LEADER 04481nam 2200637Ia 450 001 9910830542903321 005 20230829005136.0 010 $a1-283-29873-2 010 $a9786613298737 010 $a1-118-03157-1 010 $a1-118-03057-5 035 $a(CKB)2550000000056484 035 $a(EBL)694434 035 $a(OCoLC)761319787 035 $a(SSID)ssj0000555623 035 $a(PQKBManifestationID)11386065 035 $a(PQKBTitleCode)TC0000555623 035 $a(PQKBWorkID)10519217 035 $a(PQKB)10707459 035 $a(MiAaPQ)EBC694434 035 $a(EXLCZ)992550000000056484 100 $a20060208d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTheorems, corollaries, lemmas, and methods of proof$b[electronic resource] /$fRichard J. Rossi 210 $aHoboken, N.J. $cWiley$dc2006 215 $a1 online resource (338 p.) 225 1 $aPure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts ;$vv.82 300 $aDescription based upon print version of record. 311 $a0-470-04295-8 320 $aIncludes bibliographical references and index. 327 $aTheorems, Corollaries, Lemmas, and Methods of Proof; Contents; Preface; Chapter 1 - Introduction to Modern Mathematics; 1.1 Inductive and Deductive Reasoning; 1.2 Components of Modern Mathematics; 1.3 Commonly Used Mathematical Notation; EXERCISES; Chapter 2 - An Introduction to Symbolic Logic; 2.1 Statements and Propositional Functions; 2.2 Combining Statements; 2.3 Truth Tables; 2.4 Conditional Statements; 2.4.1 Converse and Contrapositive Statements; 2.4.2 Biconditional Statements; 2.5 Propositional Functions and Quantifiers; EXERCISES; Chapter 3 - Methods of Proof 327 $a3.1 Theorems, Corollaries, and Lemmas3.2 The Contrapositive and Converse of a Theorem; 3.3 Methods of Proof and Proving Theorems; 3.3.1 Direct Proof; 3.3.2 Indirect Proof; 3.4 Specialized Methods of Proof; 3.4.1 Mathematical Induction; 3.4.2 Uniqueness Proofs; 3.4.3 Existence Proofs; 3.4.4 Proof by Cases; 3.4.5 Proving Biconditional Theorems; 3.4.6 Disproving a Conjecture; 3.5 Some Final Notes on Proving Theorems; EXERCISES; Chapter 4 - Introduction to Number Theory; 4.1 Binary Operators; 4.2 Commonly Used Number Systems; 4.2.1 The Natural Numbers; 4.2.2 The Whole Numbers; 4.2.3 The Integers 327 $a4.2.4 The Rational Numbers4.2.5 The Real Numbers; 4.3 Elementary Number Theory; 4.3.1 Odd and Even Numbers; 4.3.2 Divisibility; 4.3.3 Prime Numbers; 4.3.4 Recursively Defined Numbers; EXERCISES; Chapter 5 - The Foundations of Calculus; 5.1 Functions; 5.2 Sequences of Real Numbers; 5.2.1 Convergent Sequences and Limit Theorems; 5.2.2 Monotone Sequences; 5.2.3 Cauchy Sequences; 5.3 Limits of Functions; 5.4 Continuity; 5.5 Derivatives; EXERCISES; Chapter 6 - Foundations of Algebra; 6.1 Introduction to Sets; 6.1.1 Set Algebra; 6.1.2 Element Chasing Proofs 327 $a6.1.3 Unions and Intersections of Finite Collections of Sets6.1.4 Countable and Uncountable Sets; 6.2 An Introduction to Group Theory; 6.2.1 Groups; 6.2.2 Subgroups; EXERCISES; References; Index 330 $aA hands-on introduction to the tools needed for rigorous and theoretical mathematical reasoningSuccessfully addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, Theorems, Corollaries, Lemmas, and Methods of Proof equips students with the tools needed to succeed while providing a firm foundation in the axiomatic structure of modern mathematics.This essential book:* Clearly explains the relationship between definitions, conjectures, theorems, corollaries, lemmas, and proof 410 0$aPure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts 606 $aProof theory$vTextbooks 606 $aMathematical analysis$xFoundations$vTextbooks 606 $aLogic, Symbolic and mathematical$vTextbooks 615 0$aProof theory 615 0$aMathematical analysis$xFoundations 615 0$aLogic, Symbolic and mathematical 676 $a511.3/6 676 $a511.36 700 $aRossi$b Richard J.$f1956-$0955811 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830542903321 996 $aTheorems, corollaries, lemmas, and methods of proof$92163474 997 $aUNINA