Introductory Concepts for Abstract Mathematics

Beyond calculus, mathematics grows increasingly abstract and places new demands on those first entering that realm. Many students are ill prepared for more advanced work that requires the ability to understand and construct proofs. This text helps readers bridge that gap. It teaches them to work with abstract ideas and to develop a facility with definitions, theorems, and proofs. They learn logical principles, to justify arguments by adherence to those principles, and 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, both natural and real.

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.