INTRODUCTION TO MATHEMATICAL PROOFS A TRANSITION

• Main Author: Roberts, Charles E. 1942 (Author)
• Format: Book
• Language: English
• Published: Boca Raton CRC Press 2010
• Series: Textbooks in mathematics (Boca Raton, Fla.)
• Subjects: Proof theory > Textbooks; Logic, Symbolic and mathematical > Textbooks
• Online Access: Click Here to View Status and Holdings.
• Item Description: "A Chapman & Hall book."
• Physical Description: viii, 425 pages illustrations 25 cm
• Bibliography: Includes bibliographical references and index
• ISBN: 9781420069556; 1420069551

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.