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.