in this respect, the reason being that it obeys some fundamental principles such as the compactness theorem and the completeness theorem. These principles are valuable modeltheoretic tools and, at the same time, reflect the expressive weakness of first-order logic. This weakness is the breeding ground for the freedomwhich modeltheoretic methods rest upon. By compactness, any first-order axiom system either has only finite models of limited cardinality or has infinite models. The first case is trivial because finitely many finite structures can explicitly be described by a first-order sentence. As model theory usually considers all models of an axiom system, modeltheorists were thus led to the second case, that is, to infinite structures. In fact, classical model theory of first-order logic and its generalizations to stronger languages live in the realm of the infinite.
Recursion Theory Week
Proceedings of a Conference held in Oberwolfach, West Germany, April 15-21, 1984
AvGerald E. Sacks,Gert H. Mullerm. fl.
E-bok
PDF, Engelska, 2006
712 kr
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Ernst Zermelo
An Approach to His Life and Work
AvHeinz-Dieter Ebbinghaus
E-bok
PDF, Engelska, 2007
870 kr
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Ernst Zermelo (1871-1953) is best-known for the statement of the axiom of choice and his axiomatization of set theory. However, he also worked in applied mathematics and mathematical physics. His dissertation, for example, promoted the calculus of variations, and he created the pivotal method in the theory of rating systems.
This biography attempts to shed light on all facets of Zermelo''s life and achievements. Personal and scientific aspects are kept separate as far as coherence allows, in order to enable the reader to follow the one or the other of these threads. The description of his personality owes much to conversations with his late wife Gertrud. The presentation of his work explores motivations, aims, acceptance, and influence. Selected proofs and information gleaned from unpublished notes and letters add to the analysis.
All facts presented are documented by appropriate sources. The biography contains more than 40 photos and facsimiles, most of them provided by Gertrud Zermelo and published here for the first time.
Zahlen
AvHeinz-Dieter Ebbinghaus,Hans Hermesm. fl.
Häftad, Tyska, 1992
561 kr
Skickas inom 10-15 vardagar
Die Schwierigkeit Mathematik zu lernen und zu lehren ist jedem bekannt, der einmal mit diesem Fach in Berührung gekommen ist. Begriffe wie "reelle oder komplexe Zahlen, Pi" sind zwar jedem geläufig, aber nur wenige wissen, was sich wirklich dahinter verbirgt. Die Autoren dieses Bandes geben jedem, der mehr wissen will als nur die Hülle der Begriffe, eine meisterhafte Einführung in die Magie der Mathematik und schlagen einzigartige Brücken für Studenten.Die Rezensenten der ersten beiden Auflagen überschlugen sich.
Ernst Zermelo - Collected Works/Gesammelte Werke II
Volume II/Band II - Calculus of Variations, Applied Mathematics, and Physics/Variationsrechnung, Angewandte Mathematik und Physik
AvErnst Zermelo,Heinz-Dieter Ebbinghausm. fl.
Inbunden, Engelska, 2013
2 162 kr
Skickas inom 10-15 vardagar
Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and is best-known for the first formulation of the axiom of choice. However, his papers also include pioneering work in applied mathematics and mathematical physics.This edition of his collected papers consists of two volumes. The present Volume II covers Ernst Zermelo’s work on the calculus of variations, applied mathematics, and physics.The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field who comments on the historical background, motivation, accomplishments, and influence.
Ernst Zermelo - Collected Works/Gesammelte Werke II
Volume II/Band II - Calculus of Variations, Applied Mathematics, and Physics/Variationsrechnung, Angewandte Mathematik und Physik
AvErnst Zermelo,Akihiro Kanamorim. fl.
E-bok
PDF, Engelska, 2013
2 833 kr
Läs direkt efter köp
Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and is best-known for the first formulation of the axiom of choice. However, his papers also include pioneering work in applied mathematics and mathematical physics.
This edition of his collected papers consists of two volumes. The present Volume II covers Ernst Zermelo’s work on the calculus of variations, applied mathematics, and physics.
