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Course Description

On the night before he died in a duel at age twenty, Galois wrote down the outlines of what would later become a major field of mathematics – group theory. In this work he demonstrated why no general equation exists for solving the general degree 5 (quintic) polynomials while such solutions (the quadratic equation, for example) exist for all general polynomials of lesser degree. In this class we explore the quadratic equation’s long history. We learn of the secret development of solutions for degree three and four polynomials and their use in public mathematics competitions in the Renaissance. After a tour of the history of polynomial solutions, we turn then to develop the main points of what is today called Galois Theory. We will assume a familiarity with high school algebra. All other concepts will be covered in class. This is a mathematics class: full attendance is highly encouraged since concepts build from week to week. Lecture (plus Questions) Facilitated Discussion
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