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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
An Absence Of Elephants In The Room: Religion, Philosophy, And Negative Numbers In Albert Girard’S A New Discovery In Algebra, Ethan Wilmes
An Absence Of Elephants In The Room: Religion, Philosophy, And Negative Numbers In Albert Girard’S A New Discovery In Algebra, Ethan Wilmes
Lawrence University Honors Projects
In early seventeenth-century Europe, the lines separating theology, science, and humanism were thin; what the modern reader understands as three distinct spheres of knowledge considerably overlapped with one another. Scientific discoveries and innovations coming from new technologies and foreign lands were laden with implications about theology and the human condition. While bland to all but the most fringe historians of mathematics today, the discovery of negative numbers led to a passionate and occasionally fierce epistemological debate throughout Europe. Falling outside of traditional mathematical knowledge, negative numbers found themselves in a sort of existential limbo; however useful they proved themselves to …
Constructing Surfaces With (1/(K-2)^2)(1,K-3) Singularities, Liam Patrick Keenan
Constructing Surfaces With (1/(K-2)^2)(1,K-3) Singularities, Liam Patrick Keenan
Lawrence University Honors Projects
We develop a procedure to construct complex algebraic surfaces which are stable, minimal, and of general type, possessing a T-singularity of the form (1/(k-2)2)(1,k-3).
Development Of Utility Theory And Utility Paradoxes, Timothy E. Dahlstrom
Development Of Utility Theory And Utility Paradoxes, Timothy E. Dahlstrom
Lawrence University Honors Projects
Since the pioneering work of von Neumann and Morgenstern in 1944 there have been many developments in Expected Utility theory. In order to explain decision making behavior economists have created increasingly broad and complex models of utility theory. This paper seeks to describe various utility models, how they model choices among ambiguous and lottery type situations, and how they respond to the Ellsberg and Allais paradoxes. This paper also attempts to communicate the historical development of utility models and provide a fresh perspective on the development of utility models.
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 …