Mathematical logic Books
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings
Book SynopsisOver the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.Table of ContentsPreliminaries.- Beginnings.- Partition Properties.- Forcing and Sets of Reals.- Aspects of Measurability.- Strong Hypotheses.- Determinacy.
£104.49
AV Akademikerverlag Drayage Operations at Seaports
£34.57
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Algebraic Complexity Theory
Book SynopsisThe algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.Trade ReviewP. Bürgisser, M. Clausen, M.A. Shokrollahi, and T. Lickteig Algebraic Complexity Theory "The book contains interesting exercises and useful bibliographical notes. In short, this is a nice book."—MATHEMATICAL REVIEWS From the reviews: "This book is certainly the most complete reference on algebraic complexity theory that is available hitherto. … superb bibliographical and historical notes are given at the end of each chapter. … this book would most certainly make a great textbook for a graduate course on algebraic complexity theory. … In conclusion, any researchers already working in the area should own a copy of this book. … beginners at the graduate level who have been exposed to undergraduate pure mathematics would find this book accessible." (Anthony Widjaja, SIGACT News, Vol. 37 (2), 2006)Table of Contents1. Introduction.- I. Fundamental Algorithms.- 2. Efficient Polynomial Arithmetic.- 3. Efficient Algorithms with Branching.- II. Elementary Lower Bounds.- 4. Models of Computation.- 5. Preconditioning and Transcendence Degree.- 6. The Substitution Method.- 7. Differential Methods.- III. High Degree.- 8. The Degree Bound.- 9. Specific Polynomials which Are Hard to Compute.- 10. Branching and Degree.- 11. Branching and Connectivity.- 12. Additive Complexity.- IV. Low Degree.- 13. Linear Complexity.- 14. Multiplicative and Bilinear Complexity.- 15. Asymptotic Complexity of Matrix Multiplication.- 16. Problems Related to Matrix Multiplication.- 17. Lower Bounds for the Complexity of Algebras.- 18. Rank over Finite Fields and Codes.- 19. Rank of 2-Slice and 3-Slice Tensors.- 20. Typical Tensorial Rank.- V. Complete Problems.- 21. P Versus NP: A Nonuniform Algebraic Analogue.- List of Notation.
£104.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Felix Hausdorff - Gesammelte Werke Band IA:
Book SynopsisDer Band 1A beginnt mit einem Vorwort zur Gesamtedition. Den Hauptteil des Bandes bilden Hausdorffs Arbeiten über geordnete Mengen aus den Jahren 1901-1909. Diese haben der Entwicklung der Mengenlehre nachhaltige Impulse verliehen. Sie enthalten zahlreiche für die Untersuchung geordneter Mengen grundlegende neue Begriffe sowie tiefliegendere Resultate. Alle diese Arbeiten sind sorgfältig kommentiert. Die Kommentare zeigen, dass einige von Hausdorff's Ideen und Resultaten für die moderne Grundlagenforschung hochaktuell sind. Ferner enthält der Band Hausdorff's kritische Besprechung von Russells "The Principles of Mathematics", aus dem Nachlass seine Vorlesung "Mengenlehre" von 1901 (eine der ersten Vorlesungen über dieses Gebiet überhaupt) sowie einen Essay "Hausdorff als akademischer Lehrer". Table of ContentsTeil I. Arbeiten über geordnete Mengen.– Über eine gewisse Art geordneter Mengen.- Kommentar.- Der Potenzbegriff in der Mengenlehre.- Kommentar.- Untersuchungen über Ordnungstypen I, II, III.- Untersuchungen über Ordnungstypen IV, V.- Kommentar.- Über dichte Ordnungstypen.- Kommentar.- Grundzüge einer Theorie der geordneten Mengen.- Kommentar.- Die Graduierung nach dem Endverlauf.- Comments.- Summe von N1 Mengen.- Comments.- Gaps in partially ordered sets and related problems.- Teil II. Aus dem Nachlaß zur Mengenlehre.- Mengenlehre. Vorlesung der Universität Leipzig, Sommersemester 1901.- Kommentar.- Alefsätze.- Anhänge.- Bertrand Russell, The Principles of Mathematics (Besprechung).- Kommentar.- Hausdorff als akademischer Lehrer.- Entstehung der Hausdorff-Edition.- Personenregister.- Sachregister.
£125.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Handbook of Weighted Automata
Book SynopsisThe purpose of this Handbook is to highlight both theory and applications of weighted automata. Weighted finite automata are classical nondeterministic finite automata in which the transitions carry weights. These weights may model, e. g. , the cost involved when executing a transition, the amount of resources or time needed for this,or the probability or reliability of its successful execution. The behavior of weighted finite automata can then be considered as the function (suitably defined) associating with each word the weight of its execution. Clearly, weights can also be added to classical automata with infinite state sets like pushdown automata; this extension constitutes the general concept of weighted automata. To illustrate the diversity of weighted automata, let us consider the following scenarios. Assume that a quantitative system is modeled by a classical automaton in which the transitions carry as weights the amount of resources needed for their execution. Then the amount of resources needed for a path in this weighted automaton is obtained simply as the sum of the weights of its transitions. Given a word, we might be interested in the minimal amount of resources needed for its execution, i. e. , for the successful paths realizing the given word. In this example, we could also replace the “resources” by “profit” and then be interested in the maximal profit realized, correspondingly, by a given word.Trade ReviewFrom the reviews:"This book is an excellent reference for researchers in the field, as well as students interested in this research area. The presentation of applications makes it interesting to researchers from other fields to study weighted automata. ... One of the main arguments in favor of this handbook is the completeness of its index table — usually a faulty section in such volumes. The chapters are globally well-written and self-contained, thus pleasant to read, and the efforts put to maintain consistency in vocabulary thorough the book are very appreciable." (Michaël Cadilhac, The Book Review Column 43-3, 2012)“The book presents a broad survey, theory and applications, of weighted automata, classical nondeterministic automata in which transitions carry weights. … The individual articles are written by well-known researchers in the field: they include extensive lists of references and many open problems. The book is valuable for both computer scientists and mathematicians (being interested in discrete structures).” (Cristian S. Calude, Zentralblatt MATH, Vol. 1200, 2011)Table of ContentsFoundations.- Semirings and Formal Power Series.- Fixed Point Theory.- Concepts of Weighted Recognizability.- Finite Automata.- Rational and Recognisable Power Series.- Weighted Automata and Weighted Logics.- Weighted Automata Algorithms.- Weighted Discrete Structures.- Algebraic Systems and Pushdown Automata.- Lindenmayer Systems.- Weighted Tree Automata and Tree Transducers.- Traces, Series-Parallel Posets, and Pictures: A Weighted Study.- Applications.- Digital Image Compression.- Fuzzy Languages.- Model Checking Linear-Time Properties of Probabilistic Systems.- Applications of Weighted Automata in Natural Language Processing.
£132.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Stochastic Calculus with Infinitesimals
Book SynopsisStochastic 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 financial 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 from measure theory and functional analysis or lack full 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 a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.Table of Contents1 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 Itô diffusions and associated partial differential equations.- 8 Excursion to mathematical physics: A radically elementary definition of Feynman path integrals.- 9 A radically elementary theory of Lévy processes.- 10 Final remarks.
