Introductory Concepts for Abstract Mathematics
Introductory Concepts for Abstract Mathematics by Kenneth E. Hummel, published by CRC Press on March 23, 2000, is a comprehensive resource designed to assist students transitioning from calculus to more abstract areas of mathematics. This 344-page book addresses the challenges faced by learners who may struggle with the demands of understanding and constructing proofs, emphasizing the importance of logical reasoning and clarity in mathematical writing.
Readers will find a methodical exploration of essential topics such as set theory, relations, functions, and number systems, including natural and real numbers. The book also introduces advanced concepts like infinite sets and transfinite cardinal numbers, which are often overlooked at this level. By focusing on these foundational elements, Introductory Concepts for Abstract Mathematics aims to cultivate a deeper appreciation for the beauty and coherence of mathematics, encouraging students to engage more fully with their mathematical studies.
Official synopsis Publisher
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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