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Full-Text Articles in Other Mathematics
A Comparison Of Cryptographic Methods, Christopher Gilmore
A Comparison Of Cryptographic Methods, Christopher Gilmore
Senior Honors Theses
While elliptic curve cryptography and quantum cryptography are significantly different branches of cryptography, they provide a suitable reference point for comparison of the value of developing methods used in the present and investing in methods to be used in the future. Elliptic curve cryptography is quite common today, as it is generally secure and efficient. However, as the field of cryptography advances, the value of quantum cryptography’s inherent security from its basic properties should be considered, as a fully realized quantum cryptosystem has the potential to be quite powerful. Ultimately, it is of critical importance to determine the value of …
The Effectiveness Of Professional Punters, Arthur N. Tanyel
The Effectiveness Of Professional Punters, Arthur N. Tanyel
Senior Honors Theses
Sports analytics have become a major part of how many sports fans enjoy the games they love. The trend has touched sports from football to cricket. One aspect of football that has been less discussed is punting. The current standard metrics, gross yardage and net yardage, give an idea of how a punter performed in a given season, but they also may be skewed by a number of factors, such as the skill of the offense or the punt coverage team. In this paper, we will look at some previous attempts to measure punting prowess, and then further develop a …
Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick
Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick
Senior Honors Theses
Over the past several decades, technology has continued to develop at an incredible rate, and the importance of properly securing information has increased significantly. While a variety of encryption schemes currently exist for this purpose, a number of them rely on problems, such as integer factorization, that are not resistant to quantum algorithms. With the reality of quantum computers approaching, it is critical that a quantum-resistant method of protecting information is found. After developing the proper background, we evaluate the potential of the McEliece cryptosystem for use in the post-quantum era by examining families of algebraic geometry codes that allow …
Examples Of Solving The Wave Equation In The Hyperbolic Plane, Cooper Ramsey
Examples Of Solving The Wave Equation In The Hyperbolic Plane, Cooper Ramsey
Senior Honors Theses
The complex numbers have proven themselves immensely useful in physics, mathematics, and engineering. One useful tool of the complex numbers is the method of conformal mapping which is used to solve various problems in physics and engineering that involved Laplace’s equation. Following the work done by Dr. James Cook, the complex numbers are replaced with associative real algebras. This paper focuses on another algebra, the hyperbolic numbers. A solution method like conformal mapping is developed with solutions to the one-dimensional wave equation. Applications of this solution method revolve around engineering and physics problems involving the propagation of waves. To conclude, …
Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate
Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate
Senior Honors Theses
Differential equations have bearing on practically every scientific field. Though they are prevalent in nature, they can be challenging to solve. Most of the work done in differential equations is dependent on the use of many methods to solve particular types of equations. Sophus Lie proposed a modern method of solving ordinary differential equations in the 19th century along with a coordinate free variation of finding the infinitesimal generator by combining the influential work of Élie Cartan among others in the field of differential geometry. The driving idea behind using symmetries to solve differential equations is that there exists a …