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The Fundamental Theorem of Algebra (Paperback, Softcover reprint of the original 1st ed. 1997)
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The Fundamental Theorem of Algebra (Paperback, Softcover reprint of the original 1st ed. 1997)
Series: Undergraduate Texts in Mathematics
Expected to ship within 10 - 15 working days
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The fundamental theorem of algebra states that any complex
polynomial must have a complex root. This book examines three pairs
of proofs of the theorem from three different areas of mathematics:
abstract algebra, complex analysis and topology. The first proof in
each pair is fairly straightforward and depends only on what could
be considered elementary mathematics. However, each of these first
proofs leads to more general results from which the fundamental
theorem can be deduced as a direct consequence. These general
results constitute the second proof in each pair. To arrive at each
of the proofs, enough of the general theory of each relevant area
is developed to understand the proof. In addition to the proofs and
techniques themselves, many applications such as the insolvability
of the quintic and the transcendence of e and pi are presented.
Finally, a series of appendices give six additional proofs
including a version of Gauss'original first proof. The book is
intended for junior/senior level undergraduate mathematics students
or first year graduate students, and would make an ideal "capstone"
course in mathematics.
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