Titlebook: Introduction to Mathematical Structures and Proofs; Larry J. Gerstein Textbook 2012Latest edition Springer Science+Business Media, LLC, pa

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Number Theory,ient Babylon, and still flourishing today; a subject filled with results that are beautiful and magical, and with haunting mysteries; a subject once viewed as the purest of pure mathematics—art for art’s sake—but that in recent years has been applied to problems associated with the transmission and

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Complex Numbers, understanding requires looking below the surface as well, and more generally seeing how the plant fits into the surrounding ecosystem. Similarly, to become a cardiologist one goes to medical school, not to “heart” school, because the heart functions not in isolation but as part of a larger system.

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Finite and Infinite Sets,ave given your friend at most . objects.) This will lay the foundation for the many practical counting procedures that we will develop here and in Chapter 5. In Section 4.5 we will use our work on functions and cardinality to initiate the study of languages and automata, fundamental topics in the theory of computation.

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Sets,y element of Varnish’s battle plan.” In each of these assertions something is said to be a member or element of some collection or set of things. As the examples suggest, sets are of wildly different sorts and, accordingly, “membership” can have a variety of meanings.

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Number Theory,encryption of numerical data. (Pure mathematics has become applied mathematics!) Number theory is unique in its abundance of appealing problems whose . are accessible to elementary school students, but whose . have eluded mathematicians for centuries.