The Practice of Mathematics
An Introduction to Proof Techniques and Number Systems
(First Edition)
©2021, 378 pages
Paperback list price: $144.95
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The Practice of Mathematics: An Introduction to Proof Techniques and Number Systems is designed to help students prepare for higher-level mathematics courses through an introduction to the methods and practices of logic and proof. The book uses the development of set theory and the number systems as a framework for the introduction of the various proof techniques.
As students study proof techniques, they learn about basic set theory, natural numbers, integers, rational numbers, and real numbers. Within each chapter, ideas critical to the number systems are expanded to motivate the study of more advanced topics. In this way, students are exposed to basic ideas and concepts in modern algebra, graph theory, combinatorics, real analysis, and topology.
Additionally, the text serves as an introduction to mathematics as a profession, covering mathematical disciplines, professional activities, and mathematical software. It includes a large variety of exercises that range from easy to difficult and serve to instill key concepts and provide students with opportunities for practical application.
Emphasizing the simultaneous development of proof techniques within the content of set theory and the number systems, The Practice of Mathematics is an exemplary resource for students pursuing an undergraduate degree in mathematics.
As students study proof techniques, they learn about basic set theory, natural numbers, integers, rational numbers, and real numbers. Within each chapter, ideas critical to the number systems are expanded to motivate the study of more advanced topics. In this way, students are exposed to basic ideas and concepts in modern algebra, graph theory, combinatorics, real analysis, and topology.
Additionally, the text serves as an introduction to mathematics as a profession, covering mathematical disciplines, professional activities, and mathematical software. It includes a large variety of exercises that range from easy to difficult and serve to instill key concepts and provide students with opportunities for practical application.
Emphasizing the simultaneous development of proof techniques within the content of set theory and the number systems, The Practice of Mathematics is an exemplary resource for students pursuing an undergraduate degree in mathematics.
Clifford Johnston is an associate professor of mathematics at West Chester University. He holds a Ph.D. and M.A. from Temple University, as well as a B.S.E. from Mansfield University of Pennsylvania. His professional research interests include PDEs, stochastic processes, and math on the web.
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Ebook 978-1-7935-2209-2 |
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"Clifford Johnson’s The Practice of Mathematics serves as an excellent introduction to mathematical proofs for college students. Presented in a user-friendly format with dedicated insights presented as main idea block, the text provides an easy-to-follow path for students to develop into strong mathematician. The inclusion of student insights throughout the text provides new readers with many useful points of view, giving alternate approaches to concepts. The beginning of the text provides first examples of proofs with the two-column method giving the students a nice visual of how proofs develop as they begin their own journey into mathematical proofs."
Dr. Alexander J. Furia, Assistant Professor of Mathematics, Chestnut Hill College
Dr. Alexander J. Furia, Assistant Professor of Mathematics, Chestnut Hill College
