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Nov 22, 2024
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MAT 5630 - Intro Field Theory & Classical Probs Ant
credits: 3.0
From the time of ancient Greece through the nineteenth century, two particular mathematical questions drove the creation of large amounts of mathematics. One of these questions was “which numbers are constructible?” That is, using only a compass and a straight edge, can we square a circle, double a cube or trisect an angle? The other question involved solving polynomial equations. It asked for which types of polynomials can we invent a formula similar to the quadratic formula that allows us to find their zeroes? The mathematics used to answer these questions will be traced historically, culminating in the development of field theory and the notion of field extensions in which we find our answers.
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