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Articles 1 - 7 of 7
Full-Text Articles in Other Mathematics
Strategies And Algorithms Of Sudoku, Callie Weaver
Strategies And Algorithms Of Sudoku, Callie Weaver
Mathematics Senior Capstone Papers
This paper discusses different strategies for the game of Sudoku and how those strategies relate to other problem solving techniques while also attempting to use those other techniques in a way that improves the strategies for Sudoku. This includes a thorough analysis of the general algorithm and an algorithm that is formed by the Occupancy Theorem and Preemptive Sets. This paper also compares these algorithms that directly relate to Sudoku with algorithms to similar combinatorial problems such as the Traveling Salesman problem and more. With the study of game theory becoming more popular, these strategies have also been shown to …
Folding Mathematics: A Mathematical Approach To Origami, Zachary Davis
Folding Mathematics: A Mathematical Approach To Origami, Zachary Davis
Mathematics Senior Capstone Papers
From constructing a midpoint on a line to observing specific divisions of a plane, the art form of Origami borrows many mathematical tools in order to create complex, and often symmetrical, patterns in a paper medium known as a fold. For this project, the traditional fold known as the Origami Crane/Swan will be thoroughly examined as it contains the unique property to lie completely flat when complete. This phenomenon occurs because the vertices holding the fold together are not all considered to be flat folds. The different types of vertices interacting with each other create a natural locking mechanism within …
Pisano Periods: A Comparison Study, Katherine Willrich
Pisano Periods: A Comparison Study, Katherine Willrich
Mathematics Senior Capstone Papers
The Pisano period, denoted π(n), is the period during which the Fibonacci sequence repeats after reducing the original sequence modulo n. More generally, one can similarly define Pisano periods for any linear recurrence sequence; in this paper we compare the Pisano periods of certain linear recurrence sequences with the Pisano periods of the Fibonacci sequence. We first construct recurrence sequences, defining the initial values as integers from 2 to 1000 and second values as 1. This paper discusses how the constructed sequences are related to the matrix M = [(first row) 1 1 (second row) 1 0] reduced modulo n. …
Mathematical Analysis Of The Duck Migration To Louisiana, Brandon Garcia
Mathematical Analysis Of The Duck Migration To Louisiana, Brandon Garcia
Mathematics Senior Capstone Papers
The purpose of this project is to research the relationship between duck migration and weather patterns, more specifically trying to determine if the rainfall and temperature in a given year affects the migration patterns of ducks. Duck hunters and conservation- ists alike have observed an overall decrease in the duck population in Louisiana over the past 70 years. Though some years have seen an increase, the population has not recovered to the level from the 1950s. These observations have led to many questions about what have happened to the ducks or where have the ducks gone. Using differ- ent forms …
The Riemann Curvature Tensor, Jennifer Cox
The Riemann Curvature Tensor, Jennifer Cox
Mathematics Senior Capstone Papers
A tensor is a mathematical object that has applications in areas including physics, psychology, and artificial intelligence. The Riemann curvature tensor is a tool used to describe the curvature of n-dimensional spaces such as Riemannian manifolds in the field of differential geometry. The Riemann tensor plays an important role in the theories of general relativity and gravity as well as the curvature of spacetime. This paper will provide an overview of tensors and tensor operations. In particular, properties of the Riemann tensor will be examined. Calculations of the Riemann tensor for several two and three dimensional surfaces such as that …
Personality & How Sound Affects Moods, Joe Pham
Personality & How Sound Affects Moods, Joe Pham
Mathematics Senior Capstone Papers
This research seeks to determine the personality and relationship between current moods of individuals at Louisiana Tech University by conducting a sound test of a can opening with a pre and post mood assessment, Brief Mood Introspection Scale (BMIS). The real question is “Can a sound test change mood?” Using one-way analysis of variance (ANOVA), the study is intended to examine the relationship between the pre and post (BMIS). The results indicate that there is a statistically significant relationship between both BMIS assessments. To determine if the data is significant, we must show the analysis of both BMIS and its …
Semiclassically Modeling Hydrogen At Rydberg States Immersed In Electromagnetic Fields, Jaron Williams
Semiclassically Modeling Hydrogen At Rydberg States Immersed In Electromagnetic Fields, Jaron Williams
Mathematics Senior Capstone Papers
Originally, closed-orbit theory was developed in order to analyze oscillations in the near ionization threshold (Rydberg) densities of states for atoms in strong external electric and magnetic fields. Oscillations in the density of states were ascribed to classical orbits that began and ended near the atom. In essence, observed outgoing waves following the classical path return and interfere with original outgoing waves, giving rise to oscillations. Elastic scattering from one closed orbit to another gives additional oscillations in the cross-section. This study examines how quantum theory can be properly used in combination with classical orbit theory in order to study …