Proof Theory

Author: Wolfram Pohlers
Publisher: Springer Science & Business Media
ISBN: 354069319X
Release Date: 2008-10-01
Genre: Mathematics

The kernel of this book consists of a series of lectures on in?nitary proof theory which I gave during my time at the Westfalische ̈ Wilhelms–Universitat ̈ in Munster ̈ . It was planned as a successor of Springer Lecture Notes in Mathematics 1407. H- ever, when preparing it, I decided to also include material which has not been treated in SLN 1407. Since the appearance of SLN 1407 many innovations in the area of - dinal analysis have taken place. Just to mention those of them which are addressed in this book: Buchholz simpli?ed local predicativity by the invention of operator controlled derivations (cf. Chapter 9, Chapter 11); Weiermann detected applications of methods of impredicative proof theory to the characterization of the provable recursive functions of predicative theories (cf. Chapter 10); Beckmann improved Gentzen’s boundedness theorem (which appears as Stage Theorem (Theorem 6. 6. 1) in this book) to Theorem 6. 6. 9, a theorem which is very satisfying in itself - though its real importance lies in the ordinal analysis of systems, weaker than those treated here. Besides these innovations I also decided to include the analysis of the theory (? –REF) as an example of a subtheory of set theory whose ordinal analysis only 2 0 requires a ?rst step into impredicativity. The ordinal analysis of(? –FXP) of non- 0 1 0 monotone? –de?nable inductive de?nitions in Chapter 13 is an application of the 1 analysis of(? –REF).

Proof And Computation Digitization In Mathematics Computer Science And Philosophy

Author: Mainzer Klaus
Publisher: World Scientific
ISBN: 9789813270954
Release Date: 2018-05-30
Genre: Mathematics

This 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 Predicative Foundations, Constructive Mathematics and Type Theory, Computation in Higher Types, Extraction of Programs from Proofs, and Algorithmic Aspects in Financial Mathematics. 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. Contents: Proof and Computation (K Mainzer) Constructive Convex Programming (J Berger and G Svindland) Exploring Predicativity (L Crosilla) Constructive Functional Analysis: An Introduction (H Ishihara) Program Extraction (K Miyamoto) The Data Structures of the Lambda Terms (M Sato) Provable (and Unprovable) Computability (S Wainer) Introduction to Minlog (F Wiesnet) Readership: Graduate students, researchers, and professionals in Mathematics and Computer Science. Keywords: Proof Theory;Computability Theory;Program Extraction;Constructive Analysis;PredicativityReview: Key Features: This book gathers recent contributions of distinguished experts It makes emerging fields accessible to a wider audience, appealing to a broad readership with diverse backgrounds It fills a gap between (under-)graduate level textbooks and state-of-the-art research papers

Feferman on Foundations

Author: Gerhard Jäger
Publisher: Springer
ISBN: 9783319633343
Release Date: 2018-04-04
Genre: Mathematics

This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.

Concepts of Proof in Mathematics Philosophy and Computer Science

Author: Dieter Probst
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9781501502644
Release Date: 2016-07-25
Genre: Philosophy

This book provides the reader with research arising from the Humboldt-Kolleg ‘Proof’ held in Bern in fall 2013, which gathered leading experts actively involved with the concept ‘proof’ in philosophy, mathematics and computer science. This volume aims to do justice to the breadth and depth of the subject and presents relevant current conceptions and technical advances featuring ‘proof’ in those fields.

Applied Logic for Computer Scientists

Author: Mauricio Ayala-Rincón
Publisher: Springer
ISBN: 9783319516530
Release Date: 2017-03-24
Genre: Computers

This book provides an introduction to logic and mathematical induction which are the basis of any deductive computational framework. A strong mathematical foundation of the logical engines available in modern proof assistants, such as the PVS verification system, is essential for computer scientists, mathematicians and engineers to increment their capabilities to provide formal proofs of theorems and to certify the robustness of software and hardware systems. The authors present a concise overview of the necessary computational and mathematical aspects of ‘logic’, placing emphasis on both natural deduction and sequent calculus. Differences between constructive and classical logic are highlighted through several examples and exercises. Without neglecting classical aspects of computational logic, the authors also highlight the connections between logical deduction rules and proof commands in proof assistants, presenting simple examples of formalizations of the correctness of algebraic functions and algorithms in PVS. Applied Logic for Computer Scientists will not only benefit students of computer science and mathematics but also software, hardware, automation, electrical and mechatronic engineers who are interested in the application of formal methods and the related computational tools to provide mathematical certificates of the quality and accuracy of their products and technologies.

Das Kontinuum

Author: Hermann Weyl
ISBN: UVA:X000579326
Release Date: 1932
Genre: Mathematics

Regular Solids and Isolated Singularities

Author: Klaus Lamotke
Publisher: Vieweg+Teubner Verlag
ISBN: 352808958X
Release Date: 1986-01-01
Genre: Mathematics

The last book XIII of Euclid's Elements deals with the regular solids which therefore are sometimes considered as crown of classical geometry. More than two thousand years later around 1850 Schl~fli extended the classification of regular solids to four and more dimensions. A few decades later, thanks to the invention of group and invariant theory the old three dimensional regular solid were involved in the development of new mathematical ideas: F. Klein (Lectures on the Icosa hedron and the Resolution of Equations of Degree Five, 1884) emphasized the relation of the regular solids to the finite rotation groups. He introduced complex coordinates and by means of invariant theory associated polynomial equations with these groups. These equations in turn describe isolated singularities of complex surfaces. The structure of the singularities is investigated by methods of commutative algebra, algebraic and complex analytic geometry, differential and algebraic topology. A paper by DuVal from 1934 (see the References), in which resolutions play an important rele, marked an early stage of these investigations. Around 1970 Klein's polynomials were again related to new mathematical ideas: V. I. Arnold established a hierarchy of critical points of functions in several variables according to growing com plexity. In this hierarchy Kleinls polynomials describe the "simple" critical points.


