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history-page35 - In 1830 George Peacock tried to...

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In 1830, George Peacock tried to systematize the study of algebra (like Euclid did for ge- ometry). He had a Principle of Permanence of Form that was analogous to the geometric Principle of Continuity. Boyer: “The beginnings of postulational thinking in arithmetic and algebra”. Abel and Galois laid the groundwork for these abstract structures but didn’t explicitly dis- cuss the structures themselves. Van der Waerden’s Modern Algebra in 1930 really solidified the field. Separate British/American and Continental European threads. Groups Definition: A group is a set G with a binary operation : G × G G such that: is associative: a (b c) = (a b) c for every a, b, c G . there is an identity e G such that e g = g e = e for every g G . Every g G has an inverse g 1 G with the property that g g 1 = g 1 g = e . Motivation: Solvability of Equations, Classical Geometric Constructions problems.
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