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The Foundations of Mathematics, 1st Edition
Thomas Q. Sibley
ISBN: 978-0-470-08501-1
©2009
392 pages
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Hallmark Features
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- Introduces concepts before asking students to use them in proofs so students can separate the learning of concepts from their use in proofs, leading to greater success in both.
- Builds on students' understanding of functions in general before introducing relations.
- Over 3/4 of the sections have true/false reading comprehension questions to allow students to discover if they missed an important distinction in a concept.
- Contains many false and questionable proofs to critique for practice in critically reading proofs and recognizing common errors.
- Students are asked to make conjectures when a concept is introduced in order to better understand the concepts and the need for proofs and counter-examples.
- Discusses advanced techniques of proof and an optional section carefully presents the axiom of choice and its equivalents.
- Discusses the difference between formal and everyday use of terms and the idea of mathematical definitions to make the distinction between how mathematicians use terms and how these terms are used in everyday language.
- Introduces metamathematics and the philosophy of mathematics.
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