£31.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Personelle und Statistische Wahrscheinlichkeit
Book SynopsisTable of ContentsEinleitung: Überblick über den Inhalt des zweiten Halbbandes.- III. Die logischen Grundlagen des statistischen Schließens.- 1. ,Jenseits von Popper und Carnap‘.- 1.a Programm und Abgrenzung vom Projekt einer induktiven Logik.- 1.b Die relative Häufigkeit auf lange Sicht und die Häufigkeitsdefinition der statistischen Wahrscheinlichkeit.- 1.c Der Vorschlag von Braithwaite, die statistische Wahrscheinlichkeit als theoretischen Begriff einzuführen.- 1.d Vorbereitende Betrachtungen zur Testproblematik statistischer Hypothesen.- 1.e Zusammenfassung und Ausblick.- 2. Präludium: Der intuitive Hintergrund.- 3. Die Grundaxiome. Statistische Unabhängigkeit.- 3.a Die Kolmogoroff-Axiome.- 3.b Unabhängigkeit im statistischen Sinn.- 3.c Hypothesen und Oberhypothesen.- 4. Die komparative Stützungslogik.- 4.a Vorbetrachtungen.- 4.b Einige zusätzliche Zwischenbetrachtungen.- 4.c Die Axiome der Stützungslogik.- 5. Die Likelihood-Regel.- 5.a Kombinierte statistische Aussagen.- 5.b Likelihood und Likelihood-Regel.- 6. Die Leistungsfähigkeit der Likelihood-Regel.- 6.a Die Einzelfall-Regel und ihre Begründung.- 6.b Der statistische Stützungsschluß im diskreten Fall und seine Rechtfertigung.- 6.c Übergang zum stetigen Fall.- 6.d Wahrscheinlichkeitsverteilung und Likelihoodfunktion (,Plausibilitätsverteilung‘).- 6.e Denken in Likelihoods und Bayesianismus.- 7. Vorläufiges Postludium: Ergänzende Betrachtungen zu den statistischen Grundbegriffen.- 7.a Der Begriff des statistischen Datums.- 7.b Chance und Häufigkeit auf lange Sicht.- 7.c Versuchstypen.- 8. Zufall, Grundgesamtheit und Stichprobenauswahl.- 9. Die Problematik der statistischen Testtheorie, erläutert am Beispiel zweier konkurrierender Testtheorien.- 9.a Vorbetrachtungen. Ein warnendes historisches Beispiel.- 9.b Macht und Umfang eines Tests. Die Testtheorie von Neyman-Pearson.- 9.c Die Mehrdeutigkeit der Begriffe „Annahme“ und „Verwerfung“ 159 9.d Einige kritische Bemerkungen zu den Begriffen Umfang und Macht 160 9.e Die Likelihood-Testtheorie.- 10. Probleme der Schätzungstheorie.- 10.a Vorbemerkungen.- 10.b Was ist Schätzung? Klassifikation von Schätzungen.- 10.c Einige spezielle Begriffe der statistischen Schätzungstheorie.- 10.d Die Doppeldeutigkeit von „Schätzung“ und die Mehrdeutigkeit von „Güte einer Schätzung“.- 10.e Theoretische Schätzungen und Schätzhandlungen.- 10.f Das Skalendilemma. Zwecke von Schätzungen.- 10.g Schätzungen im engeren und Schätzungen im weiteren Sinn.- 10.h Kritisches zu den Optimalitätsmerkmalen auf lange Sicht, zur Minimax-Theorie und zur Intervallschätzung.- 10.i Ein Präzisierungsversuch des Begriffes der besser gestützten Schätzung.- 10.j Ist die Schätzungstheorie von Savage das Analogon zur Testtheorie von Neyman-Pearson?.- 11. Kritische Betrachtungen zur Likelihood-Stützungs-und-Testtheorie.- 11.a Ist der Likelihood-Test schlechter als nutzlos ?.- 11.b Das Karten-Paradoxon von Kerridge.- 11.c Die logische Struktur des Stützungsbegriffs.- 12. Subjektivismus oder Objektivismus ?.- 12.a Die subjektivistische (personalistische) Kritik: de Finetti und Savage kontra Objektivismus.- 12.b Die Propensity-Interpretation der statistischen Wahrscheinlichkeit: Popper, Giere und Suppes.- 13. Versuch einer Skizze der logischen Struktur des Fiduzial-Argumentes von R. A. Fisher.- Bibliographie.- IV. ,Statistisches Schließen — Statistische Begründung — Statistische Analyse‘statt,Statistische Erklärung‘.- 1. Elf Paradoxien und Dilemmas.- (I) Die Paradoxie der Erklärung des Unwahrscheinlichen.- (II) Das Paradoxon der irrelevanten Gesetzesspezialisierung.- (III) Das Informationsdilemma.- (IV) Das Erklärungs-Bestätigungs-Dilemma.- (V) Das Paradoxon der reinen ex post facto Kausalerklärung.- (VI) Das Verzahnungsparadoxon.- (VII) Das Erklärungs-Begründungs-Dilemma.- (VIII) Das Dilemma der nomologischen Implikation.- (IX) Das ,Weltanschauungsdilemma‘.- (X) Das Argumentationsdilemma.- (XI) Das Gesetzesparadoxon.- 2. Diskussion.- 2.a Problemreduktionen.- 2.b Das Problem der nomologischen Implikation. Statistisches Schließen und statistische Begründungen.- 2.c Verzahnungen von Erklärungs- und Bestätigungsproblemen.- 2.d Die Leibniz-Bedingung. Unbehebbare intuitive Konflikte.- 3. Statistische Begründungen statt statistische Erklärungen. Der statistische Begründungsbegriff als Explikat der Einzelfall-Regel.- 4. Statistische Analysen.- 4.a Kausale Relevanz und Abschirmung.- 4.b Statistische Oberflächenanalyse und statistisch-kausale Tiefenanalyse von Minimalform.- 4.c Statistische Analyse und statistisches Situationsverständnis.- 4.d Was könnte unter „Statistische Erklärung“ verstanden werden?.- Bibliographie.- Anhang I: Indeterminismus vom zweiten Typ.- Anhang II: Das Repräsentationstheorem von B. de Finetti.- 1. Intuitiver Zugang.- 1.a Bernoulli-Wahrscheinlichkeiten und Mischungen von Bernoulli-Wahrscheinlichkeiten.- 1.b Das Problem des Lernens aus der Erfahrung.- 1.c Die Bedeutung des Begriffs der Vertauschbarkeit.- 2. Formale Skizze. Übergang zum kontinuierlichen Fall.- 2.a Vertauschbarkeit und Symmetrie.- 2.b Mischungen und Lernen aus der Erfahrung: Der Riemannsche Fall..- 2.c Mischungen im abstrakten maßtheoretischen Fall. Das Repräsentationstheorem.- 2.d Diskussion.- Bibliographie.- Anhang III: Metrisierung qualitativer Wahrscheinlichkeitsfelder.- 1. Axiomatische Theorien der Metrisierung. Extensive Größen.- 2. Metrisierung von Wahrscheinlichkeitsfeldern.- 2.a Metrisierung klassischer absoluter Wahrscheinlichkeitsfelder im endlichen und abzählbaren Fall.- 2.b Metrisierung quantenmechanischer Wahrscheinlichkeitsfelder.- 2.c Metrisierung qualitativer bedingter Wahrscheinlichkeitsfelder.- Bibliographie.- Autorenregister.- Verzeichnis der Symbole und Abkürzungen.
