Bridge to Abstract Mathematics: Mathematical Proof and Structures

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BRIDGE TO ABSTRACT MATHEMATICS Mathematical Proof and Structures ...

The Random House/Birkhaoser Mathematics Series: INVITATION TO COMPLEX ANALYSIS by R. P. Boas BRIDGE TO ABSTRACT MATHEMATICS: MAT ...

BRIDGE TO ABSTRACT MATHEMATICS Mathematical Proof and Structures Ronald E Morash University of Michigan, Dearborn The Random Hou ...

First Edition Copyright @ 1987 by Random House, Inc. All rights reserved under International and Pan-American Copyright Conventi ...

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Preface This text is directed toward the sophomore through senior levels of uni- versity mathematics, with a tilt toward the for ...

PREFACE vll IMPORTANT FEATURES Readability. The author's primary pedagogical goal in writing the text was to produce a book that ...

viii PREFACE countably infinite collections of sets. The main emphasis here is on stan- dard approaches to proving set inclusion ...

PREFACE ix among colleges and universities where such courses exist, the subject matter varies considerably. For this reason, an ...

1 x PREFACE We began the project with an extensive survey of opinions about the teaching of mathematical proof writing, and we w ...

PREFACE xi Colleagues and students at the University of Michigan, Dearborn, de- serve thanks for important suggestions and feedb ...

Contents BOOK ONE The Foundation: Sets, Logic, SETS and Mathematical Argument Basic Definitions and Notation Operations on Sets ...

CONTENTS xiii Proof by Specialization and Division into Cases 170 Proof by Mathematical Induction 178 METHODS OF MATHEMATICAL PR ...

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BRIDGE TO ABSTRACT MATHEMATICS Mathematical Proof and Structures ...

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BOOK -- -- ONE The Foundation: Sets, Logic, and SETS and Mathematical Argument ...