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Author : Noam Greenberg
Publisher : Unknown
Page : 207 pages
File Size : 50,6 Mb
Release : 2013
Category : Electronic books
ISBN : 1139892037
A comprehensive introduction to eight major approaches to computation on uncountable mathematical domains.
Author : Noam Greenberg,Joel David Hamkins,Denis Hirschfeldt,Russell Miller
Publisher : Cambridge University Press
Page : 205 pages
File Size : 53,5 Mb
Release : 2013-10-31
Category : Mathematics
ISBN : 9781107014510
A comprehensive introduction to eight major approaches to computation on uncountable mathematical domains.
Author : Noam Greenberg,Denis Roman Hirschfeldt,Joel David Hamkins,Russell Miller (Professor of mathematics)
Publisher : Unknown
Page : 197 pages
File Size : 45,6 Mb
Release : 2013
Category : Computable functions
ISBN : 1461953677
Author : Bob Konikow
Publisher : Unknown
Page : 42 pages
File Size : 48,5 Mb
Release : 2016-12-08
Category : Juvenile Nonfiction
ISBN : 1480835269
Many students think math is boring, but that's only because we too often teach it in boring ways. You don't have to worry about that problem with this book, which is filled with colorful and fun illustrations and explanations about mathematical concepts that are often overlooked in the academic world. The book is just one in a series focusing on "The Lighter Side of Mathematics." In it, you'll learn concepts such as: - What it means when something is called "an infinite set;" - When it's correct to say "the part is less than the whole;" - What it means when something is "enumerable." The facts you'll learn provide depth and dimension to the classical study of mathematics and will ignite your curiosity factor about numbers--no matter how old or young you are. If you've always struggled to understand or enjoy math, then it's time to boost your confidence by looking at it in new ways. It begins with Counting the Uncountable.
Author : Denis R Hirschfeldt
Publisher : World Scientific
Page : 232 pages
File Size : 41,7 Mb
Release : 2014-07-18
Category : Mathematics
ISBN : 9789814612630
This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions. Contents:Setting Off: An IntroductionGathering Our Tools: Basic Concepts and NotationFinding Our Path: König's Lemma and ComputabilityGauging Our Strength: Reverse MathematicsIn Defense of DisarrayAchieving Consensus: Ramsey's TheoremPreserving Our Power: ConservativityDrawing a Map: Five DiagramsExploring Our Surroundings: The World Below RT22Charging Ahead: Further TopicsLagniappe: A Proof of Liu's Theorem Readership: Graduates and researchers in mathematical logic. Key Features:This book assumes minimal background in mathematical logic and takes the reader all the way to current research in a highly active areaIt is the first detailed introduction to this particular approach to this area of researchThe combination of fully worked out arguments and exercises make this book well suited to self-study by graduate students and other researchers unfamiliar with the areaKeywords:Reverse Mathematics;Computability Theory;Computable Mathematics;Computable Combinatorics
Author : Merlin Carl
Publisher : Walter de Gruyter GmbH & Co KG
Page : 343 pages
File Size : 50,5 Mb
Release : 2019-09-23
Category : Mathematics
ISBN : 9783110496154
Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics are covered.
Author : Antonio Montalbán
Publisher : Cambridge University Press
Page : 213 pages
File Size : 46,7 Mb
Release : 2021-06-24
Category : Mathematics
ISBN : 9781108423298
Presents main results and techniques in computable structure theory together in a coherent framework for the first time in 20 years.
Author : Denis R. Hirschfeldt,Karen Lange,Richard A. Shore
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 50,6 Mb
Release : 2017-09-25
Category : Computable functions
ISBN : 9781470426576
Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory is the type spectrum of some homogeneous model of . Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model.
Author : Arnold Beckmann,Laurent Bienvenu,Nataša Jonoska
Publisher : Springer
Page : 375 pages
File Size : 53,9 Mb
Release : 2016-06-13
Category : Computers
ISBN : 9783319401898
This book constitutes the refereed proceedings of the 12th Conference on Computability in Europe, CiE 2016, held in Paris, France, in June/July 2016. The 18 revised full papers and 19 invited papers and invited extended abstracts were carefully reviewed and selected from 40 submissions. The conference CiE 2016 has six special sessions – two sessions, cryptography and information theory and symbolic dynamics, are organized for the first time in the conference series. In addition to this new developments in areas frequently covered in the CiE conference series were addressed in the following sessions: computable and constructive analysis; computation in biological systems; history and philosophy of computing; weak arithmetic.
