Theorems, corollaries, lemmas, and methods of proof:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, N.J.
Wiley
2006
|
| Series: | Pure and applied mathmatics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIII, 318 S. graph. Darst. |
| ISBN: | 0470042958 9780470042953 |
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Record in the Search Index
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| adam_text | THEOREMS, COROLLARIES, LEMMAS, AND METHODS OF PROOF RICHARD J. ROSSI
DEPARTMENT OF MATHEMATICAL SCIENCES MONTANA TECH BUTTE, MT WILEY-
INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS PREFACE XI
CHAPTER 1 * INTRODUCTION TO MODERN MATHEMATICS 1 1.1 INDUCTIVE AND
DEDUCTIVE REASONING 2 1.2 COMPONENTS OF MODERN MATHEMATICS 4 1.3
COMMONLY USED MATHEMATICAL NOTATION 10 EXERCISES 15 CHAPTER 2 * AN
INTRODUCTION TO SYMBOLIC LOGIC 17 2.1 STATEMENTS AND PROPOSITIONAL
FUNCTIONS 17 2.2 COMBINING STATEMENTS 19 2.3 TRUTH TABLES 21 2.4
CONDITIONAL STATEMENTS 31 2.4.1 CONVERSE AND CONTRAPOSITIVE STATEMENTS
33 2.4.2 BICONDITIONAL STATEMENTS 35 2.5 PROPOSITIONAL FUNCTIONS AND
QUANTIFIERS 36 EXERCISES 41 CHAPTER 3 * METHODS OF PROOF 45 3.1
THEOREMS, COROLLARIES, AND LEMMAS 45 3.2 THE CONTRAPOSITIVE AND CONVERSE
OF A THEOREM 50 3.3 METHODS OF PROOF AND PROVING THEOREMS 51 3.3.1
DIRECT PROOF 51 3.3.2 INDIRECT PROOF 58 3.4 SPECIALIZED METHODS OF PROOF
62 3.4.1 MATHEMATICAL INDUCTION 63 3.4.2 UNIQUENESS PROOFS 73 3.4.3
EXISTENCE PROOFS 75 3.4.4 PROOF BY CASES 78 3.4.5 PROVING BICONDITIONAL
THEOREMS 83 3.4.6 DISPROVING A CONJECTURE 85 3.5 SOME FINAL NOTES ON
PROVING THEOREMS 87 VIII CONTENTS EXERCISES 90 CHAPTER 4 * INTRODUCTION
TO NUMBER THEORY 97 4.1 BINARY OPERATORS 97 4.2 COMMONLY USED NUMBER
SYSTEMS 107 4.2.1 THE NATURAL NUMBERS 108 4.2.2 THE WHOLE NUMBERS 110
4.2.3 THE INTEGERS 111 4.2.4 THE RATIONAL NUMBERS 113 4.2.5 THE REAL
NUMBERS 119 4.3 ELEMENTARY NUMBER THEORY 126 4.3.1 ODD AND EVEN NUMBERS
126 4.3.2 DIVISIBILITY 131 4.3.3 PRIME NUMBERS 139 4.3.4 RECURSIVELY
DEFINED NUMBERS 146 EXERCISES 156 CHAPTER 5 * THE FOUNDATIONS OF
CALCULUS 162 5.1 FUNCTIONS 162 5.2 SEQUENCES OF REAL NUMBERS 165 5.2.1
CONVERGENT SEQUENCES AND LIMIT THEOREMS 166 5.2.2 MONOTONE SEQUENCES 184
5.2.3 CAUCHY SEQUENCES 196 5.3 LIMITS OF FUNCTIONS 200 5.4 CONTINUITY
215 5.5 DERIVATIVES 229 EXERCISES 240 CHAPTER 6 * FOUNDATIONS OF ALGEBRA
248 6.1 INTRODUCTION TO SETS 248 6.1.1 SET ALGEBRA 253 6.1.2 ELEMENT
CHASING PROOFS 255 6.1.3 UNIONS AND INTERSECTIONS OF FINITE COLLECTIONS
OF SETS 265 CONTENTS IX 6.1.4 COUNTABLE AND UNCOUNTABLE SETS 274 6.2 AN
INTRODUCTION TO GROUP THEORY 280 6.2.1 GROUPS 280 6.2.2 SUBGROUPS 294
EXERCISES 303 REFERENCES 309 INDEX 311
|
| adam_txt |
THEOREMS, COROLLARIES, LEMMAS, AND METHODS OF PROOF RICHARD J. ROSSI
DEPARTMENT OF MATHEMATICAL SCIENCES MONTANA TECH BUTTE, MT WILEY-
INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS PREFACE XI
CHAPTER 1 * INTRODUCTION TO MODERN MATHEMATICS 1 1.1 INDUCTIVE AND
DEDUCTIVE REASONING 2 1.2 COMPONENTS OF MODERN MATHEMATICS 4 1.3
COMMONLY USED MATHEMATICAL NOTATION 10 EXERCISES 15 CHAPTER 2 * AN
INTRODUCTION TO SYMBOLIC LOGIC 17 2.1 STATEMENTS AND PROPOSITIONAL
FUNCTIONS 17 2.2 COMBINING STATEMENTS 19 2.3 TRUTH TABLES 21 2.4
CONDITIONAL STATEMENTS 31 2.4.1 CONVERSE AND CONTRAPOSITIVE STATEMENTS
33 2.4.2 BICONDITIONAL STATEMENTS 35 2.5 PROPOSITIONAL FUNCTIONS AND
QUANTIFIERS 36 EXERCISES 41 CHAPTER 3 * METHODS OF PROOF 45 3.1
THEOREMS, COROLLARIES, AND LEMMAS 45 3.2 THE CONTRAPOSITIVE AND CONVERSE
OF A THEOREM 50 3.3 METHODS OF PROOF AND PROVING THEOREMS 51 3.3.1
DIRECT PROOF 51 3.3.2 INDIRECT PROOF 58 3.4 SPECIALIZED METHODS OF PROOF
62 3.4.1 MATHEMATICAL INDUCTION 63 3.4.2 UNIQUENESS PROOFS 73 3.4.3
EXISTENCE PROOFS 75 3.4.4 PROOF BY CASES 78 3.4.5 PROVING BICONDITIONAL
THEOREMS 83 3.4.6 DISPROVING A CONJECTURE 85 3.5 SOME FINAL NOTES ON
PROVING THEOREMS 87 VIII CONTENTS EXERCISES 90 CHAPTER 4 * INTRODUCTION
