04515nam 2200649Ia 450 991013957420332120170809173005.01-283-29873-297866132987371-118-03157-11-118-03057-5(CKB)2550000000056484(EBL)694434(OCoLC)761319787(SSID)ssj0000555623(PQKBManifestationID)11386065(PQKBTitleCode)TC0000555623(PQKBWorkID)10519217(PQKB)10707459(MiAaPQ)EBC694434(EXLCZ)99255000000005648420060208d2006 uy 0engur|n|---|||||txtccrTheorems, corollaries, lemmas, and methods of proof[electronic resource] /Richard J. RossiHoboken, N.J. Wileyc20061 online resource (338 p.)Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts ;v.82Description based upon print version of record.0-470-04295-8 Includes bibliographical references and index.Theorems, 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 Proof3.1 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 Integers4.2.4 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 Proofs6.1.3 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; IndexA 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 proofPure and Applied Mathematics: A Wiley Series of Texts, Monographs and TractsProof theoryTextbooksMathematical analysisFoundationsTextbooksLogic, Symbolic and mathematicalTextbooksElectronic books.Proof theoryMathematical analysisFoundationsLogic, Symbolic and mathematical511.3/6511.36Rossi Richard J.1956-955811MiAaPQMiAaPQMiAaPQBOOK9910139574203321Theorems, corollaries, lemmas, and methods of proof2163474UNINA