£44.64
Springer Fachmedien Wiesbaden Diagonalization in Formal Mathematics
Book SynopsisIn this book, Paulo Guilherme Santos studies diagonalization in formal mathematics from logical aspects to everyday mathematics. He starts with a study of the diagonalization lemma and its relation to the strong diagonalization lemma. After that, Yablo’s paradox is examined, and a self-referential interpretation is given. From that, a general structure of diagonalization with paradoxes is presented. Finally, the author studies a general theory of diagonalization with the help of examples from mathematics.Table of ContentsDiagonalization in Mathematics.- Diagonalization Lemma.- Fixed Point Theorems.- Paradoxes: Liar, Yablo’s Paradox, Curry’s Paradox.
£40.49
Springer Fachmedien Wiesbaden Berechenbarkeit: Berechnungsmodelle und
Book SynopsisIn diesem essential werden wesentliche Konzepte der Berechenbarkeitstheorie erörtert. Zunächst werden unterschiedliche Modelle der Berechenbarkeit eingeführt und ihre semantische Gleichwertigkeit gezeigt. Dieses Resultat steht in Einklang mit der Church-Turing-These, nach der jede intuitiv berechenbare Funktion partiell-rekursiv ist. Neben zentralen Instrumenten der Berechenbarkeit, wie etwa der Gödelisierung von berechenbaren Funktionen und der Existenz universeller berechenbarer Funktionen, stehen unentscheidbare Probleme im Fokus, wie etwa das Halteproblem sowie das Wortproblem für die Term-Ersetzung. Semi-entscheidbare Mengen werden beleuchtet und die zentralen Sätze von Rice und Rice-Shapiro werden skizziert. Table of ContentsBerechnungsmodelle.- Zentrale Konzepte.- Unentscheidbare Probleme.- Historie und Zusammenfassung
£9.99
Springer Fachmedien Wiesbaden Diskrete Mathematik mit Grundlagen: Lehrbuch für
Book SynopsisDieses Lehrbuch wendet sich an Leser ohne Studienvorkenntnisse, gibt eine elementare Einführung in die Diskrete Mathematik und die Welt des mathematischen Denkens und führt den Leser auf ein solides Hochschulniveau. Im Einzelnen werden elementare Logik, Mengenlehre, Beweiskonzepte und die mathematische Terminologie dafür ausführlich erklärt und durch Anwendungsbeispiele motiviert. Darauf aufbauend werden die wichtigsten Disziplinen der Diskreten Mathematik behandelt in einem Umfang, der für jedes MINT-Studium außer der Mathematik selbst ausreicht. Zahlreiche Übungsaufgaben runden das Angebot ab, die Lösungen dazu werden online zur Verfügung gestellt. Das Buch ist zum Selbststudium, als Vorlesungsbegleitung und zum Nachschlagen geeignet. Die zweite Auflage wurde vollständig überarbeitet. Das Kapitel zur Logik wurde erheblich ausgeweitet, unter anderem durch eine allgemeinverständliche Anleitung mit vielen Beispielen, wie Alltagssprache in logische Sprache übersetzt wird.Table of ContentsLogik.- Mengenlehre.- Beweisverfahren.- Zahlentheorie.- Algebraische Strukturen.- Kombinatorik.- Graphentheorie.
£27.99
Springer Fachmedien Wiesbaden Der Untergang von Mathemagika: Ein Roman über
Book SynopsisWas haben ein König und eine Prinzessin in der Mengenlehre zu suchen? Eine Menge!In dem fantastischen Königreich Mathemagika erleben die Freunde Prof und Dio eine abenteuerliche Geschichte um das rätselhafte Verschwinden eines Ministers, eine bezaubernde Prinzessin – und einen der verrücktesten Sätze der Mathematik: das Banach-Tarski-Paradoxon. Es behauptet zum Beispiel, dass man eine Kugel von Erbsengröße in endlich vielen Teilen zu einer Kugel von Sonnengröße umbauen kann. Unmöglich?Der Untergang von Mathemagika ist eine neuartige Darstellung von Mathematik, die fesselt und hineinzieht. Es ist ein Vergnügen zu lesen, wie sich eins zum anderen fügt und am Ende alles zusammenpasst.Stimme zum Buch:„Dass ein mathematischer Satz in der Hauptrolle ein so herrliches Theater machen kann, begeistert mich: Math Fiction mit Witz, Dramatik und Tiefe.“ Prof. Dr. Thomas Bedürftig, Universität HannoverTrade Review“... in das merkwürdige Mathemagika, eine Welt der Ideen, eine Welt der Mengen, verschlagen hat. ...Damit sind für den Leser die mathematischen Voraussetzungen geschaffen ...wird der mathematische Hintergrund des Paradoxons immer wieder spielerisch aufgegriffen und sehr witzig beschrieben. Das Buch bietet Vergnügen bis zur letzten Seite ...” (Hartmut Weber, in: mathematik.de, 18. Juli. 2016Table of Contents1 Die Tonne des Diogenes.- 2 Die Fütterung der Pinguine.- 3 Der König.- 4 Das Denkmal.- 5 Das Volk der Ausdehnungslosen I.- 6 Die Schlange.- 7 Das Volk der Ausdehnungslosen II.- 8 Die verrückten Schwestern.- 9 Der Krisenstab.- 10 Die Flucht.- 11 Die Prinzessin.- 12 Der Antilogos.- 13 Schluss.
£17.09
Springer Fachmedien Wiesbaden Grenzen der Mathematik: Eine Reise durch die
Book SynopsisIst die Mathematik frei von Widersprüchen? Gibt es Wahrheiten jenseits des Beweisbaren? Ist es möglich, unser mathematisches Wissen in eine einzige Zahl hineinzucodieren? Die moderne mathematische Logik des zwanzigsten Jahrhunderts gibt verblüffende Antworten auf solche Fragen. Das vorliegende Buch entführt Sie auf eine Reise durch die Kerngebiete der mathematischen Logik, hin zu den Grenzen der Mathematik. Unter anderem werden die folgenden Themen behandelt: Geschichte der mathematischen Logik, formale Systeme, axiomatische Zahlentheorie und Mengenlehre, Beweistheorie, die Gödel‘schen Unvollständigkeitssätze, Berechenbarkeitstheorie, algorithmische Informationstheorie, Modelltheorie.Das Buch enthält zahlreiche zweifarbige Abbildungen und mehr als 70 Aufgaben (mit Lösungen auf der Website zum Buch). Für die dritte Auflage wurde das Kapitel ‚Modelltheorie‘ um eine Beschreibung der von Paul Cohen entwickelten Forcing-Technik ergänzt.Table of ContentsVorwort.- 1 Historische Notizen.- 1.1 Wahrheit und Beweisbarkeit.- 1.2 Der Weg zur modernen Mathematik.- 1.3 Übungsaufgaben.- 2 Formale Systeme.- 2.1 Definition und Eigenschaften.- 2.2 Entscheidungsverfahren.- 2.3 Aussagenlogik.- 2.4 Prädikatenlogik erster Stufe.- 2.5 Prädikatenlogik mit Gleichheit.- 2.6 Prädikatenlogik höherer Stufe.- 2.7 Übungsaufgaben.- 3 Fundamente der Mathematik.- 3.1 Peano-Arithmetik.- 3.2 Axiomatische Mengenlehre.- 3.3 Übungsaufgaben.- 4 Beweistheorie.- 4.1 Gödel’sche Unvollständigkeitssätze.- 4.2 Der erste Unvollständigkeitssatz.- 4.3 Der zweite Unvollständigkeitssatz.- 4.4 Gödels Sätze richtig verstehen.- 4.5 Der Satz von Goodstein.- 4.6 Übungsaufgaben.- 5 Berechenbarkeitstheorie.- 5.1 Berechnungsmodelle.- 5.2 Die Church’sche These.- 5.3 Grenzen der Berechenbarkeit.- 5.4 Folgen für die Mathematik.- 5.5 Übungsaufgaben.- 6 Algorithmische Informationstheorie.- 6.1 Algorithmische Komplexität.- 6.2 Die Chaitin’sche Konstante.- 6.3 Unvollständigkeit formaler Systeme.- 6.4 Übungsaufgaben.- 7 Modelltheorie.- 7.1 Meta-Resultate zur Prädikatenlogik.- 7.2 Nichtstandardmodelle von PA.- 7.3 Skolem-Paradoxon.- 7.4 Boole‘sche Modelle.- 7.5 Übungsaufgaben.- Literaturverzeichnis.- Bildnachweis.- Namensverzeichnis.- Sachwortverzeichnis.