The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field who comments on the historical background, motivation, accomplishments, and influence.
Del 21 - Schriften der Mathematisch-naturwissenschaftlichen Klasse
Ernst Zermelo - Collected Works/Gesammelte Werke
Volume I/Band I - Set Theory, Miscellanea/Mengenlehre, Varia
AvErnst Zermelo,Heinz-Dieter Ebbinghausm. fl.
Inbunden, Engelska, 2010
1 839 kr
Skickas inom 10-15 vardagar
Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and best-known for the first formulation of the axiom of choice. However, his papers include also pioneering work in applied mathematics and mathematical physics.This edition of his collected papers will consist of two volumes. Besides providing a biography, the present Volume I covers set theory, the foundations of mathematics, and pure mathematics and is supplemented by selected items from his Nachlass and part of his translations of Homer's Odyssey. Volume II will contain his work in the calculus of variations, applied mathematics, and physics.The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field which comments on the historical background, motivations, accomplishments, and influence.
Ernst Zermelo - Collected Works/Gesammelte Werke
Volume I/Band I - Set Theory, Miscellanea/Mengenlehre, Varia
AvErnst Zermelo,Craig G. Fraserm. fl.
E-bok
PDF, Engelska, 2010
2 351 kr
Läs direkt efter köp
Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and best-known for the first formulation of the axiom of choice. However, his papers include also pioneering work in applied mathematics and mathematical physics.
This edition of his collected papers will consist of two volumes. Besides providing a biography, the present Volume I covers set theory, the foundations of mathematics, and pure mathematics and is supplemented by selected items from his Nachlass and part of his translations of Homer''s Odyssey. Volume II will contain his work in the calculus of variations, applied mathematics, and physics.
The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field which comments on the historical background, motivations, accomplishments, and influence.
Ernst Zermelo
An Approach to His Life and Work
AvHeinz-Dieter Ebbinghaus
Häftad, Engelska, 2010
882 kr
Skickas inom 5-8 vardagar
Ernst Zermelo (1871-1953) is best-known for the statement of the axiom of choice and his axiomatization of set theory. However, he also worked in applied mathematics and mathematical physics. His dissertation, for example, promoted the calculus of variations, and he created the pivotal method in the theory of rating systems.This biography attempts to shed light on all facets of Zermelo's life and achievements. Personal and scientific aspects are kept separate as far as coherence allows, in order to enable the reader to follow the one or the other of these threads. The description of his personality owes much to conversations with his late wife Gertrud. The presentation of his work explores motivations, aims, acceptance, and influence. Selected proofs and information gleaned from unpublished notes and letters add to the analysis.All facts presented are documented by appropriate sources. The biography contains more than 40 photos and facsimiles, most of them provided by Gertrud Zermelo and published here for the first time.
Del 21 - Schriften der Mathematisch-naturwissenschaftlichen Klasse
Ernst Zermelo - Collected Works/Gesammelte Werke
Volume I/Band I - Set Theory, Miscellanea/Mengenlehre, Varia
AvErnst Zermelo,Heinz-Dieter Ebbinghausm. fl.
Häftad, Engelska, 2012
1 952 kr
Skickas inom 10-15 vardagar
Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and best-known for the first formulation of the axiom of choice. However, his papers include also pioneering work in applied mathematics and mathematical physics.This edition of his collected papers will consist of two volumes. Besides providing a biography, the present Volume I covers set theory, the foundations of mathematics, and pure mathematics and is supplemented by selected items from his Nachlass and part of his translations of Homer's Odyssey. Volume II will contain his work in the calculus of variations, applied mathematics, and physics.The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field which comments on the historical background, motivations, accomplishments, and influence.