Author: Stefan Lüddemann
Publisher: Springer-Verlag
ISBN: 9783531196503
Release Date: 2014-09-26
Genre: Social Science

Der Kulturjournalismus befindet sich im Umbruch. Das klassische Feuilleton steht unter Begründungsdruck, gleichzeitig wachsen Formate und Zuständigkeiten des Kulturjournalismus. Das vorliegende Buch gibt einen aktuellen Überblick über ein zentrales Feld der medialen Arbeit. Die Darstellung reflektiert Kultur- und Rollenverständnis von Kulturjournalisten, verortet Kulturjournalismus im Beziehungsgefüge zwischen Kulturinstitutionen und Rezipienten. Im Blickpunkt stehen Beispiele gelungener Praxis und die Frage: Wie plant und schreibt man eigentlich guten Kulturjournalismus?

Entscheidungsverfahren f r komplexe Probleme

Author: Rudolf Grünig
Publisher: Springer-Verlag
ISBN: 9783642314605
Release Date: 2012-08-27
Genre: Business & Economics

Entscheidungen von großer Tragweite zu treffen, gehört zu den wichtigsten Aufgaben von Führungskräften. Meist handelt es sich um komplexe Entscheidungen. Die Autoren stellen ein Verfahren vor, um komplexe Probleme schrittweise zu bearbeiten. Besonderes Augenmerk gilt der Problemanalyse, der Variantenentwicklung und der Erarbeitung der Entscheidungsmatrix. Die Inhalte sind fundiert und praxisnah dargestellt, für die Neuauflage wurden sie überarbeitet und erweitert. Ein Praxis-Leitfaden, der Managern hilft, die richtigen Entscheidungen zu treffen.

Vorlesungen ber die Zahlentheorie der Quaternionen

Author: Adolf Hurwitz
Publisher: Springer-Verlag
ISBN: 9783642475368
Release Date: 2013-03-13
Genre: Mathematics

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

David Hilbert s Lectures on the Foundations of Arithmetic and Logic 1917 1933

Author: William Ewald
Publisher: Springer-Verlag
ISBN: 9783540694441
Release Date: 2013-05-14
Genre: Mathematics

The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics.

Partielle Differentialgleichungen der Geometrie und der Physik 2

Author: Friedrich Sauvigny
Publisher: Springer-Verlag
ISBN: 9783540275404
Release Date: 2005-12-05
Genre: Mathematics

Das zweibändige Lehrbuch behandelt das Gebiet der partiellen Differentialgleichungen umfassend und anschaulich. Der Autor stellt in Band 2 funktionalanalytische Lösungsmethoden vor und erläutert u. a. die Lösbarkeit von Operatorgleichungen im Banachraum, lineare Operatoren im Hilbertraum und Spektraltheorie, die Schaudersche Theorie linearer elliptischer Differentialgleichungen sowie schwache Lösungen elliptischer Differentialgleichungen.

Str mungsmaschinen

Author: Carl Pfleiderer
Publisher: Springer-Verlag
ISBN: 9783662101018
Release Date: 2013-03-09
Genre: Technology & Engineering

Dieses 1952 erstmals erschienene Standardwerk behandelt auch in seiner sechsten Auflage in vergleichender Weise alle verschiedenen Arten von Strömungsmaschinen. Dem Studenten wird ein Buch in die Hand gegeben, das über das ebenfalls im Springer-Verlag erschienene Lehrbuch Petermann "Einführung in die Strömungsmaschinen" hinausgeht und Detailwissen vertieft. Dem in der Praxis stehenden Ingenieur bietet das Buch nicht nur wertvolle Anregungen bei der Lösung von Einzelproblemen, sondern auch ein zuverlässiges Repetitorium und eine Erweiterung der theoretischen Grundlagen. Moderne Entwicklungen und neue Erkenntnisse wurden in die 6. Auflage eingearbeitet. Wegen der bestehenden Nachfrage hat der Verlag einen unveränderten Nachdruck der aktuellen 6. Auflage vorbereitet.

Grundlagen und Technologien des Ottomotors

Author: Helmut Eichlseder
Publisher: Springer Science & Business Media
ISBN: 9783211257746
Release Date: 2008-02-01
Genre: Technology & Engineering

Die Autoren aus Wissenschaft und Industrie beschreiben alle wesentlichen funktionellen Bereiche des modernen Ottomotors. Detailliert erläutern sie Theorie und Praxis, Gemischbildungsverfahren und Gemischbildner anhand praktischer Beispiele. Dabei gehen sie von den Rahmenbedingungen und verwendeten Kraftstoffen aus, die die Entwicklung bestimmen. Neben der Fremdzündung (Schadstoffbildung, Abgasnachbehandlung) behandeln sie aktuelle Entwicklungen mit homogener Selbstzündung. Der Schwerpunkt des Buches liegt auf etablierten Ottomotor-Technologien, die bereits in Serie gingen. Plus: aktuelle Ansätze der Entwicklung und zahlreiche Abbildungen.