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LEADER: 03260fam a2200373 a 4500
001 1609351
005 20220608195736.0
008 930526s1998 enka b 001 0 eng
010 $a 93014567
020 $a0521441161 (hardback)
020 $a0521446635 (pbk.)
035 $a(OCoLC)503421321
035 $a(OCoLC)ocn503421321
035 $9AKL5885CU
035 $a(NNC)1609351
035 $a1609351
040 $aDLC$cDLC$dDLC$dOrLoB$dNNC
050 00 $aQA9$b.V38 1994
082 00 $a511.3$220
100 1 $aVelleman, Daniel J.$0http://id.loc.gov/authorities/names/n93049766
245 10 $aHow to prove it :$ba structured approach /$cDaniel J. Velleman.
260 $aCambridge [England] ;$aNew York :$bCambridge University,$c1998.
300 $aix, 309 pages :$billustrations ;$c24 cm
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
504 $aIncludes bibliographical references (p. 304) and index.
505 0 $a1. Sentential Logic. 1.1. Deductive reasoning and logical connectives. 1.2. Truth tables. 1.3. Variables and sets. 1.4. Operations on sets. 1.5. The conditional and biconditional connectives -- 2. Quantificational Logic. 2.1. Quantifiers. 2.2. Equivalences involving quantifiers. 2.3. More operations on sets -- 3. Proofs. 3.1. Proof strategies. 3.2. Proofs involving negations and conditionals. 3.3. Proofs involving quantifiers. 3.4. Proofs involving conjunctions and biconditionals. 3.5. Proofs involving disjunctions. 3.6. Existence and uniqueness proofs. 3.7. More examples of proofs -- 4. Relations. 4.1. Ordered pairs and Cartesian products. 4.2. Relations. 4.3. More about relations. 4.4. Ordering relations. 4.5. Closures. 4.6. Equivalence relations -- 5. Functions. 5.1. Functions. 5.2. One-to-one and onto. 5.3. Inverses of functions. 5.4. Images and inverse images: a research project -- 6. Mathematical Induction. 6.1. Proof by mathematical induction. 6.2. More examples. 6.3. Recursion.
505 8 $a6.4. Strong induction. 6.5. Closures again -- 7. Infinite sets. 7.1. Equinumerous sets. 7.2. Countable and uncountable sets. 7.3. The Cantor-Schroder-Bernstein theorem.
520 $aMany students have trouble the first time they take a mathematics course in which proofs play a significant role. This book will prepare students for such courses by teaching them techniques for writing and reading proofs. No background beyond high school mathematics is assumed. The book begins with logic and set theory, to familiarize students with the language of mathematics and how it is interpreted.
520 8 $aThis understanding of the language of mathematics serves as the basis for a detailed discussion of the most important techniques used in proofs, when and how to use them, and how they are combined to produce complex proofs. Material on the natural numbers, relations, functions, and infinite sets provides practice in writing and reading proofs, as well as supplying background that will be valuable in most theoretical mathematics courses.
650 0 $aLogic, Symbolic and mathematical.$0http://id.loc.gov/authorities/subjects/sh85078115
650 0 $aMathematics.$0http://id.loc.gov/authorities/subjects/sh85082139
852 00 $bmat$hQA9$i.V38 1998
852 00 $bsci$hQA9$i.V38 1994