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Algebra |
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Authors: Timothy W. Jones
We give some central ideas of abstract algebra in a motivated manner starting with the construction of the integers with straight edge and compass, extrapolating axioms for these integers, finding a finite version of integers that obey these same axioms, and comparing this result with a permutation group via a Cayley table constructed using a TI84 program. Along the way we show how Lagrange, Euler, and Fermat theorems can be motivated and proven as natural results of the development. The need for and the essence of abstraction in mathematics we hope emerges.
Comments: 17 Pages.
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[v1] 2025-12-26 14:05:21
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