Proofs and Fundamentals : A First Course in Abstract Mathematics / by Ethan D. Bloch.

Por:

Bloch, Ethan D [autor]

Colaborador(es):

SpringerLink (Servicio en línea)

Tipo de material: Texto

TextoSeries Undergraduate Texts in MathematicsEditor: New York, NY : Springer New York, 2011Descripción: xxvI, 358 páginas recurso en líneaTipo de contenido:

texto

Tipo de medio:

computadora

Tipo de portador:

recurso en línea

ISBN:

9781441971272

Formatos físicos adicionales: Edición impresa:: Sin títuloClasificación LoC:

QA8.9-10.3

Recursos en línea:

Conectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)

Contenidos:

Preface to the Second Edition -- Preface to the First Edition -- To the Student -- To the Instructor -- Part I. Proofs -- 1. Informal Logic -- 2. Strategies for Proofs -- Part II. Fundamentals -- 3. Sets -- 4. Functions -- 5. Relations -- 6. Finite and Infinite Sets -- Part III. Extras -- 7. Selected Topics -- 8. Explorations -- Appendix: Properties of Numbers -- Bibliography -- Index.

Resumen: This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between computational courses such as calculus and more theoretical courses such as linear algebra, abstract algebra, and real analysis. This second edition has been significantly enhanced, while maintaining the balance of topics and careful writing of the previous edition. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences, and suggests avenues for independent student explorations. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. Reviews of the first edition: This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a 'transition' course. —Zentralblatt Math 'Proofs and Fundamentals' has many strengths. One notable strength is its excellent organization... There are large exercise sets throughout the book... the exercises are well integrated with the text and vary appropriately from easy to hard... Perhaps the book’s greatest strength is the author’s zeal and skill for helping students write mathematics better. —MAA Online

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Springer eBooks

This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between computational courses such as calculus and more theoretical courses such as linear algebra, abstract algebra, and real analysis. This second edition has been significantly enhanced, while maintaining the balance of topics and careful writing of the previous edition. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences, and suggests avenues for independent student explorations. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. Reviews of the first edition: This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a 'transition' course. —Zentralblatt Math 'Proofs and Fundamentals' has many strengths. One notable strength is its excellent organization... There are large exercise sets throughout the book... the exercises are well integrated with the text and vary appropriately from easy to hard... Perhaps the book’s greatest strength is the author’s zeal and skill for helping students write mathematics better. —MAA Online

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