Logic Sets And Numbers
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Elements Of Logic Via Numbers And Sets
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Author : D.L. Johnson
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-09-25
Elements Of Logic Via Numbers And Sets written by D.L. Johnson 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 1998-09-25 with Mathematics categories.
In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.
The Foundations Of Analysis A Straightforward Introduction
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Author : K. G. Binmore
language : en
Publisher: Cambridge University Press
Release Date : 1981-03-26
The Foundations Of Analysis A Straightforward Introduction written by K. G. Binmore and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-03-26 with Mathematics categories.
In elementary introductions to mathematical analysis, the treatment of the logical and algebraic foundations of the subject is necessarily rather skeletal. This book attempts to flesh out the bones of such treatment by providing an informal but systematic account of the foundations of mathematical analysis written at an elementary level. This book is entirely self-contained but, as indicated above, it will be of most use to university or college students who are taking, or who have taken, an introductory course in analysis. Such a course will not automatically cover all the material dealt with in this book and so particular care has been taken to present the material in a manner which makes it suitable for self-study. In a particular, there are a large number of examples and exercises and, where necessary, hints to the solutions are provided. This style of presentation, of course, will also make the book useful for those studying the subject independently of taught course.
Set Theory And Logic
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Author : Robert R. Stoll
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Set Theory And Logic written by Robert R. Stoll and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Logic Sets And Recursion
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Author : Robert L. Causey
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2006
Logic Sets And Recursion written by Robert L. Causey and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Computers categories.
The new Second Edition incorporates a wealth of exercise sets, allowing students to test themselves and review important topics discussed throughout the text."--Jacket.
The Mathematics Of Logic
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Author : Richard W. Kaye
language : en
Publisher: Cambridge University Press
Release Date : 2007-07-12
The Mathematics Of Logic written by Richard W. Kaye and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-12 with Mathematics categories.
This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis.
A First Course In Mathematical Logic And Set Theory
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Author : Michael L. O'Leary
language : en
Publisher: John Wiley & Sons
Release Date : 2015-10-21
A First Course In Mathematical Logic And Set Theory written by Michael L. O'Leary and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-21 with Mathematics categories.
A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
Basic Concepts Of Mathematics And Logic
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Author : Michael C. Gemignani
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
Basic Concepts Of Mathematics And Logic written by Michael C. Gemignani and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
This text emphasizes logic and the theory of sets. Students who take no further courses in the field will find it an excellent resource for developing an appreciation for the nature of mathematics. Others will discover the foundations for future studies — set theory, logic, counting, numbers, functions, and more. 1968 edition. 43 figures. 25 tables.
Introduction To Analysis
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Author : Arthur Mattuck
language : en
Publisher:
Release Date : 2013
Introduction To Analysis written by Arthur Mattuck and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematical analysis categories.
Logic Sets And Numbers
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Author : Louis F. Roethel
language : en
Publisher:
Release Date : 1983
Logic Sets And Numbers written by Louis F. Roethel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Mathematical Logic With Special Reference To The Natural Numbers
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Author : S. W. P. Steen
language : en
Publisher: Cambridge University Press
Release Date : 1972
Mathematical Logic With Special Reference To The Natural Numbers written by S. W. P. Steen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
This book presents a comprehensive treatment of basic mathematical logic. The author's aim is to make exact the vague, intuitive notions of natural number, preciseness, and correctness, and to invent a method whereby these notions can be communicated to others and stored in the memory. He adopts a symbolic language in which ideas about natural numbers can be stated precisely and meaningfully, and then investigates the properties and limitations of this language. The treatment of mathematical concepts in the main body of the text is rigorous, but, a section of 'historical remarks' traces the evolution of the ideas presented in each chapter. Sources of the original accounts of these developments are listed in the bibliography.