Read e-book online A Transition to Advanced Mathematics (7th Edition) PDF

By Douglas Smith, Maurice Eggen, Richard St. Andre

ISBN-10: 0495562025

ISBN-13: 9780495562023

A TRANSITION TO complex arithmetic is helping scholars make the transition from calculus to extra proofs-oriented mathematical research. the main profitable textual content of its sort, the seventh version keeps to supply an organization origin in significant ideas wanted for endured research and courses scholars to imagine and convey themselves mathematically--to study a scenario, extract pertinent evidence, and draw applicable conclusions. The authors position non-stop emphasis all through on enhancing students' skill to learn and write proofs, and on constructing their serious expertise for recognizing universal error in proofs. innovations are sincerely defined and supported with targeted examples, whereas plentiful and numerous routines supply thorough perform on either regimen and more difficult difficulties. scholars will come away with an effective instinct for the kinds of mathematical reasoning they'll have to observe in later classes and a greater knowing of ways mathematicians of all types strategy and remedy difficulties.

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Example text

Determine precisely the hypotheses (if any) and the antecedent and consequent. Replace (if necessary) the antecedent with a more usable equivalent. Replace (if necessary) the consequent by something equivalent and more readily shown. Beginning with the assumption of the antecedent, develop a chain of statements that leads to the consequent. Each statement in the chain must be deducible from its predecessors or other known results. As you write a proof, be sure it is not just a string of symbols.

Although Pythagoras is regularly given credit for the theorem named for him, the result was known to Babylonian and Indian mathematicians centuries earlier. , made his immortal contribution to mathematics with his famous text on geometry and number theory. His Elements sets forth a small number of axioms from which additional definitions and many familiar geometric results were developed in a rigorous way. Other geometries, based on different sets of axioms, did not begin to appear until the 1800s.

X) P (x) is read “there exists a unique x such that P(x)” and is true iff the truth set of P (x) has exactly one element. The symbol E! is called the unique existential quantifier. Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. 3 Quantifiers 25 Recall that for (E x) P (x) to be true it is unimportant how many elements are in the truth set of P(x), as long as there is at least one. x) P (x) to be true, the number of elements in the truth set of P(x) is crucial—there must be exactly one.

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A Transition to Advanced Mathematics (7th Edition) by Douglas Smith, Maurice Eggen, Richard St. Andre

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