Mathematical Thinking: Problem Solving and Proofs

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9780132633932: Mathematical Thinking: Problem Solving and Proofs

This survey of both discrete and continuous mathematics focuses on the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics, rather than on rote symbolic manipulation. Coverage begins with the fundamentals of mathematical language and proof techniques (such as induction); then applies them to easily-understood questions in elementary number theory and counting; then develops additional techniques of proofs via fundamental topics in discrete and continuous mathematics. Topics are addressed in the context of familiar objects; easily-understood, engaging examples; and over 700 stimulating exercises and problems, ranging from simple applications to subtle problems requiring ingenuity.

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Developing logical thinking and fundamental mathematical ideas, and using problems that pique students' mathematical curiosity, this work aims to prepare readers for all upper-division mathematics courses and improve their skills in presenting coherent arguments.

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