Elements of Logic via Numbers and Sets (Springer Undergraduate Mathematics Series) - Brossura

Libro 27 di 90: Springer Undergraduate Mathematics

Johnson, D. L.

 
9783540761235: Elements of Logic via Numbers and Sets (Springer Undergraduate Mathematics Series)
Brossura
ISBN 10: 3540761233 ISBN 13: 9783540761235
Casa editrice: Springer, 1998

Sinossi

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.

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Recensione

From the reviews: “It took me a while to appreciate the need for a course intended to introduce mathematics undergraduates to advanced mathematics after they finish the calculus sequence. ... This was the first book I found that seems really close to the core. It is well-written and very well suited to such a course.” (James M. Cargal, UMAP Journal, Vol. 31 (1), 2010)

Contenuti

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.

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Editore
Springer
Data di pubblicazione
1998
Lingua
Inglese
ISBN 10 
3540761233
ISBN 13 
9783540761235
Rilegatura
Copertina flessibile
Numero di pagine
188
Contatto del produttore
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Germania

Altre edizioni note dello stesso titolo

9781447106043: Elements of Logic via Numbers and Sets

Edizione in evidenza

ISBN 10:  1447106040 ISBN 13:  9781447106043
Casa editrice: Springer, 2011
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