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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and 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 …
The Theory Of Cryptography In Bitcoin, Can Hong
The Theory Of Cryptography In Bitcoin, Can Hong
Mathematics Senior Capstone Papers
Bitcoin is a well known virtual currency, or cryptocurrency. It was created by a group of people using the name Satoshi Nakamoto in 2008. Currently, many people are utilizing Bitcoin for personal gains and transactions. To keep transactions secure requires techniques from modern cryptography. In this paper, we explain certain aspects of the cryptography of Bitcoin. We are going to discuss two components of the cryptography of Bitcoin—hash functions and signatures. We will describe what the hash function and signature are, give some examples of hash functions, and discuss certain criteria that good hash functions should satisfy.
Periodic Points And Sharkovsky’S Theorem, Luke J. Seaton
Periodic Points And Sharkovsky’S Theorem, Luke J. Seaton
Mathematics Senior Capstone Papers
The number of periodic points of a function depends on the context. The number of complex periodic points and rational periodic points have been shown to be infinite and finite, respectively, if f is a polynomial of degree at least 2. However, the number of real periodic points can be either finite or infinite. Sharkovskys Theorem states that if p is left of q in the “Sharkovsky ordering” and the continuous function f has a point of period p, then f also has a point of period q. This statement becomes very powerful when considering a function that has points …
Bridge To Bulldogs: A Student And Financial Analysis, Rebekah Moss
Bridge To Bulldogs: A Student And Financial Analysis, Rebekah Moss
Mathematics Senior Capstone Papers
In this paper, we discuss the statistical analysis of the Bridge to Bulldogs program. The Bridge to Bulldogs program provides prospective students, who do not meet all of the admission requirements, an alternate route of admission to Louisiana Tech University. The program is offered over two consecutive quarters, either summer/fall or fall/winter. During the program, students focus on building their math skills through tutoring and special advising. We compare the Bridge students to other first-time freshman in relation to scores in Freshman level math classes. We also compare composite and Math ACT scores. Finally, we perform a financial analysis, including …
The Sir Models, Their Applications, And Approximations Of Their Rates, Christopher Cano
The Sir Models, Their Applications, And Approximations Of Their Rates, Christopher Cano
Mathematics Senior Capstone Papers
The SIR (Susceptible-Infected-Recovered) models are used to help predict the spread of diseases. The goals of this paper are: elaborating on the methods of approximating the recovery rate, infection rate, and loss of immunity rate, comparing the SIR models with these approximation methods to real world data, and determining the most accurate combination of the approximation methods for each SIR model. There are several SIR models such as the Kermack-McKendrick, SIRS, and SI models that are designed for specific diseases. Understanding the parameters of these models will assist us in maximizing their accuracy. For example, there is no explicit formula …