£32.97
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Parameterized Complexity in the Polynomial Hierarchy: Extending Parameterized Complexity Theory to Higher Levels of the Hierarchy
Book SynopsisParameterized Complexity in the Polynomial Hierarchy was co-recipient of the E.W. Beth Dissertation Prize 2017 for outstanding dissertations in the fields of logic, language, and information. This work extends the theory of parameterized complexity to higher levels of the Polynomial Hierarchy (PH). For problems at higher levels of the PH, a promising solving approach is to develop fixed-parameter tractable reductions to SAT, and to subsequently use a SAT solving algorithm to solve the problem. In this dissertation, a theoretical toolbox is developed that can be used to classify in which cases this is possible. The use of this toolbox is illustrated by applying it to analyze a wide range of problems from various areas of computer science and artificial intelligence.Table of ContentsComplexity Theory and Non-determinism.- Parameterized Complexity Theory.- Fpt-Reducibility to SAT.- The Need for a New Completeness Theory.- A New Completeness Theory.- Fpt-algorithms with Access to a SAT Oracle.- Problems in Knowledge Representation and Reasoning.- Model Checking for Temporal Logics.- Problems Related to Propositional Satisfiability.- Problems in Judgment Aggregation.- Planning Problems.- Graph Problems.- Relation to Other Topics in Complexity Theory.- Subexponential-Time Reductions.- Non-Uniform Parameterized Complexity.- Open Problems and Future Research Directions.- Conclusion.- Compendium of Parameterized Problems.- Generalization to Higher Levels of the Polynomial Hierarchy.
£62.99
Springer Fachmedien Wiesbaden L. E. J. Brouwer: Intuitionismus
Book SynopsisDer mathematische Intuitionismus war die Schöpfung des niederländischen Mathematikers L. E. J. Brouwer, der damit am Anfang des zwanzigsten Jahrhunderts eine konstruktive Neubegründung der Mathematik anstieß. Dieses Buch enthält drei Arbeiten Brouwers aus den 1920er-Jahren, die seine Ansichten und Methoden in ausgereifter Form wiedergeben, sowie Kommentare dazu. Teil I besteht aus seinen im Jahre 1927 gehaltenen Berliner Gastvorlesungen, die die Ouvertüre zu einem erweiterten und vertieften Intuitionismus darstellen. Teil II entstammt einer geplanten aber unvollendeten Monographie über die Neubegründung der Theorie der reellen Funktionen. Teil III bringt abschließend Brouwers Wiener Vortrag „Mathematik, Wissenschaft und Sprache“, in dem er auf Fragen zur philosophischen Grundlage des Intuitionismus einging. Zusammengenommen geben diese drei Texte ein Gesamtbild von Brouwers intuitionistischen Auffassungen zum Höhepunkt des Grundlagenstreits in der Mathematik.Table of ContentsEinleitung.- BERLINER GASTVORLESUNGEN.- Historische Stellung des Intuitionismus.- Der Gegenstand der intuitionistischen Mathematik: Spezies, Punkte und Räume. Das Kontinuum.- Ordnung.- Analyse des Kontinuums.- Das Haupttheorem der finiten Mengen.- Intuitionistische Kritik an einigen elementaren Theoremen.- Anmerkungen.- THEORIE DER REELLEN FUNKTIONEN.- Grundlagen aus der Theorie der Punktmengen.- Hauptbegriffe über reelle Funktionen einer Veränderlichen.- WIENER VORTRAG: MATHEMATIK, WISSENSCHAFT UND SPRACHE.
£31.34
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Kunterbunte Mathematik: Begeisternde Erkundungen
Book SynopsisDieses Buch zeichnet ein – im wahrsten Sinne des Wortes – farbenfrohes Bild von Mathematik: Es stellt eine Auswahl von mathematischen Themen vor, die mithilfe durchgehend farbig gestalteter Abbildungen und unterstützt durch möglichst einfache Erläuterungen erschlossen werden. Auf Formeln und Rechnungen wurde soweit wie möglich verzichtet.Das Buch eignet sich insbesondere für Kinder ab etwa 8 Jahren und Jugendliche. Lehrenden und Eltern bietet es entsprechende Anregungen für gemeinsame mathematische Erkundungen. Die einzelnen Kapitel sind im Wesentlichen unabhängig voneinander lesbar, sodass sie möglichst vielseitig einsetzbar sind. Durch regelmäßig eingestreute Anregungen zum Nachdenken und Anstöße für eigene Untersuchungen wird mathematisches Entdecken erlebbar. Lösungshinweise zu diesen Anregungen sowie Kopiervorlagen werden online zur Verfügung gestellt.Die Mehrzahl der Themen wird Leserinnen und Lesern der beliebten Bücher Mathematik ist schön, Mathematik ist wunderschön und Mathematik ist wunderwunderschön bekannt vorkommen – es handelt sich um eine Auswahl von Inhalten aus diesen Büchern, die hier größtenteils völlig neu aufbereitet wurden: Die Darstellungen sind im vorliegenden „kunterbunten“ Buch nochmal sehr viel anschaulicher, ausführlicher und kindgerechter. Außerdem sind weitere Themen hinzugekommen, die sich besonders für jüngere Mathematikinteressierte eignen.Table of ContentsEinfache Bausteine zum Parkettieren.- Flächenteilungen.- Muster aus bunten Steinen.- Keltische Knoten.- Muster legen mit quadratischen Fliesen und Karten.- Wortschlangen und Wege im Rechteck-Raster.- Regelmäßige Vielecke und Sterne.- Das verschwundene Quadrat.- Parkettieren mit goldenen Dreiecken.- Magische Quadrate.- Würfel und Würfelspiele.- Entdeckungen mit Quadratzahlen und Potenzen.
£18.99
Springer Risse im Fundament
Book Synopsis.- Von den Zahlen bis zur Unendlichkeit..- Mengen, Logik und die Grundlagenkrise..- Mathematische Fundamente und Gödels Entdeckung..- Gödel, Turing und die Grenzen der Beweisbarkeit.
