As an offshoot of an undergraduate foundations course the author has taught for years at Trinity College, this text aims to bridge the gap between basic calculus studies and abstract algebra and real analysis. Seven sections cover logic and proof, naive set theory, functions and relations, algebraic and order properties of number systems, transfinite cardinal numbers, and axiom of choice and ordinal numbers. Parenthetical comments are interspersed to help students connect concepts. Concludes with a reading list, and hints/ solutions to selected exercises. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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.
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