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Why Prove it Again? - Alternative Proofs in Mathematical Practice (Paperback, Softcover reprint of the original 1st ed. 2015)
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Why Prove it Again? - Alternative Proofs in Mathematical Practice (Paperback, Softcover reprint of the original 1st ed. 2015)
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This monograph considers several well-known mathematical theorems
and asks the question, "Why prove it again?" while examining
alternative proofs. It explores the different rationales
mathematicians may have for pursuing and presenting new proofs of
previously established results, as well as how they judge whether
two proofs of a given result are different. While a number of books
have examined alternative proofs of individual theorems, this is
the first that presents comparative case studies of other methods
for a variety of different theorems. The author begins by laying
out the criteria for distinguishing among proofs and enumerates
reasons why new proofs have, for so long, played a prominent role
in mathematical practice. He then outlines various purposes that
alternative proofs may serve. Each chapter that follows provides a
detailed case study of alternative proofs for particular theorems,
including the Pythagorean Theorem, the Fundamental Theorem of
Arithmetic, Desargues' Theorem, the Prime Number Theorem, and the
proof of the irreducibility of cyclotomic polynomials. Why Prove It
Again? will appeal to a broad range of readers, including
historians and philosophers of mathematics, students, and
practicing mathematicians. Additionally, teachers will find it to
be a useful source of alternative methods of presenting material to
their students.
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