£18.99
Springer Fachmedien Wiesbaden Einführung in die Mathematische Logik: Ein
Book SynopsisDieses umfassende Lehrbuch wurde geschrieben für Studenten und Dozenten der Mathematik und Informatik, und wegen der ausführlichen Darstellung der Gödelschen Unvollständigkeitssätze auch für Fachstudenten der Philosophischen Logik. Für diese Neuauflage wurde der Text sachlich und stilistisch vollständig überarbeitet, er enthält verbesserte Beweise und Übungen mit Lösungshinweisen sowie eine historisch orientierte Einleitung. Das Buch kann ganz unabhängig von Vorlesungen aber auch zum Selbststudium genutzt werden. Table of ContentsAussagenlogik - Prädikatenlogik - Syntax und Semantik - Der Gödelsche Vollständigkeitssatz - Nichtstandardmodelle - Logikprogammierung - Resolution und Unifikation - Elemente der Modelltheorie - Ehrenfeucht-Spiele und Ultraprodukte - Entscheidbarkeit, Unentscheidbarkeit und Unvollständigkeit - Lösungshinweise zu den Übungen
£26.59
Springer Verlag Logica: Volume 1 - Dimostrazioni e modelli al
Book SynopsisGli autori, basandosi sulla loro esperienza di ricerca, propongono in due volumi un testo di riferimento per acquisire una solida formazione specialistica nella logica.Nei due volumi vengono presentati in maniera innovativa e rigorosa temi di logica tradizionalmente affrontati nei corsi universitari di secondo livello.Questo primo volume è dedicato ai teoremi fondamentali sulla logica del primo ordine e alle loro principali conseguenze.Il testo è rivolto in particolare agli studenti dei corsi di laurea magistrale.Table of Contents1 Introduzione.- 2 Alcune nozioni preliminari.- 3 Dimostrabilità e soddisfacibilità.- 4 Verso la teoria della dimostrazione: il teorema del taglio per LK.- 5 Verso la teoria dei modelli: alcune conseguenze del teorema di compattezza.
£18.99
Springer Philosophy of Mathematics Today
Book SynopsisMathematics is often considered as a body of knowledge that is essen tially independent of linguistic formulations, in the sense that, once the content of this knowledge has been grasped, there remains only the problem of professional ability, that of clearly formulating and correctly proving it. However, the question is not so simple, and P. Weingartner's paper (Language and Coding-Dependency of Results in Logic and Mathe matics) deals with some results in logic and mathematics which reveal that certain notions are in general not invariant with respect to different choices of language and of coding processes. Five example are given: 1) The validity of axioms and rules of classical propositional logic depend on the interpretation of sentential variables; 2) The language dependency of verisimilitude; 3) The proof of the weak and strong anti inductivist theorems in Popper's theory of inductive support is not invariant with respect to limitative criteria put on classical logic; 4) The language-dependency of the concept of provability; 5) The language dependency of the existence of ungrounded and paradoxical sentences (in the sense of Kripke). The requirements of logical rigour and consistency are not the only criteria for the acceptance and appreciation of mathematical proposi tions and theories.Table of ContentsGeneral Philosophical Perspectives.- Logic, Mathematics, Ontology.- From Certainty to Fallibility in Mathematics?.- Moderate Mathematical Fictionism.- Language and Coding-Dependency of Results in Logic and Mathematics.- What is a Profound Result in Mathematics?.- The Hylemorphic Schema in Mathematics.- Foundational Approaches.- Categorical Foundations of the Protean Character of Mathematics.- Category Theory and Structuralism in Mathematics: Syntactical Considerations.- Reflection in Set Theory. The Bernays-Levy Axiom System.- Structuralism and the Concept of Set.- Aspects of Mathematical Experience.- Logicism Revisited in the Propositional Fragment of Le?niewski’s Ontology.- The Applicability of Mathematics.- The Relation of Mathematics to the Other Sciences.- Mathematics and Physics.- The Mathematical Overdetermination of Physics.- Gödel’s Incompleteness Theorem and Quantum Thermodynamic Limits.- Mathematical Models in Biology.- The Natural Numbers as a Universal Library.- Mathematical Symmetry Principles in the Scientific World View.- Historical Considerations.- Mathematics and Logics. Hungarian Traditions and the Philosophy of Non-Classical Logic.- Umfangslogik, Inhaltslogik, Theorematic Reasoning.
£85.49
Griddlers.Net Griddlers Logic Puzzles - Triddlers Black and
Book Synopsis
£17.17
World Scientific Publishing Co Pte Ltd Mathematical Logic For Computer Science (2nd
Book SynopsisMathematical logic is essentially related to computer science. This book describes the aspects of mathematical logic that are closely related to each other, including classical logic, constructive logic, and modal logic. This book is intended to attend to both the peculiarities of logical systems and the requirements of computer science.In this edition, the revisions essentially involve rewriting the proofs, increasing the explanations, and adopting new terms and notations.Table of ContentsPart 1 Prerequisites: sets; inductive definitions and proofs; notations. Part 2 Classical propositional logic: propositions and connectives; propositional language; semantics; tautological consequence; formal deduction; disjunctive and conjunctive normal forms; adequate sets of connectives. Part 3 Classical first-order logic: proposition functions and quantifiers; first-order language; semantics; logical consequence; formal deduction; prenex normal form. Part 4 Axiomatic deduction system: axiomatic deduction system; relation between the two deduction systems. Part 5 Soundness and completeness: satisfiability and validity; soundness; completeness of propositional logic; completeness of first-order logic; completeness of first-order logic with equality; independence. Part 6 Compactness, Lowenheim-Skolem, and Herbrand theorems: compactness; Lowenheim-Skolem's theorem; Herbrand's theorem. Part 7 Constructive logic: constructivity of proofs; semantics; formal deduction; soundness; completeness. Part 8 Modal propositional logic: modal propositional language; semantics; formal deduction; soundness; completeness of T; completeness of S4, B, S5. Part 9 Modal first-order logic: modal first-order language; semantics; formal deduction; soundness; completeness; equality.
£65.55
World Scientific Publishing Co Pte Ltd Proceedings Of The Sixth Asian Logic Conference
Book SynopsisThis volume collects written versions of invited and contributed talks presented at the conference. It covers many areas of logic and the foundations of mathematics, as well as computer science.Table of ContentsSeminormal fine measures on Pk(lambda), Y. Abe; recursion theory and weak fragments of Peano arithmetic - a study of definable cuts, C.T. Chong and Y. Yang; lattice embedding into d-r.e. degrees preserving 0 and 1, D. Ding and L. Qian; on stationary reflection principles, Q. Feng; decidability and undecidability in the enumerable Turing degrees, S. Lempp; a note on weak segments of PFA, T. Miyamoto; linear set theory with strict comprehension, M. Shirahata; a solution to a problem of Marek and Truszcy ski, K. Su and H. Chen; DNK and natural reasoning, M. Yasugi and M. Nakata; Asian logic conferences, M. Yasugi; other papers.
£80.75
World Scientific Publishing Co Pte Ltd Algebraic Theory Of Automata And Languages
Book SynopsisAlthough there are some books dealing with algebraic theory of automata, their contents consist mainly of Krohn-Rhodes theory and related topics. The topics in the present book are rather different. For example, automorphism groups of automata and the partially ordered sets of automata are systematically discussed. Moreover, some operations on languages and special classes of regular languages associated with deterministic and nondeterministic directable automata are dealt with. The book is self-contained and hence does not require any knowledge of automata and formal languages.
