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Physical Sciences and Mathematics Commons™
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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
“Product Development: Model Rockets As Toys”, Kelly W. Remijan
“Product Development: Model Rockets As Toys”, Kelly W. Remijan
Teacher Resources
No abstract provided.
"American Football: Field Goals And Quadratic Functions”, Kelly W. Remijan
"American Football: Field Goals And Quadratic Functions”, Kelly W. Remijan
Teacher Resources
No abstract provided.
"Crash Reconstruction: Stopping Distance”, Kelly W. Remijan
"Crash Reconstruction: Stopping Distance”, Kelly W. Remijan
Teacher Resources
No abstract provided.
An Analysis And Comparison Of Knot Polynomials, Hannah Steinhauer
An Analysis And Comparison Of Knot Polynomials, Hannah Steinhauer
Senior Honors Projects, 2020-current
Knot polynomials are polynomial equations that are assigned to knot projections based on the mathematical properties of the knots. They are also invariants, or properties of knots that do not change under ambient isotopy. In other words, given an invariant α for a knot K, α is the same for any projection of K. We will define these knot polynomials and explain the processes by which one finds them for a given knot projection. We will also compare the relative usefulness of these polynomials.
Curving Towards Bézout: An Examination Of Plane Curves And Their Intersection, Camron Alexander Robey Cohen
Curving Towards Bézout: An Examination Of Plane Curves And Their Intersection, Camron Alexander Robey Cohen
Honors Papers
One area of interest in studying plane curves is intersection. Namely, given two plane curves, we are interested in understanding how they intersect. In this paper, we will build the machinery necessary to describe this intersection. Our discussion will include developing algebraic tools, describing how two curves intersect at a given point, and accounting for points at infinity by way of projective space. With all these tools, we will prove Bézout’s theorem, a robust description of the intersection between two curves relating the degrees of the defining polynomials to the number of points in the intersection.
Gröbner Bases And Systems Of Polynomial Equations, Rachel Holmes
Gröbner Bases And Systems Of Polynomial Equations, Rachel Holmes
All Graduate Theses, Dissertations, and Other Capstone Projects
This paper will explore the use and construction of Gröbner bases through Buchberger's algorithm. Specifically, applications of such bases for solving systems of polynomial equations will be discussed. Furthermore, we relate many concepts in commutative algebra to ideas in computational algebraic geometry.