A Logical Introduction to Proof

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9781461436300: A Logical Introduction to Proof

The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.

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From the Back Cover:

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.

Review:

From the reviews:

“Cunningham (Buffalo State, SUNY) focuses on the strategies for different proof techniques. ... The well-written text is consistent in its focus, which should help students. The book includes sufficient, appropriate exercises. ... contains ample notes to guide students through most of the exercises. Whether used for a course or as a reference for students learning proof techniques, this book is certainly worthy of consideration. Summing Up: Highly recommended. Lower-division undergraduates through graduate students.” (J. R. Burke, Choice, Vol. 51 (1), September, 2013)

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Daniel W. Cunningham
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Descripción Springer-Verlag New York Inc., 2012. HRD. Estado de conservación: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería IP-9781461436300

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Descripción Springer, 2012. Estado de conservación: New. Nº de ref. de la librería UA9781461436300

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Descripción Springer 2012-09-19, 2012. Hardcover. Estado de conservación: New. Nº de ref. de la librería NU-LBR-01118062

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Descripción Springer, 2012. Hardback. Estado de conservación: NEW. 9781461436300 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0304827

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Descripción Springer-Verlag New York Inc., United States, 2012. Hardback. Estado de conservación: New. 2013 ed.. Language: English . Brand New Book. The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs. Nº de ref. de la librería LIB9781461436300

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Descripción Springer-Verlag New York Inc., United States, 2012. Hardback. Estado de conservación: New. 2013 ed.. Language: English . Brand New Book. The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs. Nº de ref. de la librería LIB9781461436300

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Descripción Springer-Verlag New York Inc., 2012. HRD. Estado de conservación: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Nº de ref. de la librería IP-9781461436300

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Descripción Springer-Verlag Gmbh Sep 2012, 2012. Buch. Estado de conservación: Neu. Neuware - 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. 356 pp. Englisch. Nº de ref. de la librería 9781461436300

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Descripción Springer, 2017. Hardcover. Estado de conservación: New. Never used! This item is printed on demand. Nº de ref. de la librería 1461436303

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