£85.50
World Scientific Publishing Co Pte Ltd Essays On Non-classical Logic
Book SynopsisThis book covers a broad range of up-to-date issues in non-classical logic that are of interest not only to philosophical and mathematical logicians but also to computer scientists and researchers in artificial intelligence. The problems addressed range from methodological issues in paraconsistent and deontic logic to the revision theory of truth and infinite Turing machines. The book identifies a number of important current trends in contemporary non-classical logic. Among them are dialogical and substructural logic, the classification of concepts of negation, truthmaker theory, and mathematical and foundational aspects of modal and temporal logic.Table of ContentsFine-Grained Theories of Time (P Blackburn); Revision Sequences and Computers with an Infinite Amount of Time (B Lowe); On Frege's Nightmare: A Combination of Intuitionistic, Free and Paraconsistent Logics (S Rahman); Truthmakers, Entailment and Necessity (S Read); Global Definability in Basic Modal Logic (M de Rijke & H Sturm); Ackermann's Implication for Typefree Logic (K Robering); Why Dialogical Logic? (H Ruckert); Semantics for Constructive Negations (Y Shramko); Recent Trends in Paraconsistent Logic (M Urchs); Obligations, Authorities, and History Dependence (H Wansing).
£68.40
World Scientific Publishing Co Pte Ltd Relations: Concrete, Abstract, And Applied - An
Book SynopsisThe book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This is done not only by presenting theoretical results but also by giving hints to some of the many interesting application areas (also including their respective theoretical basics).This book is a new — and the first of its kind — compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples.This book is unique by the spectrum of the topics it handles. As indicated in its title these are:
£139.50
World Scientific Publishing Co Pte Ltd Global Solution For Sudoku
Book SynopsisThe present book aims to provide systematic and reliable techniques, called the global solution, for Sudoku puzzles. Any proper Sudoku puzzle, which has one and only one solution of Sudoku, can be solved by anyone following the techniques provided in this book. Specific symbols are introduced to express the 6 basic rules of the Sudoku global solution, as the results, those Sudoku solving techniques are presented similar to the annotations in chess. Finnish mathematician Arto Inkala proposed 'the most difficult Sudoku puzzle' in 2007. Then, he designed another difficult Sudoku puzzle in 2012, named 'the thing Everest'. In the present book the solving process of those two difficult Sudoku puzzles are illustrated reliably by the specific symbols of the global solution step by step.
£33.25
World Scientific Publishing Co Pte Ltd Global Solution For Sudoku
Book SynopsisThe present book aims to provide systematic and reliable techniques, called the global solution, for Sudoku puzzles. Any proper Sudoku puzzle, which has one and only one solution of Sudoku, can be solved by anyone following the techniques provided in this book. Specific symbols are introduced to express the 6 basic rules of the Sudoku global solution, as the results, those Sudoku solving techniques are presented similar to the annotations in chess. Finnish mathematician Arto Inkala proposed 'the most difficult Sudoku puzzle' in 2007. Then, he designed another difficult Sudoku puzzle in 2012, named 'the thing Everest'. In the present book the solving process of those two difficult Sudoku puzzles are illustrated reliably by the specific symbols of the global solution step by step.
£15.00
World Scientific Publishing Co Pte Ltd Science Of Learning Mathematical Proofs, The: An
Book SynopsisCollege students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduction utilizes recent research in neuroscience regarding how the brain learns best. Rather than jumping right into proofs, students are first taught how to change their mindset about learning, how to persevere through difficult problems, how to work successfully in a group, and how to reflect on their learning. With these tools in place, students then learn logic and problem solving as a further foundation.Next various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, and mathematical induction are introduced. These proof techniques are introduced using the context of number theory. The last chapter uses Calculus as a way for students to apply the proof techniques they have learned.
£33.25
World Scientific Publishing Co Pte Ltd Science Of Learning Mathematical Proofs, The: An
Book SynopsisCollege students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduction utilizes recent research in neuroscience regarding how the brain learns best. Rather than jumping right into proofs, students are first taught how to change their mindset about learning, how to persevere through difficult problems, how to work successfully in a group, and how to reflect on their learning. With these tools in place, students then learn logic and problem solving as a further foundation.Next various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, and mathematical induction are introduced. These proof techniques are introduced using the context of number theory. The last chapter uses Calculus as a way for students to apply the proof techniques they have learned.
£76.00
World Scientific Publishing Co Pte Ltd Mathematical Labyrinths. Pathfinding
Book SynopsisMathematical Labyrinths. Pathfinding provides an overview of various non-standard problems and the approaches to their solutions. The essential idea is a framework laid upon the reader on how to solve nonconventional problems — particularly in the realm of mathematics and logic. It goes over the key steps in approaching a difficult problem, contemplating a plan for its solution, and discusses set of mental models to solve math problems.The book is not a routine set of problems. It is rather an entertaining and educational journey into the fascinating world of mathematical reasoning and logic. It is about finding the best path to a solution depending on the information given, asking and answering the right questions, analyzing and comparing alternative approaches to problem solving, searching for generalizations and inventing new problems. It also considers as an important pedagogical tool playing mathematical and logical games, deciphering mathematical sophisms, and interpreting mathematical paradoxes.It is suitable for mathematically talented and curious students in the age range 10-20. There are many 'Eureka'- type, out of the ordinary, fun problems that require bright idea and insight. These intriguing and thought-provoking brainteasers and logic puzzles should be enjoyable by the audience of almost any age group, from 6-year-old children to 80-year-old and older adults.Table of ContentsEntering the Labyrinth; What? Why? How?; The Clue is in the Question; Thinking Outside the Box; "Precise Steps" Problems. Playing Preferans; Transformations of Plane; Geometrical Constructions with Restricted Elements; "Inventing" a Problem; Related Problems; Alternative Solutions Search; "Eureka";
£76.00
World Scientific Publishing Co Pte Ltd Mathematical Labyrinths. Pathfinding
Book SynopsisMathematical Labyrinths. Pathfinding provides an overview of various non-standard problems and the approaches to their solutions. The essential idea is a framework laid upon the reader on how to solve nonconventional problems — particularly in the realm of mathematics and logic. It goes over the key steps in approaching a difficult problem, contemplating a plan for its solution, and discusses set of mental models to solve math problems.The book is not a routine set of problems. It is rather an entertaining and educational journey into the fascinating world of mathematical reasoning and logic. It is about finding the best path to a solution depending on the information given, asking and answering the right questions, analyzing and comparing alternative approaches to problem solving, searching for generalizations and inventing new problems. It also considers as an important pedagogical tool playing mathematical and logical games, deciphering mathematical sophisms, and interpreting mathematical paradoxes.It is suitable for mathematically talented and curious students in the age range 10-20. There are many 'Eureka'- type, out of the ordinary, fun problems that require bright idea and insight. These intriguing and thought-provoking brainteasers and logic puzzles should be enjoyable by the audience of almost any age group, from 6-year-old children to 80-year-old and older adults.Table of ContentsEntering the Labyrinth; What? Why? How?; The Clue is in the Question; Thinking Outside the Box; "Precise Steps" Problems. Playing Preferans; Transformations of Plane; Geometrical Constructions with Restricted Elements; "Inventing" a Problem; Related Problems; Alternative Solutions Search; "Eureka";
£33.25
World Scientific Publishing Co Pte Ltd Innovative Teaching: Best Practices From Business
Book SynopsisInnovative Teaching: Best Practices from Business and Beyond for Mathematics Teachers provides educators with new and exciting ways to introduce material and methods to motivate and engage students by showing how some of the techniques commonly used in the business world — and beyond — are applicable to the world of education. It also offers educators practical advice with regard to the changing culture of education, keeping up with technology, navigating politics at work, interacting with colleagues, developing leadership skills, group behavior, and gender differences.Innovative Teaching demonstrates how the classroom environment is similar to the marketplace. Educators, like businesses, for example, must capture and hold the attention of their audience while competing with a constant stream of 'noise.' With the introduction of the Internet and the wide use of social media, promoters understand that they must not only engage their audience, but also incorporate audience feedback into the promotional work and product or service they offer. Innovative Teaching shows educators how to take the best practices from business — and beyond — and recombine these resources for appropriate use in the classroom.
