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A Logical Introduction to Proof
A Logical Introduction to Proof is a unique textbook that uses a logic-first approach to train and guide undergraduates through a transition or "bridge" course between calculus and advanced mathematics courses. The author's approach prepares the student for the rigors required in f...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York : Imprint: Springer,
2013.
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| Edición: | 1st ed. 2013. |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-1-4614-3631-7 | ||
| 003 | DE-He213 | ||
| 005 | 20220120002544.0 | ||
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| 008 | 120919s2013 xxu| s |||| 0|eng d | ||
| 020 | |a 9781461436317 |9 978-1-4614-3631-7 | ||
| 024 | 7 | |a 10.1007/978-1-4614-3631-7 |2 doi | |
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| 100 | 1 | |a Cunningham, Daniel W. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 2 | |a A Logical Introduction to Proof |h [electronic resource] / |c by Daniel W. Cunningham. |
| 250 | |a 1st ed. 2013. | ||
| 264 | 1 | |a New York, NY : |b Springer New York : |b Imprint: Springer, |c 2013. | |
| 300 | |a XVI, 356 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 505 | 0 | |a Preface -- The Greek Alphabet -- 1. Propositional Logic -- 2. Predicate Logic -- 3. Proof Strategies and Diagrams -- 4. Mathematical Induction -- 5. Set Theory -- 6. Functions -- 7. Relations -- 8. Core Concepts in Abstract Algebra -- 9. Core Concepts in Real Analysis -- A Summary of Strategies -- References -- List of Symbols. Index. | |
| 520 | |a A Logical Introduction to Proof is a unique textbook that uses a logic-first approach to train and guide undergraduates through a transition or "bridge" course between calculus and advanced mathematics courses. The author's approach prepares the student for the rigors required in future mathematics courses and is appropriate for majors in mathematics, computer science, engineering, as well as other applied mathematical sciences. It may also be beneficial as a supplement for students at the graduate level who need guidance or reference for writing proofs. Core topics covered are logic, sets, relations, functions, and induction, where logic is the instrument for analyzing the structure of mathematical assertions and is a tool for composing mathematical proofs. Exercises are given at the end of each section within a chapter. Chapter 1 focuses on propositional logic while Chapter 2 is devoted to the logic of quantifiers. Chapter 3 methodically presents the key strategies that are used in mathematical proofs; each presented as a proof diagram. Every proof strategy is carefully illustrated by a variety of mathematical theorems concerning the natural, rational, and real numbers. Chapter 4 focuses on mathematical induction and concludes with a proof of the fundamental theorem of arithmetic. Chapters 5 through 7 introduce students to the essential concepts that appear in all branches of mathematics. Chapter 8 introduces the basic structures of abstract algebra: groups, rings, quotient groups, and quotient rings. Finally, Chapter 9 presents proof strategies that explicitly show students how to deal with the fundamental definitions that they will encounter in real analysis, followed by numerous examples of proofs that use these strategies. The appendix provides a useful summary of strategies for dealing with proofs. | ||
| 650 | 0 | |a Mathematics. | |
| 650 | 0 | |a Mathematical logic. | |
| 650 | 1 | 4 | |a Mathematics. |
| 650 | 2 | 4 | |a Mathematical Logic and Foundations. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9781461436300 |
| 776 | 0 | 8 | |i Printed edition: |z 9781461436324 |
| 776 | 0 | 8 | |i Printed edition: |z 9781489990990 |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-1-4614-3631-7 |z Texto Completo |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||