Introduction to proof through number theory:
Cover -- Title page -- Contents -- Preface -- Philosophy about learning and teaching -- Content of this book -- Style of this book -- Problem solving -- LaTeX -- Origins -- Further reading -- Acknowledgments -- Notations and Symbols -- Chapter 1. Evens, Odds, and Primes: A Taste of Number Theory --...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
2023
|
| Schriftenreihe: | Pure and applied undergraduate texts
61 |
| Schlagworte: | |
| Online-Zugang: | DE-188 |
| Zusammenfassung: | Cover -- Title page -- Contents -- Preface -- Philosophy about learning and teaching -- Content of this book -- Style of this book -- Problem solving -- LaTeX -- Origins -- Further reading -- Acknowledgments -- Notations and Symbols -- Chapter 1. Evens, Odds, and Primes: A Taste of Number Theory -- 1.1. A first excursion into prime numbers -- 1.2. Even and odd integers -- 1.3. Calculating primes and the sieve of Eratosthenes -- 1.4. Division -- 1.5. Greatest common divisor -- 1.6. Statement of prime factorization -- 1.7*. Perfect numbers -- 1.8*. One of the Mersenne conjectures 1.9*. Twin primes: An excursion into the unknown -- 1.10*. Goldbach's conjecture -- 1.11. Hints and partial solutions for the exercises -- Chapter 2. Mathematical Induction -- 2.1. Mathematical induction -- 2.2. Rates of growth of functions -- 2.3. Sums of powers of the first positive integers -- 2.4. Strong mathematical induction -- 2.5. Fibonacci numbers -- 2.6. Recursive definitions -- 2.7. Arithmetic and algebraic equalities and inequalities -- 2.8. Hints and partial solutions for the exercises -- Chapter 3. Logic: Implications, Contrapositives, Contradictions, and Quantifiers 3.1. The need for rigor -- 3.2. Statements -- 3.3. Truth teller and liar riddle: Asking the right question -- 3.4*. Logic puzzles -- 3.5. Logical connectives -- 3.6. Implications -- 3.7. Contrapositive -- 3.8. Proof by contradiction -- 3.9. Pythagorean triples -- 3.10. Quantifiers -- 3.11. Hints and partial solutions for the exercises -- Chapter 4. The Euclidean Algorithm and Its Consequences -- 4.1. The Division Theorem -- 4.2. There are an infinite number of primes -- 4.3. The Euclidean algorithm -- 4.4. Consequences of the Division Theorem -- 4.5. Solving linear Diophantine equations |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | 1 Online-Ressource (xviii, 442 Seiten) Illustrationen |
| ISBN: | 9781470472580 1470472589 |
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| 520 | 3 | |a 1.9*. Twin primes: An excursion into the unknown -- 1.10*. Goldbach's conjecture -- 1.11. Hints and partial solutions for the exercises -- Chapter 2. Mathematical Induction -- 2.1. Mathematical induction -- 2.2. Rates of growth of functions -- 2.3. Sums of powers of the first positive integers -- 2.4. Strong mathematical induction -- 2.5. Fibonacci numbers -- 2.6. Recursive definitions -- 2.7. Arithmetic and algebraic equalities and inequalities -- 2.8. Hints and partial solutions for the exercises -- Chapter 3. Logic: Implications, Contrapositives, Contradictions, and Quantifiers | |
| 520 | 3 | |a 3.1. The need for rigor -- 3.2. Statements -- 3.3. Truth teller and liar riddle: Asking the right question -- 3.4*. Logic puzzles -- 3.5. Logical connectives -- 3.6. Implications -- 3.7. Contrapositive -- 3.8. Proof by contradiction -- 3.9. Pythagorean triples -- 3.10. Quantifiers -- 3.11. Hints and partial solutions for the exercises -- Chapter 4. The Euclidean Algorithm and Its Consequences -- 4.1. The Division Theorem -- 4.2. There are an infinite number of primes -- 4.3. The Euclidean algorithm -- 4.4. Consequences of the Division Theorem -- 4.5. Solving linear Diophantine equations | |
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Datensatz im Suchindex
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| adam_text | |
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| author | Chow, Bennett 1962- |
| author_GND | (DE-588)136099793 |
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| dewey-full | 511.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/6 |
| dewey-search | 511.3/6 |
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| id | DE-604.BV050036376 |
| illustrated | Illustrated |
| indexdate | 2025-01-28T11:07:14Z |
