# Introduction to Mathematical Proofs: A Transition

CRC Press, Jun 24, 2009 - Mathematics - 433 pages

Shows How to Read & Write Mathematical Proofs
Ideal Foundation for More Advanced Mathematics Courses

Introduction to Mathematical Proofs: A Transition facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize theorem proving. It helps students develop the skills necessary to write clear, correct, and concise proofs.

Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs.

Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It will prepare them to succeed in more advanced mathematics courses, such as abstract algebra and geometry.

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### Contents

 Logic 1 Deductive Mathematical Systems and Proofs 69 Set Theory 125 Relations 175 Functions 219 Mathematical Induction 261 Cardinalities of Sets 275
 Proofs from Real Analysis 297 Proofs from Group Theory 325 Reading and Writing Mathematical Proofs 349 Answers to Selected Exercises 357 References 415 Index 417 Copyright