Del 23 - Schriften der Mathematisch-naturwissenschaftlichen Klasse
Ernst Zermelo - Collected Works/Gesammelte Werke II
Volume II/Band II - Calculus of Variations, Applied Mathematics, and Physics/Variationsrechnung, Angewandte Mathematik und Physik
AvErnst Zermelo,Heinz-Dieter Ebbinghausm. fl.
Häftad, Engelska, 2015
2 162 kr
Skickas inom 10-15 vardagar
Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and is best-known for the first formulation of the axiom of choice. However, his papers also include pioneering work in applied mathematics and mathematical physics.This edition of his collected papers consists of two volumes. The present Volume II covers Ernst Zermelo’s work on the calculus of variations, applied mathematics, and physics.The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field who comments on the historical background, motivation, accomplishments, and influence.
Zahlen
AvReinhold Remmert,Alexander Prestelm. fl.
E-bok
PDF, Tyska, 2013
570 kr
Läs direkt efter köp
Die Schwierigkeit Mathematik zu lernen und zu lehren ist jedem bekannt, der einmal mit diesem Fach in Berührung gekommen ist. Begriffe wie "reelle oder komplexe Zahlen, Pi" sind zwar jedem geläufig, aber nur wenige wissen, was sich wirklich dahinter verbirgt. Die Autoren dieses Bandes geben jedem, der mehr wissen will als nur die Hülle der Begriffe, eine meisterhafte Einführung in die Magie der Mathematik und schlagen einzigartige Brücken für Studenten.
Die Rezensenten der ersten beiden Auflagen überschlugen sich.
Zahlen
AvReinhold Remmert,Alexander Prestelm. fl.
E-bok
PDF, Tyska, 2013
537 kr
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Aus den Besprechungen: "Ein Mathematikbuch der Superlativen, für Mathematiker (jeder Schattierung) und Nichtmathematiker (denen völlig unbekannte Dimensionen der Mathematik eröffnet werden - künstlerische, magische, historische, philosophische, wissenschaftstheoretische, "unlogische", phantasieerfüllte usw.). Der Aufbau ist meisterhaft, die Lektüre höchst anregend und leicht lesbar." Monatshefte für Mathematik #1 "Ein gelungenes Werk, das dem Vorurteil entgegenwirkt, Mathematik bestehe nur aus isolierten Theorien." Die NEUE HOCHSCHULE #1 "Das Lesen ist ein Genuß, den man sich nicht entgehen lassen sollte." Jahresbericht der Deutschen Mathematiker-Vereinigung #1
Finite Model Theory
First Edition
AvJorg Flum,Heinz-Dieter Ebbinghaus
E-bok
PDF, Engelska, 2013
1 140 kr
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Finite model theory has its origin in classical model theory, but owes its systematic development to research from complexity theory. The book presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed- point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. Other topics include DATALOG languages, quantifiers and oracles, 0-1 laws, and optimization and approximation problems. The book is written in such a way that the resp. parts on model theory and descriptive complexity theory may be read independently.
O-Bibliography of Mathematical Logic
Model Theory
AvHeinz-Dieter Ebbinghaus
E-bok
PDF, Engelska, 2013
710 kr
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Ω-Bibliography of Mathematical Logic
Model Theory
AvHeinz-Dieter Ebbinghaus
Häftad, Engelska, 2013
546 kr
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Gert H. Muller The growth of the number of publications in almost all scientific areas, as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica- tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic- ularly if they do not have an extensive library available in their neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some- where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg 11. Non-classical Logics W. Rautenberg 111. Model Theory H. -D. Ebbinghaus IV. Recursion Theory P. G. Hinman V. Set Theory A. R. Blass VI.ProofTheory; Constructive Mathematics J. E. Kister; D. van Dalen & A. S. Troelstra.
Ernst Zermelo
An Approach to His Life and Work
AvHeinz Dieter Ebbinghaus,Volker Peckhaus
Inbunden, Engelska, 2015
637 kr
