Reading, Writing, and Proving [recurso electrónico] : A Closer Look at Mathematics / by Ulrich Daepp, Pamela Gorkin.

Por: Daepp, Ulrich [author.]Colaborador(es): Gorkin, Pamela [author.] | SpringerLink (Online service)Tipo de material: TextoTextoSeries Undergraduate Texts in MathematicsEditor: New York, NY : Springer New York, 2011Descripción: XIV, 378 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9781441994790Tema(s): Mathematics | Global analysis (Mathematics) | Logic, Symbolic and mathematical | Number theory | Mathematics | Mathematical Logic and Foundations | Analysis | Number TheoryFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 511.3 Clasificación LoC:QA8.9-10.3Recursos en línea: Libro electrónicoTexto
Contenidos:
-Preface. -1. The How, When, and Why of Mathematics -- 2. Logically Speaking -- 3.Introducing the Contrapositive and Converse -- 4. Set Notation and Quantifiers -- 5. Proof Techniques -- 6. Sets -- 7. Operations on Sets -- 8. More on Operations on Sets -- 9. The Power Set and the Cartesian Product -- 10. Relations -- 11. Partitions -- 12. Order in the Reals -- 13. Consequences of the Completeness of (\Bbb R) -- 14. Functions, Domain, and Range.- 15. Functions, One-to-One, and Onto -- 16. Inverses -- 17. Images and Inverse Images -- 18. Mathematical Induction -- 19. Sequences -- 20. Convergence of Sequences of Real Numbers -- 21. Equivalent Sets -- 22. Finite Sets and an Infinite Set -- 23. Countable and Uncountable Sets -- 24. The Cantor-Schröder-Bernstein Theorem -- 25. Metric Spaces -- 26. Getting to Know Open and Closed Sets -- 27. Modular Arithmetic -- 28. Fermat’s Little Theorem -- 29. Projects -- Appendix -- References -- Index.
En: Springer eBooksResumen: Reading, Writing, and Proving is designed to guide mathematics students during their transition from algorithm-based courses such as calculus, to theorem and proof-based courses. This text not only introduces the various proof techniques and other foundational principles of higher mathematics in great detail, but also assists and inspires students to develop the necessary abilities to read, write, and prove using mathematical definitions, examples, and theorems that are required for success in navigating advanced mathematics courses. In addition to an introduction to mathematical logic, set theory, and the various methods of proof, this textbook prepares students for future courses by providing a strong foundation in the fields of number theory, abstract algebra, and analysis. Also included are a wide variety of examples and exercises as well as a rich selection of unique projects that provide students with an opportunity to investigate a topic independently or as part of a collaborative effort. New features of the Second Edition include the addition of formal statements of definitions at the end of each chapter; a new chapter featuring the Cantor–Schröder–Bernstein theorem with a spotlight on the continuum hypothesis; over 200 new problems; two new student projects; and more. An electronic solutions manual to selected problems is available online.  From the reviews of the First Edition: “The book…emphasizes Pòlya’s four-part framework for problem solving (from his book How to Solve It)…[it] contains more than enough material for a one-semester course, and is designed to give the instructor wide leeway in choosing topics to emphasize…This book has a rich selection of problems for the student to ponder, in addition to "exercises" that come with hints or complete solutions…I was charmed by this book and found it quite enticing.” – Marcia G. Fung for MAA Reviews “… A book worthy of serious consideration for courses whose goal is to prepare students for upper-division mathematics courses. Summing Up: Highly recommended.” – J. R. Burke, Gonzaga University for CHOICE Reviews
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Existencias
Tipo de ítem Biblioteca actual Colección Signatura Copia número Estado Fecha de vencimiento Código de barras
Libro Electrónico Biblioteca Electrónica
Colección de Libros Electrónicos QA8.9 -10.3 (Browse shelf(Abre debajo)) 1 No para préstamo 372236-2001

-Preface. -1. The How, When, and Why of Mathematics -- 2. Logically Speaking -- 3.Introducing the Contrapositive and Converse -- 4. Set Notation and Quantifiers -- 5. Proof Techniques -- 6. Sets -- 7. Operations on Sets -- 8. More on Operations on Sets -- 9. The Power Set and the Cartesian Product -- 10. Relations -- 11. Partitions -- 12. Order in the Reals -- 13. Consequences of the Completeness of (\Bbb R) -- 14. Functions, Domain, and Range.- 15. Functions, One-to-One, and Onto -- 16. Inverses -- 17. Images and Inverse Images -- 18. Mathematical Induction -- 19. Sequences -- 20. Convergence of Sequences of Real Numbers -- 21. Equivalent Sets -- 22. Finite Sets and an Infinite Set -- 23. Countable and Uncountable Sets -- 24. The Cantor-Schröder-Bernstein Theorem -- 25. Metric Spaces -- 26. Getting to Know Open and Closed Sets -- 27. Modular Arithmetic -- 28. Fermat’s Little Theorem -- 29. Projects -- Appendix -- References -- Index.

Reading, Writing, and Proving is designed to guide mathematics students during their transition from algorithm-based courses such as calculus, to theorem and proof-based courses. This text not only introduces the various proof techniques and other foundational principles of higher mathematics in great detail, but also assists and inspires students to develop the necessary abilities to read, write, and prove using mathematical definitions, examples, and theorems that are required for success in navigating advanced mathematics courses. In addition to an introduction to mathematical logic, set theory, and the various methods of proof, this textbook prepares students for future courses by providing a strong foundation in the fields of number theory, abstract algebra, and analysis. Also included are a wide variety of examples and exercises as well as a rich selection of unique projects that provide students with an opportunity to investigate a topic independently or as part of a collaborative effort. New features of the Second Edition include the addition of formal statements of definitions at the end of each chapter; a new chapter featuring the Cantor–Schröder–Bernstein theorem with a spotlight on the continuum hypothesis; over 200 new problems; two new student projects; and more. An electronic solutions manual to selected problems is available online.  From the reviews of the First Edition: “The book…emphasizes Pòlya’s four-part framework for problem solving (from his book How to Solve It)…[it] contains more than enough material for a one-semester course, and is designed to give the instructor wide leeway in choosing topics to emphasize…This book has a rich selection of problems for the student to ponder, in addition to "exercises" that come with hints or complete solutions…I was charmed by this book and found it quite enticing.” – Marcia G. Fung for MAA Reviews “… A book worthy of serious consideration for courses whose goal is to prepare students for upper-division mathematics courses. Summing Up: Highly recommended.” – J. R. Burke, Gonzaga University for CHOICE Reviews

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