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Cover: 9783540761235 | Elements of Logic via Numbers and Sets | D. L. Johnson | Taschenbuch
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Elements of Logic via Numbers and Sets
Taschenbuch von D. L. Johnson
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung
This is an elementary text, aimed at first-year undergraduates, which has
been designed to bridge the gap between school and university mathematics
and to emphasise the importance of proofs - both how to follow a proof and
how to construct a proof. The book lays the foundation for most of the key
subjects studied in an undergraduate degree program, and provides numerous
exercises and a bibliography with suggestions for further and background
reading.
Inhaltsverzeichnis
1. Numbers.- 1.1 Arithmetic Progressions.- 1.2 Proof by Contradiction.- 1.3 Proof by Contraposition.- 1.4 Proof by Induction.- 1.5 Inductive Definition.- 1.6 The Well-ordering Principle.- 2. Logic.- 2.1 Propositions.- 2.2 Truth Tables.- 2.3 Syllogisms.- 2.4 Quantifiers.- 3. Sets.- 3.1 Introduction.- 3.2 Operations.- 3.3 Laws.- 3.4 The Power Set.- 4. Relations.- 4.1 Equivalence Relations.- 4.2 Congruences.- 4.3 Number Systems.- 4.4 Orderings.- 5. Maps.- 5.1 Terminology and Notation.- 5.2 Examples.- 5.3 Injections, Surjections and Bijections.- 5.4 Peano's Axioms.- 6. Cardinal Numbers.- 6.1 Cardinal Arithmetic.- 6.2 The Cantor-Schroeder-Bernstein theorem.- 6.3 Countable Sets.- 6.4 Uncountable Sets.- Solutions to Exercises.- Guide to the Literature.- Dramatis Personae.
Details
Erscheinungsjahr: 1998
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 188
Reihe: Springer Undergraduate Mathematics Series
Inhalt: x
188 S.
ISBN-13: 9783540761235
ISBN-10: 3540761233
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Johnson, D. L.
Auflage: 1998
Hersteller: Springer Berlin
Springer London
Springer Undergraduate Mathematics Series
Maße: 235 x 178 x 11 mm
Von/Mit: D. L. Johnson
Erscheinungsdatum: 14.01.1998
Gewicht: 0,338 kg
preigu-id: 106848375
Zusammenfassung
This is an elementary text, aimed at first-year undergraduates, which has
been designed to bridge the gap between school and university mathematics
and to emphasise the importance of proofs - both how to follow a proof and
how to construct a proof. The book lays the foundation for most of the key
subjects studied in an undergraduate degree program, and provides numerous
exercises and a bibliography with suggestions for further and background
reading.
Inhaltsverzeichnis
1. Numbers.- 1.1 Arithmetic Progressions.- 1.2 Proof by Contradiction.- 1.3 Proof by Contraposition.- 1.4 Proof by Induction.- 1.5 Inductive Definition.- 1.6 The Well-ordering Principle.- 2. Logic.- 2.1 Propositions.- 2.2 Truth Tables.- 2.3 Syllogisms.- 2.4 Quantifiers.- 3. Sets.- 3.1 Introduction.- 3.2 Operations.- 3.3 Laws.- 3.4 The Power Set.- 4. Relations.- 4.1 Equivalence Relations.- 4.2 Congruences.- 4.3 Number Systems.- 4.4 Orderings.- 5. Maps.- 5.1 Terminology and Notation.- 5.2 Examples.- 5.3 Injections, Surjections and Bijections.- 5.4 Peano's Axioms.- 6. Cardinal Numbers.- 6.1 Cardinal Arithmetic.- 6.2 The Cantor-Schroeder-Bernstein theorem.- 6.3 Countable Sets.- 6.4 Uncountable Sets.- Solutions to Exercises.- Guide to the Literature.- Dramatis Personae.
Details
Erscheinungsjahr: 1998
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 188
Reihe: Springer Undergraduate Mathematics Series
Inhalt: x
188 S.
ISBN-13: 9783540761235
ISBN-10: 3540761233
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Johnson, D. L.
Auflage: 1998
Hersteller: Springer Berlin
Springer London
Springer Undergraduate Mathematics Series
Maße: 235 x 178 x 11 mm
Von/Mit: D. L. Johnson
Erscheinungsdatum: 14.01.1998
Gewicht: 0,338 kg
preigu-id: 106848375
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