An Introduction to Proofs with Set Theory (Record no. 85142)
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| fixed length control field | 04520nam a22005295i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-02426-9 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240730163930.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 220601s2020 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783031024269 |
| -- | 978-3-031-02426-9 |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 510 |
| 100 1# - AUTHOR NAME | |
| Author | Ashlock, Daniel. |
| 245 13 - TITLE STATEMENT | |
| Title | An Introduction to Proofs with Set Theory |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2020. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | XV, 233 p. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Synthesis Lectures on Mathematics & Statistics, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | Preface -- Acknowledgments -- Introduction and Review of Background Material -- Boolean Logic and Truth (Values) -- Quantified Predicates, Rules of Inference, and Arguments -- Mathematical Proofs -- Intuitive Set Theory -- Mathematical Induction -- Functions -- The Integers and Beyond -- Counting Things -- Relations -- Number Bases, Number Systems, and Operations -- Many Infinities: Cardinal Numbers -- Many Infinities: Ordinal Numbers -- Paradoxes and Axiomatic Set Theory -- Bibliography -- Authors' Biographies -- Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This text is intended as an introduction to mathematical proofs for students. It is distilled from the lecture notes for a course focused on set theory subject matter as a means of teaching proofs. Chapter 1 contains an introduction and provides a brief summary of some background material students may be unfamiliar with. Chapters 2 and 3 introduce the basics of logic for students not yet familiar with these topics. Included is material on Boolean logic, propositions and predicates, logical operations, truth tables, tautologies and contradictions, rules of inference and logical arguments. Chapter 4 introduces mathematical proofs, including proof conventions, direct proofs, proof-by-contradiction, and proof-by-contraposition. Chapter 5 introduces the basics of naive set theory, including Venn diagrams and operations on sets. Chapter 6 introduces mathematical induction and recurrence relations. Chapter 7 introduces set-theoretic functions and covers injective, surjective, and bijective functions, as well as permutations. Chapter 8 covers the fundamental properties of the integers including primes, unique factorization, and Euclid's algorithm. Chapter 9 is an introduction to combinatorics; topics included are combinatorial proofs, binomial and multinomial coefficients, the Inclusion-Exclusion principle, and counting the number of surjective functions between finite sets. Chapter 10 introduces relations and covers equivalence relations and partial orders. Chapter 11 covers number bases, number systems, and operations. Chapter 12 covers cardinality, including basic results on countable and uncountable infinities, and introduces cardinal numbers. Chapter 13 expands on partial orders and introduces ordinal numbers. Chapter 14 examines the paradoxes of naive set theory and introduces and discusses axiomatic set theory. This chapter also includes Cantor's Paradox, Russel's Paradox, a discussion of axiomatic theories, an exposition on Zermelo‒Fraenkel Set Theory with the Axiom of Choice, and a brief explanation of Gödel's Incompleteness Theorems. |
| 700 1# - AUTHOR 2 | |
| Author 2 | Lee, Colin. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://doi.org/10.1007/978-3-031-02426-9 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 264 #1 - | |
| -- | Cham : |
| -- | Springer International Publishing : |
| -- | Imprint: Springer, |
| -- | 2020. |
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| -- | text |
| -- | txt |
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| -- | computer |
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| -- | rdamedia |
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| -- | online resource |
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| -- | text file |
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| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Statistics . |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Engineering mathematics. |
| 650 14 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Statistics. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Engineering Mathematics. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| -- | 1938-1751 |
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| -- | ZDB-2-SXSC |
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