Designed for students preparing to engage in their first struggles to understand mathematics independently, this book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition, and how to discover the outline of a proof in the form of the theorem. It is intended to be used interactively, frequently asking the reader to pause and work on an example or a problem before continuing, and encouraging the student to learn from failed attempts at solving problems.
Reihe
Auflage
1st ed. 1996. Corr. 3rd printing 1999
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Lower undergraduate
Editions-Typ
Illustrationen
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 13 mm
Gewicht
ISBN-13
978-0-387-94617-7 (9780387946177)
DOI
10.1007/978-1-4612-3998-7
Schweitzer Klassifikation
1 Examples.- 1.1 Propaganda.- 1.2 Basic Examples for Definitions.- 1.3 Basic Examples for Theorems.- 1.4 Extended Examples.- 1.5 Notational Interlude.- 1.6 Examples Again: Standard Sources.- 1.7 Non-examples for Definitions.- 1.8 Non-examples for Theorems.- 1.9 Summary and More Propaganda.- 1.10 What Next?.- 2 Informal Language and Proof.- 2.1 Ordinary Language Clues.- 2.2 Real-Life Proofs vs. Rules of Thumb.- 2.3 Proof Forms for Implication.- 2.4 Two More Proof Forms.- 2.5 The Other Shoe, and Propaganda.- 3 For mal Language and Proof.- 3.1 Propaganda.- 3.2 Formal Language: Basics.- 3.3 Quantifiers.- 3.4 Finding Proofs from Structure.- 3.5 Summary, Propaganda, and What Next?.- 4 Laboratories.- 4.1 Lab I: Sets by Example.- 4.2 Lab II: Functions by Example.- 4.3 Lab III: Sets and Proof.- 4.4 Lab IV: Functions and Proof.- 4.5 Lab V: Function of Sets.- 4.6 Lab VI: Families of Sets.- A Theoretical Apologia.- B Hints.- References.
