Foundations of Higher Mathematics: Exploration and Proof

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9780201125870: Foundations of Higher Mathematics: Exploration and Proof

Foundations of Higher Mathematics: Exploration and Proof is the ideal text to bridge the crucial gap between the standard calculus sequence and upper division mathematics courses. The book takes a fresh approach to the subject: it asks students to explore mathematical principles on their own and challenges them to think like mathematicians. Two unique features–an exploration approach to mathematics and an intuitive and integrated presentation of logic based on predicate calculus–distinguish the book from the competition. Both features enable students to own the mathematics they're working on. As a result, your students develop a stronger motivation to tackle upper-level courses and gain a deeper understanding of concepts presented.

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This text is designed for students who need a transitional course to bridge the gap between the standard calculus sequence and a variety of upper division mathematics courses, where the ability to think like a mathematician is critical. It provides both technical details and broad outlines of proofs. It shows how to investigate a problem and develop ideas, as well as how to test those ideas, and, if appropriate, prove that they are correct.

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