Titlebook: Making Transcendence Transparent; An intuitive approac Edward B. Burger,Robert Tubbs Textbook 2004 E.B. Burger and R. Tubbs 2004 complex an

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Textbook 2004is focus is threefold. Firstly, this body of work requires only the mathematical techniques and tools familiar to advanced undergraduate mathematics students, and thus this area can be appreciated by a wide range of readers. Secondly, the ideas behind modem transcendence results are almost always an

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s and tools familiar to advanced undergraduate mathematics students, and thus this area can be appreciated by a wide range of readers. Secondly, the ideas behind modem transcendence results are almost always an978-1-4419-1948-9978-1-4757-4114-8

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he authors inject a bit of literary flair in their expositioThe Journey Ahead At the heart of transcendental number theory lies an intriguing paradox: While essen- tially all numbers are transcendental, establishing the transcendence of a particular number is a monumental task. Thus transcendental n

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,1.4142135623730950488016887242…,und, but, more importantly, attempt to provide a framework within which the theory of transcendence will find its rightful place in our quest for an understanding of the intrinsic properties of numbers.

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,4.1132503787829275171735818151…,In this chapter we consider numbers of the form ea, where .. is . nonzero algebraic number. As we indicated to at the close of the previous chapter, here we will prove the following result due to Charles Hermite and Ferdinand Lindemann.

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