An Introduction to Mathematical Proofs (Record no. 71195)
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| fixed length control field | 05880cam a2200577Mu 4500 |
| 001 - CONTROL NUMBER | |
| control field | 9780429322587 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20220711212407.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 191123s2019 xx o 000 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9781000709629 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 1000709620 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9781000709803 |
| -- | (ePub ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 1000709809 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9781000709711 |
| -- | (Mobipocket ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 100070971X |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780429322587 |
| -- | (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 0429322585 |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 510 |
| 100 1# - AUTHOR NAME | |
| Author | Loehr, Nicholas A. |
| 245 13 - TITLE STATEMENT | |
| Title | An Introduction to Mathematical Proofs |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Milton : |
| Publisher | CRC Press LLC, |
| Year of publication | 2019. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 1 online resource (413 p.). |
| 490 1# - SERIES STATEMENT | |
| Series statement | Textbooks in Mathematics Ser. |
| 500 ## - GENERAL NOTE | |
| Remark 1 | Description based upon print version of record. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | <P>Logic</P><P>Propositions; Logical Connectives; Truth Tables</P><P>Logical Equivalence; IF-Statements</P><P>IF, IFF, Tautologies, and Contradictions</P><P>Tautologies; Quantifiers; Universes</P><P>Properties of Quantifiers: Useful Denials</P><P>Denial Practice; Uniqueness</P><P></P><B><P>Proofs</P></B><P>Definitions, Axioms, Theorems, and Proofs</P><P>Proving Existence Statements and IF Statements</P><P>Contrapositive Proofs; IFF Proofs</P><P>Proofs by Contradiction; OR Proofs</P><P>Proof by Cases; Disproofs</P><P>Proving Universal Statements; Multiple Quantifiers</P><P>More Quantifier Properties and Proofs (Optional)</P><P></P><B><P>Sets</P></B><P>Set Operations; Subset Proofs</P><P>More Subset Proofs; Set Equality Proofs</P><P>More Set Quality Proofs; Circle Proofs; Chain Proofs</P><P>Small Sets; Power Sets; Contrasting ? and ⁶</P><P>Ordered Pairs; Product Sets</P><P>General Unions and Intersections</P><P>Axiomatic Set Theory (Optional)</P><P></P><B><P>Integers</P></B><P>Recursive Definitions; Proofs by Induction</P><P>Induction Starting Anywhere: Backwards Induction</P><P>Strong Induction</P><P>Prime Numbers; Division with Remainder</P><P>Greatest Common Divisors; Euclid's GCD Algorithm</P><P>More on GCDs; Uniqueness of Prime Factorizations</P><P>Consequences of Prime Factorization (Optional)</P><P></P><B><P>Relations and Functions</P></B><P>Relations; Images of Sets under Relations</P><P>Inverses, Identity, and Composition of Relations</P><P>Properties of Relations</P><P>Definition of Functions</P><P>Examples of Functions; Proving Equality of Functions</P><P>Composition, Restriction, and Gluing</P><P>Direct Images and Preimages</P><P>Injective, Surjective, and Bijective Functions</P><P>Inverse Functions</P><P></P><B><P>Equivalence Relations and Partial Orders</P></B><P>Reflexive, Symmetric, and Transitive Relations</P><P>Equivalence Relations</P><P>Equivalence Classes</P><P>Set Partitions</P><P>Partially Ordered Sets</P><P>Equivalence Relations and Algebraic Structures (Optional)</P><P></P><B><P>Cardinality</P></B><P>Finite Sets</P><P>Countably Infinite Sets</P><P>Countable Sets</P><P>Uncountable Sets</P><P></P><B><P>Real Numbers (Optional)</P></B><P>Axioms for R; Properties of Addition</P><P>Algebraic Properties of Real Numbers</P><P>Natural Numbers, Integers, and Rational Numbers</P><P>Ordering, Absolute Value, and Distance</P><P>Greatest Elements, Least Upper Bounds, and Completeness</P><P></P><B><P>Suggestions for Further Reading</P></B> |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | An Introduction to Mathematical Proofs presents fundamental material on logic, proof methods, set theory, number theory, relations, functions, cardinality, and the real number system. The text uses a methodical, detailed, and highly structured approach to proof techniques and related topics. No prerequisites are needed beyond high-school algebra. New material is presented in small chunks that are easy for beginners to digest. The author offers a friendly style without sacrificing mathematical rigor. Ideas are developed through motivating examples, precise definitions, carefully stated theorems, clear proofs, and a continual review of preceding topics. Features Study aids including section summaries and over 1100 exercises Careful coverage of individual proof-writing skills Proof annotations and structural outlines clarify tricky steps in proofs Thorough treatment of multiple quantifiers and their role in proofs Unified explanation of recursive definitions and induction proofs, with applications to greatest common divisors and prime factorizations About the Author: Nicholas A. Loehr is an associate professor of mathematics at Virginia Technical University. He has taught at College of William and Mary, United States Naval Academy, and University of Pennsylvania. He has won many teaching awards at three different schools. He has published over 50 journal articles. He also authored three other books for CRC Press, including Combinatorics, Second Edition, and Advanced Linear Algebra. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://www.taylorfrancis.com/books/9780429322587 |
| 856 42 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 336 ## - | |
| -- | text |
| -- | rdacontent |
| 336 ## - | |
| -- | still image |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | rdacarrier |
| 588 ## - | |
| -- | OCLC-licensed vendor bibliographic record. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Proof theory. |
| 650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | MATHEMATICS / Mathematical Analysis |
| 650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | MATHEMATICS / Logic |
| 650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | MATHEMATICS / Set Theory |
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