Complexity Of Proofs And Their Transformations In Axiomatic Theories
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Complexity Of Proofs And Their Transformations In Axiomatic Theories
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Author : V. P. Orevkov
language : en
Publisher: American Mathematical Soc.
Release Date :
Complexity Of Proofs And Their Transformations In Axiomatic Theories written by V. P. Orevkov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
This book develops the tool of logical deduction schemata by using it to establish upper and lower bounds on the complexity of proofs and their transformations in axiomatized theories.
Function Theory In Several Complex Variables
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Author : Toshio Nishino
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Function Theory In Several Complex Variables written by Toshio Nishino and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
'Kiyoshi Oka, at the beginning of his research, regarded the collection of problems which he encountered in the study of domains of holomorphy as large mountains which separate today and tomorrow. Thus, he believed that there could be no essential progress in analysis without climbing over these mountains ... this book is a worthwhile initial step for the reader in order to understand the mathematical world which was created by Kiyoshi Oka.' -- from the Preface. This book explains results in the theory of functions of several complex variables which were mostly established from the late nineteenth century through to the middle of the twentieth century. In the work, the author introduces the mathematical world created by his advisor, Kiyoshi Oka. In this volume, Oka's work is divided into two parts. The first is the study of analytic functions in univalent domains in ${\mathbf C}n$. Here Oka proved that three concepts are equivalent: domains of holomorphy, holomorphically convex domains, and pseudoconvex domains; and moreover that the Poincaré problem, the Cousin problems, and the Runge problem, when stated properly, can be solved in domains of holomorphy satisfying the appropriate conditions. The second part of Oka's work established a method for the study of analytic functions defined in a ramified domain over ${\mathbf C}n$ in which the branch points are considered as interior points of the domain. Here analytic functions in an analytic space are treated, which is a slight generalization of a ramified domain over ${\mathbf C}n$. In writing the book, the author's goal was to bring to readers a real understanding of Oka's original papers. This volume is an English translation of the original Japanese edition, published by the University of Tokyo Press (Japan). It would make a suitable course text for advanced graduate level introductions to several complex variables.
Geometric Theory Of Functions Of A Complex Variable
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Author : Gennadiĭ Mikhaĭlovich Goluzin
language : en
Publisher: American Mathematical Soc.
Release Date : 1969
Geometric Theory Of Functions Of A Complex Variable written by Gennadiĭ Mikhaĭlovich Goluzin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Functions of complex variables categories.
An Introduction To Proof Theory
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Author : Paolo Mancosu
language : en
Publisher: Oxford University Press
Release Date : 2021
An Introduction To Proof Theory written by Paolo Mancosu and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
"Proof theory is a central area of mathematical logic of special interest to philosophy . It has its roots in the foundational debate of the 1920s, in particular, in Hilbert's program in the philosophy of mathematics, which called for a formalization of mathematics, as well as for a proof, using philosophically unproblematic, "finitary" means, that these systems are free from contradiction. Structural proof theory investigates the structure and properties of proofs in different formal deductive systems, including axiomatic derivations, natural deduction, and the sequent calculus. Central results in structural proof theory are the normalization theorem for natural deduction, proved here for both intuitionistic and classical logic, and the cut-elimination theorem for the sequent calculus. In formal systems of number theory formulated in the sequent calculus, the induction rule plays a central role. It can be eliminated from proofs of sequents of a certain elementary form: every proof of an atomic sequent can be transformed into a "simple" proof. This is Hilbert's central idea for giving finitary consistency proofs. The proof requires a measure of proof complexity called an ordinal notation. The branch of proof theory dealing with mathematical systems such as arithmetic thus has come to be called ordinal proof theory. The theory of ordinal notations is developed here in purely combinatorial terms, and the consistency proof for arithmetic presented in detail"--
Handbook Of Proof Theory
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Author : S.R. Buss
language : en
Publisher: Elsevier
Release Date : 1998-07-09
Handbook Of Proof Theory written by S.R. Buss and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-09 with Mathematics categories.
This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.
Introduction To Complex Analysis
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Author : Junjiro Noguchi
language : en
Publisher: American Mathematical Soc.
Release Date : 2008-04-09
Introduction To Complex Analysis written by Junjiro Noguchi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-09 with Mathematics categories.
This book describes a classical introductory part of complex analysis for university students in the sciences and engineering and could serve as a text or reference book. It places emphasis on rigorous proofs, presenting the subject as a fundamental mathematical theory. The volume begins with a problem dealing with curves related to Cauchy's integral theorem. To deal with it rigorously, the author gives detailed descriptions of the homotopy of plane curves. Since the residue theorem is important in both pure and applied mathematics, the author gives a fairly detailed explanation of how to apply it to numerical calculations; this should be sufficient for those who are studying complex analysis as a tool.
Computer Science Logic
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Author : Leszek Pacholski
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-07-18
Computer Science Logic written by Leszek Pacholski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-18 with Computers categories.
This volume contains revised refereed versions of the best papers presented during the CSL '94 conference, held in Kazimierz, Poland in September 1994; CSL '94 is the eighth event in the series of workshops held for the third time as the Annual Conference of the European Association for Computer Science Logic. The 38 papers presented were selected from a total of 151 submissions. All important aspects of the methods of mathematical logic in computer science are addressed: lambda calculus, proof theory, finite model theory, logic programming, semantics, category theory, and other logical systems. Together, these papers give a representative snapshot of the area of logical foundations of computer science.
Identities Of Algebras And Their Representations
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Author : I︠U︡riĭ Pitrimovich Razmyslov
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Identities Of Algebras And Their Representations written by I︠U︡riĭ Pitrimovich Razmyslov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
During the past forty years, a new trend in the theory of associative algebras, Lie algebras, and their representations has formed under the influence of mathematical logic and universal algebra, namely, the theory of varieties and identities of associative algebras, Lie algebras, and their representations. The last twenty years have seen the creation of the method of 2-words and $\alpha$-functions, which allowed a number of problems in the theory of groups, rings, Lie algebras, and their representations to be solved in a unified way. The possibilities of this method are far from exhausted. This book sums up the applications of the method of 2-words and $\alpha$-functions in the theory of varieties and gives a systematic exposition of contemporary achievements in the theory of identities of algebras and their representations closely related to this method. The aim is to make these topics accessible to a wider group of mathematicians.
Infinite Dimensional Lie Groups
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Author : Hideki Omori
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-11-07
Infinite Dimensional Lie Groups written by Hideki Omori and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-07 with categories.
This book develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinite-dimensional Lie groups all the real, primitive, infinite transformation groups studied by E. Cartan. The book discusses several noncommutative algebras such as Weyl algebras and algebras of quantum groups and their automorphism groups. The notion of a noncommutative manifold is described, and the deformation quantization of certain algebras is discussed from the viewpoint of Lie algebras. This edition is a revised version of the book of the same title published in Japanese in 1979.
Riemannian Geometry
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Author : Takashi Sakai
language : en
Publisher: American Mathematical Soc.
Release Date : 1996-01-01
Riemannian Geometry written by Takashi Sakai and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.
This volume is an English translation of Sakai's textbook on Riemannian Geometry which was originally written in Japanese and published in 1992. The author's intent behind the original book was to provide to advanced undergraduate and graudate students an introduction to modern Riemannian geometry that could also serve as a reference. The book begins with an explanation of the fundamental notion of Riemannian geometry. Special emphasis is placed on understandability and readability, to guide students who are new to this area. The remaining chapters deal with various topics in Riemannian geometry, with the main focus on comparison methods and their applications.