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001 9780429322587
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006 m d
007 cr cnu---unuuu
008 191123s2019 xx o 000 0 eng d
040 _aOCoLC-P
_beng
_cOCoLC-P
020 _a9781000709629
020 _a1000709620
020 _a9781000709803
_q(ePub ebook)
020 _a1000709809
020 _a9781000709711
_q(Mobipocket ebook)
020 _a100070971X
020 _a9780429322587
_q(ebook)
020 _a0429322585
020 _z9780367338237 (hbk.)
024 7 _a10.1201/9780429322587
_2doi
035 _a(OCoLC)1128466687
035 _a(OCoLC-P)1128466687
050 4 _aQA39.2
072 7 _aMAT
_x034000
_2bisacsh
072 7 _aMAT
_x018000
_2bisacsh
072 7 _aMAT
_x028000
_2bisacsh
072 7 _aPB
_2bicssc
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.
300 _a1 online resource (413 p.).
336 _atext
_2rdacontent
336 _astill image
_2rdacontent
337 _acomputer
_2rdamedia
338 _aonline resource
_2rdacarrier
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
650 7 _aMATHEMATICS / Logic
_2bisacsh
650 7 _aMATHEMATICS / Set Theory
_2bisacsh
856 4 0 _3Taylor & Francis
_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
999 _c74564
_d74564