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[2] viXra:2512.0125 [pdf] submitted on 2025-12-26 14:05:21
Authors: Timothy W. Jones
Comments: 17 Pages.
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.
Category: Algebra
[1] viXra:2512.0058 [pdf] submitted on 2025-12-13 00:22:55
Authors: Long Yat Damian Lau
Comments: 23 Pages. (Note by viXra Admin: Please cite listed scientific references and submit article written with AI assistance to ai.viXra.org)
Often renowned as the greatest human invention in history, the laws of matrices have great contributions to calculus, linear transformations, computer algorithms, to name but a few. However, differ from research topics such as Non-Euclidean Geometry and Partial Differential Equations, the fractional indices of matrices have barely garnered our attention. In this study, we would investigate the properties of matrices, focusing on the nature of the square root of two by two matrices, some popular approaches, and most importantly reveal a set of new formulas that could typically solve all the given scenarios.
Category: Algebra
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