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This biography sheds light on all facets of the life and the achievements of Ernst Zermelo (1871-1953). Zermelo is best-known for the statement of the axiom of choice and his axiomatization of set theory. However, he also worked in applied mathematics and mathematical physics. His dissertation, for example, promoted the calculus of variations, and he created the pivotal method in the theory of rating systems.The presentation of Zermelo's work explores motivations, aims, acceptance, and influence. Selected proofs and information gleaned from letters add to the analysis. The description of his personality owes much to conversations with his late wife Gertrud.This second edition provides additional information. The system of citations has been adapted to that of Zermelo's Collected Works in order to facilitate side-by-side reading and thus profit from the thorough commentaries written for the Collected Works by experts in the respective fields.All facts presented are documented by appropriate sources. The biography contains nearly 50 photos and facsimiles.
Ernst Zermelo
An Approach to His Life and Work
AvVolker Peckhaus,Heinz Dieter Ebbinghaus
E-bok
PDF, Engelska, 2015
789 kr
Läs direkt efter köp
This biography sheds light on all facets of the life and the achievements of Ernst Zermelo (1871-1953). Zermelo is best-known for the statement of the axiom of choice and his axiomatization of set theory. However, he also worked in applied mathematics and mathematical physics. His dissertation, for example, promoted the calculus of variations, and he created the pivotal method in the theory of rating systems.
The presentation of Zermelo''s work explores motivations, aims, acceptance, and influence. Selected proofs and information gleaned from letters add to the analysis. The description of his personality owes much to conversations with his late wife Gertrud.
This second edition provides additional information. The system of citations has been adapted to that of Zermelo''s Collected Works in order to facilitate side-by-side reading and thus profit from the thorough commentaries written for the Collected Works by experts in the respective fields.
All facts presented are documented by appropriate sources. The biography contains nearly 50 photos and facsimiles.
Ernst Zermelo
An Approach to His Life and Work
AvHeinz Dieter Ebbinghaus,Volker Peckhaus
Häftad, Engelska, 2016
600 kr
Skickas inom 10-15 vardagar
This biography sheds light on all facets of the life and the achievements of Ernst Zermelo (1871-1953). Zermelo is best-known for the statement of the axiom of choice and his axiomatization of set theory. However, he also worked in applied mathematics and mathematical physics. His dissertation, for example, promoted the calculus of variations, and he created the pivotal method in the theory of rating systems.The presentation of Zermelo's work explores motivations, aims, acceptance, and influence. Selected proofs and information gleaned from letters add to the analysis. The description of his personality owes much to conversations with his late wife Gertrud.This second edition provides additional information. The system of citations has been adapted to that of Zermelo's Collected Works in order to facilitate side-by-side reading and thus profit from the thorough commentaries written for the Collected Works by experts in the respective fields.All facts presented are documented by appropriate sources. The biography contains nearly 50 photos and facsimiles.
Einführung in die mathematische Logik
AvHeinz-Dieter Ebbinghaus,Jörg Flumm. fl.
Häftad, Tyska, 2018
460 kr
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Was ist ein mathematischer Beweis? Wie lassen sich Beweise rechtfertigen? Gibt es Grenzen der Beweisbarkeit? Ist die Mathematik widerspruchsfrei? Kann man das Auffinden mathematischer Beweise Computern übertragen? Erst im 20. Jahrhundert ist es der mathematischen Logik gelungen, weitreichende Antworten auf diese Fragen zu geben. Im vorliegenden Werk werden die Ergebnisse systematisch zusammengestellt; im Mittelpunkt steht dabei die Logik erster Stufe. Die Lektüre setzt – außer einer gewissen Vertrautheit mit der mathematischen Denkweise – keine spezifischen Kenntnisse voraus. Für die vorliegende 6. Auflage wurde der Text überarbeitet und durch die Darstellung zweier für Logik und Informatik wichtiger Entscheidbarkeitsresultate erweitert.
Einführung in die mathematische Logik
AvWolfgang Thomas,Jorg Flumm. fl.
E-bok
PDF, Tyska, 2018
474 kr
