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Articles 1 - 19 of 19
Full-Text Articles in Physical Sciences and Mathematics
The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, Jeffrey Brown
The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, Jeffrey Brown
Honors Theses
The Creation of a Video Review Guide for the Free-Response Section of the Advanced Placement Calculus Exam follows the creation of a resource to help students prepare for the College Board’s Advanced Placement Calculus Exam. This project originated out of the authors personal experiences in preparing for this exam. The goal of the project was to create an accessible resource that reviews content, provides insights into the Advanced Placement exam, and creates successful habits in student responses. This paper, chronologically, details the development of the resource and a reflection on the final product and future uses.
Common Core In Tennessee: An Analysis Of Eighth Grade Mathematics Standards, Hayley Little
Common Core In Tennessee: An Analysis Of Eighth Grade Mathematics Standards, Hayley Little
Honors Theses
Since their introduction in 2010, the Common Core State Standards (CCSS) have been a highly controversial topic in educational reform. Though the standards are not a product of the federal government and are not federally mandated, they do represent a push towards national academic standards in America. For states such as Tennessee, educational policies of the past pushed them to lower their academic standards in order to create the illusion of success. Those states are now some of the places that have seen the most change with the adoption of the CCSS. It still remains somewhat unclear, however, which changes …
Primality Proving Based On Eisenstein Integers, Miaoqing Jia
Primality Proving Based On Eisenstein Integers, Miaoqing Jia
Honors Theses
According to the Berrizbeitia theorem, a highly efficient method for certifying the primality of an integer N ≡ 1 (mod 3) can be created based on pseudocubes in the ordinary integers Z. In 2010, Williams and Wooding moved this method into the Eisenstein integers Z[ω] and defined a new term, Eisenstein pseudocubes. By using a precomputed table of Eisenstein pseudocubes, they created a new algorithm in this context to prove primality of integers N ≡ 1 (mod 3) in a shorter period of time. We will look at the Eisenstein pseudocubes and analyze how this new algorithm works with the …
Reading Between The Lines: Verifying Mathematical Language, Tristan Johnson
Reading Between The Lines: Verifying Mathematical Language, Tristan Johnson
Honors Theses
A great deal of work has been done on automatically generating automated proofs of formal statements. However, these systems tend to focus on logic-oriented statements and tactics as well as generating proofs in formal language. This project examines proofs written in natural language under a more general scope of mathematics. Furthermore, rather than attempting to generate natural language proofs for the purpose of solving problems, we automatically verify human-written proofs in natural language. To accomplish this, elements of discourse parsing, semantic interpretation, and application of an automated theorem prover are implemented.
Noether's Theorem: Symmetry And Conservation, Tristan Johnson
Noether's Theorem: Symmetry And Conservation, Tristan Johnson
Honors Theses
A common calculus problem is to find an input that optimizes (maximizes or minimizes) a function. An extension of this problem is to find a function that optimizes an expression depending on the function. This paper studies how small (differentiable) variations of functions give us more information about expressions dependent on these functions. Specifically, Noether’s Theorem states that in a system of functions, each differential symmetry – or small variation where the system is invariant– constructs a conserved quantity. We will describe, interpret and prove Noether’s Theorem using techniques from linear algebra, differential geometry, and the calculus of variations. Furthermore, …
General Relativity And Differential Geometry, Harry Hausner
Resonance Varieties Of Pure Braid-Like Groups, Jared Able
Resonance Varieties Of Pure Braid-Like Groups, Jared Able
Honors Theses
No abstract provided.
The Simple Zeros Of The Riemann Zeta-Function, Melissa N. Miller
The Simple Zeros Of The Riemann Zeta-Function, Melissa N. Miller
Honors Theses
There have been many tables of primes produced since antiquity. In 348 BC Plato studied the divisors of the number 5040. In 1202 Fibonacci gave an example with a list of prime numbers up to 100. By the 1770's a table of number factorizations up to two million was constructed. In 1859 Riemann demonstrated that the key to the deeper understanding of the distribution of prime numbers lies in the study of a certain complex-valued function, called the zeta-function. In 1973 Montgomery used explicit formulas to study the pair correlation of the zeros of the zeta-function and their relationship to …
Present Value Calculations In Personal Injury, Nicholas J. Klinka
Present Value Calculations In Personal Injury, Nicholas J. Klinka
Honors Theses
No abstract provided.
Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent
Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent
Honors Theses
The present paper builds on the idea of composing music via fractals, specifically the Sierpiński Triangle and the Sierpiński Pedal Triangle. The resulting methods are intended to produce not just a series of random notes, but a series that we think pleases the ear. One method utilizes the iterative process of generating the Sierpiński Triangle and Sierpiński Pedal Triangle via matrix operations by applying this process to a geometric configuration of note names. This technique designs the largest components of the musical work first, then creates subsequent layers where each layer adds more detail.