Author : Paola Bonizzoni,Vasco Brattka,Benedikt Löwe
Publisher : Springer
Page : 446 pages
File Size : 54,9 Mb
Release : 2013-06-03
Category : Computers
ISBN : 9783642390531
This book constitutes the refereed proceedings of the 9th Conference on Computability in Europe, CiE 2013, held in Milan, Italy, in July 2013. The 48 revised papers presented together with 1 invited lecture and 2 tutorials were carefully reviewed and selected with an acceptance rate of under 31,7%. Both the conference series and the association promote the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences such as physics and biology, and also including the promotion of related non-scientific fields such as philosophy and history of computing.
Author : Rod Downey
Publisher : Cambridge University Press
Page : 540 pages
File Size : 48,7 Mb
Release : 2014-05
Category : Computers
ISBN : 9781107043480
A collection of essays celebrating the influence of Alan Turing's work in logic, computer science and related areas.
Author : Christian S. Calude,Jose Felix Gomes da Costa,Nachum Dershowitz,Elisabete Freire,Grzegorz Rozenberg
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 54,9 Mb
Release : 2009-08-28
Category : Computers
ISBN : 9783642037443
This book constitutes the refereed proceedings of the 8th International Conference on Unconventional Computation, UC 2009, held in Ponta Delgada, Portugal, in September 2009. The 18 revised full papers presented together with 8 invited talks, 3 tutorials and 5 posters were carefully reviewed and selected from 40 submissions. The papers are devoted to all aspects of unconventional computation ranging from theoretical and experimental aspects to various applications. Typical topics are: natural computing including quantum; cellular, molecular, neural and evolutionary computing; chaos and dynamical system-based computing; and various proposals for computational mechanisms that go beyond the Turing model.
Author : Jack John Bulloff,Thomas Campell Holyoke,S.W. Hahn
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642867453
Dr. KURT GODEL'S sixtieth birthday (April 28, 1966) and the thirty fifth anniversary of the publication of his theorems on undecidability were celebrated during the 75th Anniversary Meeting of the Ohio Ac ademy of Science at The Ohio State University, Columbus, on April 22, 1966. The celebration took the form of a Festschrift Symposium on a theme supported by the late Director of The Institute for Advanced Study at Princeton, New Jersey, Dr. J. ROBERT OPPENHEIMER: "Logic, and Its Relations to Mathematics, Natural Science, and Philosophy." The symposium also celebrated the founding of Section L (Mathematical Sciences) of the Ohio Academy of Science. Salutations to Dr. GODEL were followed by the reading of papers by S. F. BARKER, H. B. CURRY, H. RUBIN, G. E. SACKS, and G. TAKEUTI, and by the announcement of in-absentia papers contributed in honor of Dr. GODEL by A. LEVY, B. MELTZER, R. M. SOLOVAY, and E. WETTE. A short discussion of "The II Beyond Godel's I" concluded the session.
Author : Jerzy Pogonowski
Publisher : LIT Verlag Münster
Page : 128 pages
File Size : 43,6 Mb
Release : 2024-05-19
Category : Electronic
ISBN : 9783643913104
This volume contains four essays which may attract the attention of those readers, who are interested in mathematical cognition The main issues and questions addressed include: How do we achieve understanding of mathematical notions and ideas? What benefits can be obtained from mistakes of great mathematicians? Which mathematical objects are standard and which are pathological? Is it possible characterize the intended models of mathematical theories in a unique way?
Author : Raymond L. Wilder,Mathematics
Publisher : Courier Corporation
Page : 354 pages
File Size : 46,8 Mb
Release : 2012-01-01
Category : Mathematics
ISBN : 9780486488202
This classic undergraduate text by an eminent educator acquaints students with the fundamental concepts and methods of mathematics. In addition to introducing many noteworthy historical figures from the eighteenth through the mid-twentieth centuries, the book examines the axiomatic method, set theory, infinite sets, the linear continuum and the real number system, and groups. Additional topics include the Frege-Russell thesis, intuitionism, formal systems, mathematical logic, and the cultural setting of mathematics. Students and teachers will find that this elegant treatment covers a vast amount of material in a single reasonably concise and readable volume. Each chapter concludes with a set of problems and a list of suggested readings. An extensive bibliography and helpful indexes conclude the text.