£66.50
World Scientific Publishing Co Pte Ltd Innovative Teaching: Best Practices From Business
Book SynopsisInnovative Teaching: Best Practices from Business and Beyond for Mathematics Teachers provides educators with new and exciting ways to introduce material and methods to motivate and engage students by showing how some of the techniques commonly used in the business world — and beyond — are applicable to the world of education. It also offers educators practical advice with regard to the changing culture of education, keeping up with technology, navigating politics at work, interacting with colleagues, developing leadership skills, group behavior, and gender differences.Innovative Teaching demonstrates how the classroom environment is similar to the marketplace. Educators, like businesses, for example, must capture and hold the attention of their audience while competing with a constant stream of 'noise.' With the introduction of the Internet and the wide use of social media, promoters understand that they must not only engage their audience, but also incorporate audience feedback into the promotional work and product or service they offer. Innovative Teaching shows educators how to take the best practices from business — and beyond — and recombine these resources for appropriate use in the classroom.
£33.25
World Scientific Publishing Co Pte Ltd Proof And Computation Ii: From Proof Theory And
Book SynopsisThis book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
£121.50
World Scientific Publishing Company Topics In Model Theory
Book Synopsis
£52.25
World Scientific Publishing Co Pte Ltd Mathematics For Computation (M4c)
Book SynopsisThe overall topic of the volume, Mathematics for Computation (M4C), is mathematics taking crucially into account the aspect of computation, investigating the interaction of mathematics with computation, bridging the gap between mathematics and computation wherever desirable and possible, and otherwise explaining why not.Recently, abstract mathematics has proved to have more computational content than ever expected. Indeed, the axiomatic method, originally intended to do away with concrete computations, seems to suit surprisingly well the programs-from-proofs paradigm, with abstraction helping not only clarity but also efficiency.Unlike computational mathematics, which rather focusses on objects of computational nature such as algorithms, the scope of M4C generally encompasses all the mathematics, including abstract concepts such as functions. The purpose of M4C actually is a strongly theory-based and therefore, is a more reliable and sustainable approach to actual computation, up to the systematic development of verified software.While M4C is situated within mathematical logic and the related area of theoretical computer science, in principle it involves all branches of mathematics, especially those which prompt computational considerations. In traditional terms, the topics of M4C include proof theory, constructive mathematics, complexity theory, reverse mathematics, type theory, category theory and domain theory.The aim of this volume is to provide a point of reference by presenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions.
£121.50
World Scientific Publishing Co Pte Ltd Laws Of Form: A Fiftieth Anniversary
Book SynopsisLaws of Form is a seminal work in foundations of logic, mathematics and philosophy published by G Spencer-Brown in 1969. The book provides a new point of view on form and the role of distinction, markedness and the absence of distinction (the unmarked state) in the construction of any universe. A conference was held August 8-10, 2019 at the Old Library, Liverpool University, 19 Abercromby Square, L697ZN, UK to celebrate the 50th anniversary of the publication of Laws of Form and to remember George Spencer-Brown, its author. The book is a collection of papers introducing and extending Laws of Form written primarily by people who attended the conference in 2019.
£157.50
World Scientific Publishing Co Pte Ltd Temporal Logic: From Philosophy And Proof Theory
Book SynopsisCalculi of temporal logic are widely used in modern computer science. The temporal organization of information flows in the different architectures of laptops, the Internet, or supercomputers would not be possible without appropriate temporal calculi. In the age of digitalization and High-Tech applications, people are often not aware that temporal logic is deeply rooted in the philosophy of modalities. A deep understanding of these roots opens avenues to the modern calculi of temporal logic which have emerged by extension of modal logic with temporal operators. Computationally, temporal operators can be introduced in different formalisms with increasing complexity such as Basic Modal Logic (BML), Linear-Time Temporal Logic (LTL), Computation Tree Logic (CTL), and Full Computation Tree Logic (CTL*). Proof-theoretically, these formalisms of temporal logic can be interpreted by the sequent calculus of Gentzen, the tableau-based calculus, automata-based calculus, game-based calculus, and dialogue-based calculus with different advantages for different purposes, especially in computer science.The book culminates in an outlook on trendsetting applications of temporal logics in future technologies such as artificial intelligence and quantum technology. However, it will not be sufficient, as in traditional temporal logic, to start from the everyday understanding of time. Since the 20th century, physics has fundamentally changed the modern understanding of time, which now also determines technology. In temporal logic, we are only just beginning to grasp these differences in proof theory which needs interdisciplinary cooperation of proof theory, computer science, physics, technology, and philosophy.
£66.50
World Scientific Publishing Co Pte Ltd Transition To Proofs
Book SynopsisThis textbook is aimed at transitioning high-school students who have already developed proficiency in mathematical problem solving from numerical-answer problems to proof-based mathematics. It serves to guide students on how to write and understand mathematical proofs. It covers proof techniques that are commonly used in several areas of mathematics, especially number theory, combinatorics, and analysis. In addition to just teaching the mechanics of proofs, this book showcases key materials in these areas, thus introducing readers to interesting mathematics along with proof techniques.
£99.00
World Scientific Publishing Co Pte Ltd Aspects Of Computation And Automata Theory With
Book SynopsisThis volume results from two programs that took place at the Institute for Mathematical Sciences at the National University of Singapore: Aspects of Computation — in Celebration of the Research Work of Professor Rod Downey (21 August to 15 September 2017) and Automata Theory and Applications: Games, Learning and Structures (20-24 September 2021).The first program was dedicated to the research work of Rodney G. Downey, in celebration of his 60th birthday. The second program covered automata theory whereby researchers investigate the other end of computation, namely the computation with finite automata, and the intermediate level of languages in the Chomsky hierarchy (like context-free and context-sensitive languages).This volume contains 17 contributions reflecting the current state-of-art in the fields of the two programs.
£130.50
World Scientific Publishing Co Pte Ltd Tale Of Discrete Mathematics A A Journey Through
Book SynopsisTopics covered in Discrete Mathematics have become essential tools in many areas of studies in recent years. This is primarily due to the revolution in technology, communications, and cyber security. The book treats major themes in a typical introductory modern Discrete Mathematics course: Propositional and predicate logic, proof techniques, set theory (including Boolean algebra, functions and relations), introduction to number theory, combinatorics and graph theory.An accessible, precise, and comprehensive approach is adopted in the treatment of each topic. The ability of abstract thinking and the art of writing valid arguments are emphasized through detailed proof of (almost) every result. Developing the ability to think abstractly and roguishly is key in any areas of science, information technology and engineering. Every result presented in the book is followed by examples and applications to consolidate its comprehension. The hope is that the reader ends up developing both the abstract reasoning as well as acquiring practical skills.All efforts are made to write the book at a level accessible to first-year students and to present each topic in a way that facilitates self-directed learning. Each chapter starts with basic concepts of the subject at hand and progresses gradually to cover more ground on the subject. Chapters are divided into sections and subsections to facilitate readings. Each section ends with its own carefully chosen set of practice exercises to reenforce comprehension and to challenge and stimulate readers.As an introduction to Discrete Mathematics, the book is written with the smallest set of prerequisites possible. Familiarity with basic mathematical concepts (usually acquired in high school) is sufficient for most chapters. However, some mathematical maturity comes in handy to grasp some harder concepts presented in the book.