A Fractional Boundary Value Problem, Grant Yost
A Fractional Boundary Value Problem, Grant Yost
Honors Theses
We consider a fractional boundary value problem with various boundary conditions. This boundary value problem has two components, one fractional derivative of alpha degree with alpha between n-1 and n, and a fractional derivative of beta degree with beta between 0 and n-2. We prove existence and uniqueness of solutions, and show some examples that were found using a MATLAB simulation.
Domain Representability And Topological Completeness, Matthew D. Devilbiss
Domain Representability And Topological Completeness, Matthew D. Devilbiss
Honors Theses
Topological completeness properties seek to generalize the definition of complete metric space to the context of topologies. Chapter 1 gives an overview of some of these properties. Chapter 2 introduces domain theory, a field originally intended for use in theoretical computer science. Finally, Chapter 3 examines how this computer-scientific notion can be employed in the study of topological completeness in the form of domain representability. The connections between domain representability and other topological completeness properties are subsequently examined.
Superstable Semigroups, Stephanie Olsen
Perfect Matchings And Their Applications, Amanda Mayhall
Perfect Matchings And Their Applications, Amanda Mayhall
Honors Theses
No abstract provided.
Tablet Usage In Secondary Mathematics Education And Recommendations For Improving Its Effectiveness In The Classroom, Meghan T. Dwyer
Tablet Usage In Secondary Mathematics Education And Recommendations For Improving Its Effectiveness In The Classroom, Meghan T. Dwyer
Honors Theses
As part of my honor's thesis project at Assumption College, I have been researching the ways that teachers are currently using tablets in their secondary mathematics classrooms. My thesis compares the benefits and drawbacks of having tablets in classrooms, tablets for every student, or no tablets at all. In the spring, I collected survey feedback from mathematics teachers in four different local school districts. I analyzed the data in order to determine the ways tablets are being used in classrooms, the reasons preventing teachers from fully integrating tablets into their instruction, the impacts training has had on tablet use, and …
Real-Time Translation Of American Sign Language Using Wearable Technology, Jackson Taylor
Real-Time Translation Of American Sign Language Using Wearable Technology, Jackson Taylor
Honors Theses
The goal of this work is to implement a real-time system using wearable technology for translating American Sign Language (ASL) gestures into audible form. This system could be used to facilitate conversations between individuals who do and do not communicate using ASL. We use as our source of input the Myo armband, an affordable commercially-available wearable technology equipped with on-board accelerometer, gyroscope, and electromyography sensors. We investigate the performance of two different classification algorithms in this context: linear discriminant analysis and k-Nearest Neighbors (k-NN) using various distance metrics. Using the k-NN classifier and windowed dynamic time …
Cameron-Liebler Line Classes And Partial Difference Sets, Uthaipon Tantipongipat
Cameron-Liebler Line Classes And Partial Difference Sets, Uthaipon Tantipongipat
Honors Theses
The work consists of three parts. The first is a study of Cameron-Liebler line classes which receive much attention recently. We studied a new construction of infinite family of Cameron-Liebler line classes presented in the paper by Tao Feng, Koji Momihara, and Qing Xiang (rst introduced in 2014), and summarized our attempts to generalize this construction to discover any new Cameron-Liebler line classes or partial difference sets (PDSs) resulting from the Cameron-Liebler line classes. The second is our approach to finding PDS in non-elementary abelian groups. Our attempt eventually led to the same general construction of PDS presented in John …
Nonexistence Of Nonquadratic Kerdock Sets In Six Variables, John Clikeman
Nonexistence Of Nonquadratic Kerdock Sets In Six Variables, John Clikeman
Honors Theses
Kerdock sets are maximally sized sets of boolean functions such that the sum of any two functions in the set is bent. This paper modifies the methodology of a paper by Phelps (2015) to the problem of finding Kerdock sets in six variables containing non-quadratic elements. Using a computer search, we demonstrate that no Kerdock sets exist containing non-quadratic six- variable bent functions, and that the largest bent set containing such functions has size 8.
Partitioning Groups With Difference Sets, Rebecca Funke
Partitioning Groups With Difference Sets, Rebecca Funke
Honors Theses
This thesis explores the use of difference sets to partition algebraic groups. Difference sets are a tool belonging to both group theory and combinatorics that provide symmetric properties that can be map into over mathematical fields such as design theory or coding theory. In my work, I will be taking algebraic groups and partitioning them into a subgroup and multiple McFarland difference sets. This partitioning can then be mapped to an association scheme. This bridge between difference sets and association schemes have important contributions to coding theory.