Reverse Mathematics PDF Download
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Author | : John Stillwell |
Publisher | : Princeton University Press |
Total Pages | : 198 |
Release | : 2019-09-24 |
Genre | : Mathematics |
ISBN | : 0691196419 |
Download Reverse Mathematics Book in PDF, ePub and Kindle
This volume presents reverse mathematics to a general mathematical audience for the first time. Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. to logic.
Author | : Damir D. Dzhafarov |
Publisher | : Springer Nature |
Total Pages | : 498 |
Release | : 2022-07-25 |
Genre | : Computers |
ISBN | : 3031113675 |
Download Reverse Mathematics Book in PDF, ePub and Kindle
Reverse mathematics studies the complexity of proving mathematical theorems and solving mathematical problems. Typical questions include: Can we prove this result without first proving that one? Can a computer solve this problem? A highly active part of mathematical logic and computability theory, the subject offers beautiful results as well as significant foundational insights. This text provides a modern treatment of reverse mathematics that combines computability theoretic reductions and proofs in formal arithmetic to measure the complexity of theorems and problems from all areas of mathematics. It includes detailed introductions to techniques from computable mathematics, Weihrauch style analysis, and other parts of computability that have become integral to research in the field. Topics and features: Provides a complete introduction to reverse mathematics, including necessary background from computability theory, second order arithmetic, forcing, induction, and model construction Offers a comprehensive treatment of the reverse mathematics of combinatorics, including Ramsey's theorem, Hindman's theorem, and many other results Provides central results and methods from the past two decades, appearing in book form for the first time and including preservation techniques and applications of probabilistic arguments Includes a large number of exercises of varying levels of difficulty, supplementing each chapter The text will be accessible to students with a standard first year course in mathematical logic. It will also be a useful reference for researchers in reverse mathematics, computability theory, proof theory, and related areas. Damir D. Dzhafarov is an Associate Professor of Mathematics at the University of Connecticut, CT, USA. Carl Mummert is a Professor of Computer and Information Technology at Marshall University, WV, USA.
Author | : Stephen George Simpson |
Publisher | : Cambridge University Press |
Total Pages | : 461 |
Release | : 2009-05-29 |
Genre | : Mathematics |
ISBN | : 052188439X |
Download Subsystems of Second Order Arithmetic Book in PDF, ePub and Kindle
This volume examines appropriate axioms for mathematics to prove particular theorems in core areas.
Author | : Stephen G. Simpson |
Publisher | : Cambridge University Press |
Total Pages | : 401 |
Release | : 2017-03-30 |
Genre | : Mathematics |
ISBN | : 1108637221 |
Download Reverse Mathematics 2001 Book in PDF, ePub and Kindle
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Reverse mathematics is a program of research in the foundations of mathematics, motivated by two foundational questions: 'what are appropriate axioms for mathematics?' and 'what are the logical strengths of particular axioms and particular theorems?' This volume, the twenty-first publication in the Lecture Notes in Logic series, contains twenty-four original research papers from respected authors that present exciting new developments in reverse mathematics and subsystems of second order arithmetic since 1998.
Author | : Stephen G. Ross |
Publisher | : CRC Press |
Total Pages | : 416 |
Release | : 2005-09-01 |
Genre | : Mathematics |
ISBN | : 1439864284 |
Download Reverse Mathematics 2001 Book in PDF, ePub and Kindle
Reverse Mathematics is a program of research in the foundations of mathematics, motivated by the foundational questions of what are appropriate axioms for mathematics, and what are the logical strengths of particular axioms and particular theorems. The book contains 24 original papers by leading researchers. These articles exhibit the exciting rece
Author | : Denis R Hirschfeldt |
Publisher | : World Scientific |
Total Pages | : 231 |
Release | : 2014-07-18 |
Genre | : Mathematics |
ISBN | : 9814612634 |
Download Slicing The Truth: On The Computable And Reverse Mathematics Of Combinatorial Principles Book in PDF, ePub and Kindle
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.
Author | : Denise Gaskins |
Publisher | : Tabletop Academy Press |
Total Pages | : 288 |
Release | : 2012-09-04 |
Genre | : Education |
ISBN | : 1892083248 |
Download Let's Play Math Book in PDF, ePub and Kindle
Author | : David Reed Solomon |
Publisher | : |
Total Pages | : 456 |
Release | : 1998 |
Genre | : |
ISBN | : |
Download Reverse Mathematics and Ordered Groups Book in PDF, ePub and Kindle
Author | : Oscar Levin |
Publisher | : Createspace Independent Publishing Platform |
Total Pages | : 238 |
Release | : 2018-07-30 |
Genre | : |
ISBN | : 9781724572639 |
Download Discrete Mathematics Book in PDF, ePub and Kindle
Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.
Author | : Marc Peter Deisenroth |
Publisher | : Cambridge University Press |
Total Pages | : 392 |
Release | : 2020-04-23 |
Genre | : Computers |
ISBN | : 1108569323 |
Download Mathematics for Machine Learning Book in PDF, ePub and Kindle
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.