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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978-1-4419-1948-9E.B. Burger and R. Tubbs 2004

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,0.1100010000000000000000010000…,mber is defined not by what it . but rather by what it is .. What will become apparent as we develop the classical theory of transcendental numbers is that every demonstration of the transcendence of a particular number is indirect—a number is shown to be transcendental by showing that it is not algebraic.

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,2.7182818284590452353602874713…,rough this chapter sets the stage for much of what follows in our future explorations. To foreshadow the fundamental strategies to come, we open with Joseph Fourier’s 1815 clever proof of Euler’s result that . is irrational.

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,,wer series. Specifically, we consider transcendence issues within the setting of function fields in a single variable over a finite field. While this theory has important implications in many different areas of mathematics, our goal here is to discover an object in this context that is analogous to the all-important exponential function ...

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,0.1100010000000000000000010000…,mber is defined not by what it . but rather by what it is .. What will become apparent as we develop the classical theory of transcendental numbers is that every demonstration of the transcendence of a particular number is indirect—a number is shown to be transcendental by showing that it is not alg

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