Effective Mathematics Of The Uncountable
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Effective Mathematics of the Uncountable
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Author | : Noam Greenberg |
Publsiher | : Unknown |
Total Pages | : 207 |
Release | : 2013 |
Genre | : Electronic books |
ISBN | : 1139892037 |
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A comprehensive introduction to eight major approaches to computation on uncountable mathematical domains.
Effective Mathematics of the Uncountable
Author | : Noam Greenberg,Joel David Hamkins,Denis Hirschfeldt,Russell Miller |
Publsiher | : Cambridge University Press |
Total Pages | : 205 |
Release | : 2013-10-31 |
Genre | : Mathematics |
ISBN | : 9781107014510 |
Download Effective Mathematics of the Uncountable Book in PDF, Epub and Kindle
A comprehensive introduction to eight major approaches to computation on uncountable mathematical domains.
Effective Mathematics of the Uncountable
![Effective Mathematics of the Uncountable](https://youbookinc.com/wp-content/uploads/2024/06/cover.jpg)
Author | : Noam Greenberg,Denis Roman Hirschfeldt,Joel David Hamkins,Russell Miller (Professor of mathematics) |
Publsiher | : Unknown |
Total Pages | : 197 |
Release | : 2013 |
Genre | : Computable functions |
ISBN | : 1461953677 |
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Counting the Uncountable
Author | : Bob Konikow |
Publsiher | : Unknown |
Total Pages | : 42 |
Release | : 2016-12-08 |
Genre | : Juvenile Nonfiction |
ISBN | : 1480835269 |
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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.
Slicing the Truth
Author | : Denis R Hirschfeldt |
Publsiher | : World Scientific |
Total Pages | : 232 |
Release | : 2014-07-18 |
Genre | : Mathematics |
ISBN | : 9789814612630 |
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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
Ordinal Computability
Author | : Merlin Carl |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 343 |
Release | : 2019-09-23 |
Genre | : Mathematics |
ISBN | : 9783110496154 |
Download Ordinal Computability Book in PDF, Epub and Kindle
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.
Computable Structure Theory
Author | : Antonio Montalbán |
Publsiher | : Cambridge University Press |
Total Pages | : 213 |
Release | : 2021-06-24 |
Genre | : Mathematics |
ISBN | : 9781108423298 |
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Presents main results and techniques in computable structure theory together in a coherent framework for the first time in 20 years.
Induction Bounding Weak Combinatorial Principles and the Homogeneous Model Theorem
Author | : Denis R. Hirschfeldt,Karen Lange,Richard A. Shore |
Publsiher | : American Mathematical Soc. |
Total Pages | : 101 |
Release | : 2017-09-25 |
Genre | : Computable functions |
ISBN | : 9781470426576 |
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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.