£121.50
World Scientific Publishing Company Mathematical Foundations Of Information Sciences
Book Synopsis
£66.50
World Scientific Publishing Co Pte Ltd Artificial Intelligence Of Neuromorphic Systems
Book SynopsisThis book argues for neuromorphic systems as a technology of the future, which are oriented towards the energy efficiency of natural brains. Energy efficiency is a dramatic claim in times of environmental and climate challenges which should consider the sustainability goals of the United Nations (UN). Mathematically, neuromorphic computing is connected to analogue ('real') computing, which theoretically overcomes the limits of digital Turing computability. Therefore, the book also considers material sciences and engineering sciences which start to realize neuromorphic computing in hardware. Other mathematical formalisms such as quantum mechanics also open up new solutions (e.g., quantum computing) beyond the limits of digital Turing computability. These research fields are no longer merely of theoretical interest, they promise increasing innovation power of market interest. Nevertheless, neuromorphic computing is connected with deep logical, mathematical, and epistemic questions. Does it open new avenues to Artificial General Intelligence (AGI)? All these tendencies of research and innovation demonstrate that we need more integrated research in the foundations of logic, mathematics, physics, engineering sciences, cognitive science, and philosophy. The book is a plea for this kind of research.
£121.50
World Scientific Publishing Co Pte Ltd Mathematical Foundations Of Information Sciences
Book SynopsisThis is a concise book that introduces students to the basics of logical thinking and important mathematical structures that are critical for a solid understanding of logical formalisms themselves as well as for building the necessary background to tackle other fields that are based on these logical principles. Despite its compact and small size, it includes many solved problems and quite a few end-of-section exercises that will help readers consolidate their understanding of the material.This textbook is essential reading for anyone interested in the logical foundations of Informatics, Computer Science, Data Science, Artificial Intelligence, and other related areas. Written with undergraduate students in these disciplines in mind, this book can very well serve the needs of interested and curious readers who wish to get a grasp of the logical principles upon which these fields are built. This book does not require readers to possess math skills beyond those learned in high school.
£33.25
World Scientific Publishing Company Set Theory And Foundations Of Mathematics An
Book Synopsis
£61.75
Springer Verlag, Singapore Statistical Learning with Math and Python: 100
Book SynopsisThe most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of machine learning and data science by considering math problems and building Python programs. As the preliminary part, Chapter 1 provides a concise introduction to linear algebra, which will help novices read further to the following main chapters. Those succeeding chapters present essential topics in statistical learning: linear regression, classification, resampling, information criteria, regularization, nonlinear regression, decision trees, support vector machines, and unsupervised learning. Each chapter mathematically formulates and solves machine learning problems and builds the programs. The body of a chapter is accompanied by proofs and programs in an appendix, with exercises at the end of the chapter. Because the book is carefully organized to provide the solutions to the exercises in each chapter, readers can solve the total of 100 exercises by simply following the contents of each chapter. This textbook is suitable for an undergraduate or graduate course consisting of about 12 lectures. Written in an easy-to-follow and self-contained style, this book will also be perfect material for independent learning.Table of ContentsChapter 1: Linear Algebra.- Chapter 2: Linear Regression.- Chapter 3: Classification.- Chapter 4: Resampling.- Chapter 5: Information Criteria.- Chapter 6: Regularization.- Chapter 7: Nonlinear Regression.- Chapter 8: Decision Trees.- Chapter 9: Support Vector Machine.- Chapter 10: Unsupervised Learning.
£26.99
Springer Verlag, Singapore Sparse Estimation with Math and R: 100 Exercises
Book SynopsisThe most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of sparse estimation by considering math problems and building R programs. Each chapter introduces the notion of sparsity and provides procedures followed by mathematical derivations and source programs with examples of execution. To maximize readers’ insights into sparsity, mathematical proofs are presented for almost all propositions, and programs are described without depending on any packages. The book is carefully organized to provide the solutions to the exercises in each chapter so that readers can solve the total of 100 exercises by simply following the contents of each chapter.This textbook is suitable for an undergraduate or graduate course consisting of about 15 lectures (90 mins each). Written in an easy-to-follow and self-contained style, this book will also be perfect material for independent learning by data scientists, machine learning engineers, and researchers interested in linear regression, generalized linear lasso, group lasso, fused lasso, graphical models, matrix decomposition, and multivariate analysis.This book is one of a series of textbooks in machine learning by the same author. Other titles are: - Statistical Learning with Math and R (https://www.springer.com/gp/book/9789811575679) - Statistical Learning with Math and Python (https://www.springer.com/gp/book/9789811578762) - Sparse Estimation with Math and PythonTable of ContentsChapter 1: Linear Regression.- Chapter 2: Generalized Linear Regression.- Chapter 3: Group Lasso.- Chapter 4: Fused Lasso.- Chapter 5: Graphical Model.- Chapter 6: Matrix Decomposition.- Chapter 7: Multivariate Analysis.
£26.99
Springer Verlag, Singapore Advances in Mathematical Logic: Dedicated to the
Book SynopsisGaisi Takeuti was one of the most brilliant, genius, and influential logicians of the 20th century. He was a long-time professor and professor emeritus of mathematics at the University of Illinois at Urbana-Champaign, USA, before he passed away on May 10, 2017, at the age of 91. Takeuti was one of the founders of Proof Theory, a branch of mathematical logic that originated from Hilbert's program about the consistency of mathematics. Based on Gentzen's pioneering works of proof theory in the 1930s, he proposed a conjecture in 1953 concerning the essential nature of formal proofs of higher-order logic now known as Takeuti's fundamental conjecture and of which he gave a partial positive solution. His arguments on the conjecture and proof theory in general have had great influence on the later developments of mathematical logic, philosophy of mathematics, and applications of mathematical logic to theoretical computer science. Takeuti's work ranged over the whole spectrum of mathematical logic, including set theory, computability theory, Boolean valued analysis, fuzzy logic, bounded arithmetic, and theoretical computer science. He wrote many monographs and textbooks both in English and in Japanese, and his monumental monograph Proof Theory, published in 1975, has long been a standard reference of proof theory. He had a wide range of interests covering virtually all areas of mathematics and extending to physics. His publications include many Japanese books for students and general readers about mathematical logic, mathematics in general, and connections between mathematics and physics, as well as many essays for Japanese science magazines. This volume is a collection of papers based on the Symposium on Advances in Mathematical Logic 2018. The symposium was held September 18–20, 2018, at Kobe University, Japan, and was dedicated to the memory of Professor Gaisi Takeuti. Table of ContentsS. Fuchino and A. Ottenbreit Ottenbreit Maschio Rodrigues, Reflection principles, generic large cardinals, and the Continuum Problem.- D. Ikegami and N. Trang, On supercompactness of ω1.- S. Iwata, Interpolation properties for Sacchetti’s logics.- T. Kurahashi, Rosser provability and the second incompleteness theorem.- H. Kurokawa, On Takeuti’s early view of the concept of set.- Yo Matsubara and T. Usuba, On Countable Stationary Towers.- M. Ozawa, Reforming Takeuti’s Quantum Set Theory to Satisfy De Morgan’s Laws.- T. Usuba, Choiceless Lowenheim-Skolem property and uniform definability of grounds.- M. Yasugi, Y. Tsujii, T. Mori, Irrational-based computability of functions.- M. Yasugi, “Gaisi Takeuti’s finitist standpoint” and its mathematical embodiment.- Y. Yoshinobu, Properness under closed forcing.
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