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Theorems, Corollaries, Lemmas, and Methods of Proof
Richard J. Rossi,
Montana Tech, The Univ. of Montana
ISBN: 978-0-470-04295-3
©2006
318 pages
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Description
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The primary purpose of this text is to introduce math majors, who have completed a calculus sequence, to the axiomatic makeup of modern mathematics. Heavy emphasis is placed on the writing of clear and understandable proofs. Detailed algorithms are given for proving several different types of mathematical results including algorithms for forward direct proofs; proof by contrapositive; proof by contradiction; mathematical induction; existence proofs; uniqueness proofs; proofs of biconditional theorems; closure proofs; and proof by cases. Special pedagogy used in this book include detailed algorithms outlining each type of proof; many examples that show the scratch work phase leading to the proof; topic discussion that covers a wide range of core courses required in most undergraduate programs in mathematics; a large number of examples; and a large number of exercises.
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