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The Kronecker-Weber Theorem: An Exposition, Amber Verser
The Kronecker-Weber Theorem: An Exposition, Amber Verser
Lawrence University Honors Projects
This paper is an investigation of the mathematics necessary to understand the Kronecker-Weber Theorem. Following an article by Greenberg, published in The American Mathematical Monthly in 1974, the presented proof does not use class field theory, as the most traditional treatments of the theorem do, but rather returns to more basic mathematics, like the original proofs of the theorem. This paper seeks to present the necessary mathematical background to understand the proof for a reader with a solid undergraduate background in abstract algebra. Its goal is to make what is usually an advanced topic in the study of algebraic number …
Iterative Statistical Verification Of Probabilistic Plans, Colin M. Potts
Iterative Statistical Verification Of Probabilistic Plans, Colin M. Potts
Lawrence University Honors Projects
Artificial intelligence seeks to create intelligent agents. An agent can be anything: an autopilot, a self-driving car, a robot, a person, or even an anti-virus system. While the current state-of-the-art may not achieve intelligence (a rather dubious thing to quantify) it certainly achieves a sense of autonomy. A key aspect of an autonomous system is its ability to maintain and guarantee safety—defined as avoiding some set of undesired outcomes. The piece of software responsible for this is called a planner, which is essentially an automated problem solver. An advantage computer planners have over humans is their ability to consider and …