TO NUMBER THEORY 97 4.1 BINARY OPERATORS 97 4.2 COMMONLY USED NUMBER
SYSTEMS 107 4.2.1 THE NATURAL NUMBERS 108 4.2.2 THE WHOLE NUMBERS 110
4.2.3 THE INTEGERS 111 4.2.4 THE RATIONAL NUMBERS 113 4.2.5 THE REAL
NUMBERS 119 4.3 ELEMENTARY NUMBER THEORY 126 4.3.1 ODD AND EVEN NUMBERS
126 4.3.2 DIVISIBILITY 131 4.3.3 PRIME NUMBERS 139 4.3.4 RECURSIVELY
DEFINED NUMBERS 146 EXERCISES 156 CHAPTER 5 * THE FOUNDATIONS OF
CALCULUS 162 5.1 FUNCTIONS 162 5.2 SEQUENCES OF REAL NUMBERS 165 5.2.1
CONVERGENT SEQUENCES AND LIMIT THEOREMS 166 5.2.2 MONOTONE SEQUENCES 184
5.2.3 CAUCHY SEQUENCES 196 5.3 LIMITS OF FUNCTIONS 200 5.4 CONTINUITY
215 5.5 DERIVATIVES 229 EXERCISES 240 CHAPTER 6 * FOUNDATIONS OF ALGEBRA
248 6.1 INTRODUCTION TO SETS 248 6.1.1 SET ALGEBRA 253 6.1.2 ELEMENT
CHASING PROOFS 255 6.1.3 UNIONS AND INTERSECTIONS OF FINITE COLLECTIONS
OF SETS 265 CONTENTS IX 6.1.4 COUNTABLE AND UNCOUNTABLE SETS 274 6.2 AN
INTRODUCTION TO GROUP THEORY 280 6.2.1 GROUPS 280 6.2.2 SUBGROUPS 294
EXERCISES 303 REFERENCES 309 INDEX 311 |
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| spelling | Rossi, Richard J. Verfasser aut Theorems, corollaries, lemmas, and methods of proof Richard J. Rossi Hoboken, N.J. Wiley 2006 XIII, 318 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathmatics Includes bibliographical references and index Analyse mathématique - Fondements - Manuels d'enseignement supérieur Logique symbolique et mathématique - Manuels d'enseignement supérieur Preuve, Théorie de la - Manuels d'enseignement supérieur Wiskunde gtt Mathematik Proof theory Textbooks Mathematical analysis Foundations Textbooks Logic, Symbolic and mathematical Textbooks Beweistheorie (DE-588)4145177-6 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Beweistheorie (DE-588)4145177-6 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014910100&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rossi, Richard J. Theorems, corollaries, lemmas, and methods of proof Analyse mathématique - Fondements - Manuels d'enseignement supérieur Logique symbolique et mathématique - Manuels d'enseignement supérieur Preuve, Théorie de la - Manuels d'enseignement supérieur Wiskunde gtt Mathematik Proof theory Textbooks Mathematical analysis Foundations Textbooks Logic, Symbolic and mathematical Textbooks Beweistheorie (DE-588)4145177-6 gnd |
| subject_GND | (DE-588)4145177-6 (DE-588)4123623-3 |
| title | Theorems, corollaries, lemmas, and methods of proof |
| title_auth | Theorems, corollaries, lemmas, and methods of proof |
| title_exact_search | Theorems, corollaries, lemmas, and methods of proof |
| title_exact_search_txtP | Theorems, corollaries, lemmas, and methods of proof |
| title_full | Theorems, corollaries, lemmas, and methods of proof Richard J. Rossi |
| title_fullStr | Theorems, corollaries, lemmas, and methods of proof Richard J. Rossi |
| title_full_unstemmed | Theorems, corollaries, lemmas, and methods of proof Richard J. Rossi |
| title_short | Theorems, corollaries, lemmas, and methods of proof |
| title_sort | theorems corollaries lemmas and methods of proof |
| topic | Analyse mathématique - Fondements - Manuels d'enseignement supérieur Logique symbolique et mathématique - Manuels d'enseignement supérieur Preuve, Théorie de la - Manuels d'enseignement supérieur Wiskunde gtt Mathematik Proof theory Textbooks Mathematical analysis Foundations Textbooks Logic, Symbolic and mathematical Textbooks Beweistheorie (DE-588)4145177-6 gnd |
| topic_facet | Analyse mathématique - Fondements - Manuels d'enseignement supérieur Logique symbolique et mathématique - Manuels d'enseignement supérieur Preuve, Théorie de la - Manuels d'enseignement supérieur Wiskunde Mathematik Proof theory Textbooks Mathematical analysis Foundations Textbooks Logic, Symbolic and mathematical Textbooks Beweistheorie Lehrbuch |
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