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Was ist ein mathematischer Beweis? Wie lassen sich Beweise rechtfertigen? Gibt es Grenzen der Beweisbarkeit? Ist die Mathematik widerspruchsfrei? Kann man das Auffinden mathematischer Beweise Computern übertragen? Erst im 20. Jahrhundert ist es der mathematischen Logik gelungen, weitreichende Antworten auf diese Fragen zu geben. Im vorliegenden Werk werden die Ergebnisse systematisch zusammengestellt; im Mittelpunkt steht dabei die Logik erster Stufe. Die Lektüre setzt – außer einer gewissen Vertrautheit mit der mathematischen Denkweise – keine spezifischen Kenntnisse voraus. Für die vorliegende 6. Auflage wurde der Text überarbeitet und durch die Darstellung zweier für Logik und Informatik wichtiger Entscheidbarkeitsresultate erweitert.
Einführung in die Mengenlehre
AvHeinz-Dieter Ebbinghaus
Häftad, Tyska, 2021
359 kr
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Die Mengenlehre ist eine eigenständige mathematische Disziplin. Zugleich ist sie eine Grundlagendisziplin, die für alle mathematischen Gebiete ein begriffliches Gerüst bereithält. In dieser Universalität offenbart sich eine große Tragweite des Mengenbegriffs und seiner Axiomatisierung. Die vorliegende Einführung gibt daher nicht nur einen Einblick in die Theorie und belegt deren Bedeutung für die Mathematik, sie behandelt auch Methoden und Ergebnisse, die auf eine möglichst weitgehende Rechtfertigung der mengentheoretischen Axiomsysteme zielen. Geschichtliche und erkenntnistheoretische Betrachtungen runden das Bild ab.Das Buch setzt keine spezifischen mathematischen Kenntnisse voraus. Es richtet sich an alle, die an den Grundlagen der Mathematik interessiert und mit Gedankengängen mathematischer Prägung vertraut sind. Rund 200 Übungsaufgaben mit Lösungshinweisen bieten eine zusätzliche Hilfe, insbesondere dann, wenn man das Buch zur eigenständigen Erarbeitung des dargebotenen Stoffes nutzen möchte. Die Neuauflage ist vollständig durchgesehen und enthält jetzt eine systematische Behandlung der konstruktiblen Hierarchie, die Beweise der relativen Widerspruchsfreiheit des Auswahlaxioms und der Cantorschen Kontinuumshypothese erlaubt.
Einführung in die Mengenlehre
AvHeinz-Dieter Ebbinghaus
E-bok
PDF, Tyska, 2021
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Die Mengenlehre ist eine eigenständige mathematische Disziplin. Zugleich ist sie eine Grundlagendisziplin, die für alle mathematischen Gebiete ein begriffliches Gerüst bereithält. In dieser Universalität offenbart sich eine große Tragweite des Mengenbegriffs und seiner Axiomatisierung. Die vorliegende Einführung gibt daher nicht nur einen Einblick in die Theorie und belegt deren Bedeutung für die Mathematik, sie behandelt auch Methoden und Ergebnisse, die auf eine möglichst weitgehende Rechtfertigung der mengentheoretischen Axiomsysteme zielen. Geschichtliche und erkenntnistheoretische Betrachtungen runden das Bild ab.
Das Buch setzt keine spezifischen mathematischen Kenntnisse voraus. Es richtet sich an alle, die an den Grundlagen der Mathematik interessiert und mit Gedankengängen mathematischer Prägung vertraut sind. Rund 200 Übungsaufgaben mit Lösungshinweisen bieten eine zusätzliche Hilfe, insbesondere dann, wenn man das Buch zur eigenständigen Erarbeitung des dargebotenen Stoffes nutzen möchte.
Die Neuauflage ist vollständig durchgesehen und enthält jetzt eine systematische Behandlung der konstruktiblen Hierarchie, die Beweise der relativen Widerspruchsfreiheit des Auswahlaxioms und der Cantorschen Kontinuumshypothese erlaubt.

Heinz-Dieter Ebbinghaus – författare

Numbers

Numbers

Mathematical Logic

Mathematical Logic

Mathematical Logic

Recursion Theory Week

Finite Model Theory

Finite Model Theory

Recursion Theory Week

Ernst Zermelo

Zahlen

Ernst Zermelo - Collected Works/Gesammelte Werke II

Ernst Zermelo - Collected Works/Gesammelte Werke II

Ernst Zermelo - Collected Works/Gesammelte Werke

Ernst Zermelo - Collected Works/Gesammelte Werke

Ernst Zermelo

Ernst Zermelo - Collected Works/Gesammelte Werke

Ernst Zermelo - Collected Works/Gesammelte Werke II

Zahlen

Zahlen

Finite Model Theory

O-Bibliography of Mathematical Logic

Ω-Bibliography of Mathematical Logic

Ernst Zermelo

Ernst Zermelo

Ernst Zermelo

Einführung in die mathematische Logik

Einführung in die mathematische Logik

Einführung in die Mengenlehre

Einführung in die Mengenlehre