## ABSTRACT

Beyond calculus, the world of mathematics grows increasingly abstract and places new and challenging demands on those venturing into that realm. As the focus of calculus instruction has become increasingly computational, it leaves many students ill prepared for more advanced work that requires the ability to understand and construct proofs.

Introductory Concepts for Abstract Mathematics helps readers bridge that gap. It teaches them to work with abstract ideas and develop a facility with definitions, theorems, and proofs. They learn logical principles, and to justify arguments not by what seems right, but by strict adherence to principles of logic and proven mathematical assertions - and they learn to write clearly in the language of mathematics

The author achieves these goals through a methodical treatment of set theory, relations and functions, and number systems, from the natural to the real. He introduces topics not usually addressed at this level, including the remarkable concepts of infinite sets and transfinite cardinal numbers

Introductory Concepts for Abstract Mathematics takes readers into the world beyond calculus and ensures their voyage to that world is successful. It imparts a feeling for the beauty of mathematics and its internal harmony, and inspires an eagerness and increased enthusiasm for moving forward in the study of mathematics.

## TABLE OF CONTENTS

part |2 pages

SECTION I LOGIC AND PROOF

part |2 pages

SECTION II: SETS

part |2 pages

SECTION III: FUNCTIONS AND RELATIONS

part |2 pages

SECTION IV: ALGEBRAIC AND ORDER PROPERTIES OF NUMBER SYSTEMS

part |2 pages

SECTION V: TRANSFINITE CARDINAL NUMBERS

part |2 pages

SECTION VI: AXIOM OF CHOICE AND