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| 001 | 9780429322587 | ||
| 003 | FlBoTFG | ||
| 005 | 20220724194521.0 | ||
| 006 | m d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 191123s2019 xx o 000 0 eng d | ||
| 040 |
_aOCoLC-P _beng _cOCoLC-P |
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| 020 | _a9781000709629 | ||
| 020 | _a1000709620 | ||
| 020 |
_a9781000709803 _q(ePub ebook) |
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| 020 | _a1000709809 | ||
| 020 |
_a9781000709711 _q(Mobipocket ebook) |
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| 020 | _a100070971X | ||
| 020 |
_a9780429322587 _q(ebook) |
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| 020 | _a0429322585 | ||
| 020 | _z9780367338237 (hbk.) | ||
| 024 | 7 |
_a10.1201/9780429322587 _2doi |
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| 035 | _a(OCoLC)1128466687 | ||
| 035 | _a(OCoLC-P)1128466687 | ||
| 050 | 4 | _aQA39.2 | |
| 072 | 7 |
_aMAT _x034000 _2bisacsh |
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_aMAT _x018000 _2bisacsh |
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_aMAT _x028000 _2bisacsh |
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_aPB _2bicssc |
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| 082 | 0 | 4 |
_a510 _223 |
| 100 | 1 | _aLoehr, Nicholas A. | |
| 245 | 1 | 3 |
_aAn Introduction to Mathematical Proofs _h[electronic resource]. |
| 260 |
_aMilton : _bCRC Press LLC, _c2019. |
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| 300 | _a1 online resource (413 p.). | ||
| 336 |
_atext _2rdacontent |
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| 336 |
_astill image _2rdacontent |
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| 337 |
_acomputer _2rdamedia |
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| 338 |
_aonline resource _2rdacarrier |
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| 490 | 1 | _aTextbooks in Mathematics Ser. | |
| 500 | _aDescription based upon print version of record. | ||
| 505 | 0 | _a<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 | _aAn 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. | ||
| 588 | _aOCLC-licensed vendor bibliographic record. | ||
| 650 | 0 | _aProof theory. | |
| 650 | 7 |
_aMATHEMATICS / Mathematical Analysis _2bisacsh |
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| 650 | 7 |
_aMATHEMATICS / Logic _2bisacsh |
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| 650 | 7 |
_aMATHEMATICS / Set Theory _2bisacsh |
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| 856 | 4 | 0 |
_3Read Online _uhttps://www.taylorfrancis.com/books/9780429322587 |
| 856 | 4 | 2 |
_3OCLC metadata license agreement _uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf |
| 942 |
_2lcc _cEBK |
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| 999 |
_c18529 _d18529 |
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