| institution | BVB |
| isbn | 9781470472580 1470472589 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035374217 |
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| owner | DE-188 |
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| physical | 1 Online-Ressource (xviii, 442 Seiten) Illustrationen |
| psigel | ZDB-30-PQE |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Pure and applied undergraduate texts |
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| spelling | Chow, Bennett 1962- Verfasser (DE-588)136099793 aut Introduction to proof through number theory Bennett Chow Providence, Rhode Island American Mathematical Society 2023 1 Online-Ressource (xviii, 442 Seiten) Illustrationen txt rdacontent c rdamedia cr rdacarrier Pure and applied undergraduate texts 61 Includes bibliographical references and index Cover -- Title page -- Contents -- Preface -- Philosophy about learning and teaching -- Content of this book -- Style of this book -- Problem solving -- LaTeX -- Origins -- Further reading -- Acknowledgments -- Notations and Symbols -- Chapter 1. Evens, Odds, and Primes: A Taste of Number Theory -- 1.1. A first excursion into prime numbers -- 1.2. Even and odd integers -- 1.3. Calculating primes and the sieve of Eratosthenes -- 1.4. Division -- 1.5. Greatest common divisor -- 1.6. Statement of prime factorization -- 1.7*. Perfect numbers -- 1.8*. One of the Mersenne conjectures 1.9*. Twin primes: An excursion into the unknown -- 1.10*. Goldbach's conjecture -- 1.11. Hints and partial solutions for the exercises -- Chapter 2. Mathematical Induction -- 2.1. Mathematical induction -- 2.2. Rates of growth of functions -- 2.3. Sums of powers of the first positive integers -- 2.4. Strong mathematical induction -- 2.5. Fibonacci numbers -- 2.6. Recursive definitions -- 2.7. Arithmetic and algebraic equalities and inequalities -- 2.8. Hints and partial solutions for the exercises -- Chapter 3. Logic: Implications, Contrapositives, Contradictions, and Quantifiers 3.1. The need for rigor -- 3.2. Statements -- 3.3. Truth teller and liar riddle: Asking the right question -- 3.4*. Logic puzzles -- 3.5. Logical connectives -- 3.6. Implications -- 3.7. Contrapositive -- 3.8. Proof by contradiction -- 3.9. Pythagorean triples -- 3.10. Quantifiers -- 3.11. Hints and partial solutions for the exercises -- Chapter 4. The Euclidean Algorithm and Its Consequences -- 4.1. The Division Theorem -- 4.2. There are an infinite number of primes -- 4.3. The Euclidean algorithm -- 4.4. Consequences of the Division Theorem -- 4.5. Solving linear Diophantine equations bisacsh / MATHEMATICS / Logic Proof theory Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf General Mathematical logic and foundations Combinatorics Mathematics education Computer science Beweis (DE-588)4132532-1 s Mathematik (DE-588)4037944-9 s Zahlentheorie (DE-588)4067277-3 s DE-604 Erscheint auch als Druck-Ausgabe, Paperback 978-1-4704-7027-2 Pure and applied undergraduate texts 61 (DE-604)BV050063958 61 |
| spellingShingle | Chow, Bennett 1962- Introduction to proof through number theory bisacsh / MATHEMATICS / Logic Proof theory Number theory Zahlentheorie (DE-588)4067277-3 gnd Beweis (DE-588)4132532-1 gnd Mathematik (DE-588)4037944-9 gnd Pure and applied undergraduate texts |
| subject_GND | (DE-588)4067277-3 (DE-588)4132532-1 (DE-588)4037944-9 |
| title | Introduction to proof through number theory |
| title_auth | Introduction to proof through number theory |
| title_exact_search | Introduction to proof through number theory |
| title_full | Introduction to proof through number theory Bennett Chow |
| title_fullStr | Introduction to proof through number theory Bennett Chow |
| title_full_unstemmed | Introduction to proof through number theory Bennett Chow |
| title_short | Introduction to proof through number theory |
| title_sort | introduction to proof through number theory |
| topic | bisacsh / MATHEMATICS / Logic Proof theory Number theory Zahlentheorie (DE-588)4067277-3 gnd Beweis (DE-588)4132532-1 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | bisacsh / MATHEMATICS / Logic Proof theory Number theory Zahlentheorie Beweis Mathematik |
| volume_link | (DE-604)BV050063958 |
| work_keys_str_mv | AT chowbennett introductiontoproofthroughnumbertheory |