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基本説明
Explains what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples exercises.
Full Description
This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course. This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers are provided, enabling students to practice on their own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments.
Contents
List of Symbols; Preface; Introduction and Basic Terminology; General Suggestions; Some Basic Techniques Used in Proving a Theorem of the Form "If A, then B"; Special Types of Theorems; Review Exercises; Exercises Without Solutions; Collection of "Proofs"; Solutions for the Exercises at the End of the Sections and the Review Exercises; Other Books on the Subject of Proofs and Mathematical Writing; Index
