Search Constraints
Filtering by:
Type
Peacock Scholarship
Remove constraint Type: Peacock Scholarship
Publisher
Saint Peter's University
Remove constraint Publisher: Saint Peter's University
Subject
Mathematics
Remove constraint Subject: Mathematics
1 - 11 of 11
Number of results to display per page
Search Results
- Description:
- Zeckendorf explored the decomposition of integers into sums of nonconsecutive Fibonacci numbers. Thinking of each Fibonacci number in the sequence as being inside a ‘bin’, Zeckendorf’s rule for “legal” decompositions can be reworded as sums of numbers in bins separated by 1 or more bins. Zeckendorf never explored sequences that result when the bins are enlarged to include more than one number or when “legal” decompositions are redefined to require more bins between summands. We do both these things. Another aspect we look at is how these sequences are created. The Fibonacci Sequence has the well known recurrence relation fn = fn−1 +fn−2. Our sequences have a similar single recurrence relation. Also, we have found that given different initial conditions, very similar sequences are produced. We examine where the same terms appear and explain why this is the case. Additionally, we discuss different types of ratios between terms in a given sequence. More specifically, we will examine the quotients of consecutive numbers as well as ratios of summands. Our results show that ratios made up of terms coming from the same relative positions are approximately equal. This research is of particular interest considering that the quotients of terms in the Fibonacci Sequence approach the Golden Ratio, a very special number found in many diverse areas of mathematics. While our quotient values are different, the fact that specific numbers are approached is an important similarity between our sequences and the Fibonacci Sequence. This is not surprising considering that sequences produced in literature have been shown to share significant connections with the Fibonacci Sequence. Nevertheless, the specific question of ratios in any variation of the Fibonacci Sequence has never been explored.
- Subject:
- Mathematics
- Creator:
- Gotshall, Daniel
- Contributor:
- Dr. Dawn Nelson, Thesis Advisor
- Owner:
- lsquillante@saintpeters.edu
- Publisher:
- Saint Peter's University
- Date Uploaded:
- 06/09/2020
- Date Modified:
- 06/09/2020
- Date Created:
- April 20, 2020
- Rights Statement:
- In Copyright
- Resource Type:
- Research Paper
- Description:
- One of the assumptions of the two-sample t-test is that it should only be applied to pairs of samples if both samples were drawn from normal populations or if the samples are sufficiently large. In practice, many researchers check if this assumption is met by pre-testing. The pre-test allows them to determine whether to use a parametric or non-parametric test. This research explores the probability of the Type I error of a two-stage and a one-stage hypothesis test performed on two independent samples, both of which were drawn from different populations, such as the normal distribution, the uniform distribution, and the mixed-normal distribution. The first step of the two-stage hypothesis test is to apply the Shapiro-Wilk test to pre-test for normality of the samples. The second step is to apply the Mann-Whitney test or the two-sample t-test, depending on the outcome of the first step. The one-stage hypothesis test with no preliminary testing performs all t-tests on the two independent samples. The probability of the Type I errors for different pairs of samples is calculated by running simulations in R. I also investigate the effect of different sample sizes and non-homogeneity of variance in both procedures. I conclude by comparing the robustness of the two-stage procedure to the robustness of the t-test.
- Subject:
- Mathematics
- Creator:
- Castellon, Elda Eunice
- Contributor:
- Dr. Rebecca Conley, Thesis Advisor
- Owner:
- lsquillante@saintpeters.edu
- Publisher:
- Saint Peter's University
- Date Uploaded:
- 06/10/2020
- Date Modified:
- 06/10/2020
- Date Created:
- April 20, 2020
- Rights Statement:
- In Copyright
- Resource Type:
- Research Paper
- Description:
- This thesis concerns a variant of Bulgarian Solitaire, called Austrian solitaire, introduced by Akin and Davis. A primary result is the derivation of a formula for the number of states under Austrian Solitaire. This thesis characterizes the Garden of Eden states. The thesis also gives a possible characterization for the fixed points and examines other cycle states with various conclusions.
- Subject:
- Mathematics
- Creator:
- Bastola, Kapil
- Contributor:
- Dr. Brian Hopkins, Thesis Advisor
- Owner:
- lsquillante@saintpeters.edu
- Publisher:
- Saint Peter's University
- Date Uploaded:
- 10/14/2020
- Date Modified:
- 10/14/2020
- Date Created:
- Fall 2012
- Rights Statement:
- In Copyright
- Resource Type:
- Research Paper
- Description:
- Recently, game theory has gained much interest from many mathematicians as well as economists and psychologists. The simplest and most popular games studied in this field are the 2 X 2 games, which involve two players with two different choices each; each player makes his or her decision individually, but his or her choice will affect the outcome for both that player as well as for the other player. Within these 2 X 2 games, each player has his or her own preference in terms of what outcomes are best for them; for each of the four possible outcomes in these 2 X 2 games, each player also receives a certain payoff, which could be a good or bad payoff. If both players have the same ordering of outcomes, then the game is called symmetric, meaning if the players were switched, the outcomes would be in the same order as initially. In this paper, I show the results I found while researching the connections between these symmetric 2 X 2 games. The twelve total symmetric 2 X 2 games can be shown on a 2D x-y axis; these games can be separated into six different sectors. In each section, the games involved can be manipulated, when transitioning to another game with different payoff preferences, to one common game. When one game is changed to another by simply swapping two of the payoffs, a transition game in between these games appears; by doing a simple operation to these transition games, I was able to find one universal game in each sector. This proves that these are more closely related than mathematicians previously believed. If one has an interest in game theory, wants to learn about an interesting topic in mathematics, or just wants to see what one can do with the power of mathematics, one can read all about the 2 X 2 symmetric games in When Prisoners Enter Battle: Natural Connections in 2 X 2 Symmetric Games.
- Subject:
- Mathematics
- Creator:
- Heilig, Sarah
- Contributor:
- Dr. Brian Hopkins, Thesis Advisor
- Owner:
- lsquillante@saintpeters.edu
- Publisher:
- Saint Peter's University
- Date Uploaded:
- 10/14/2020
- Date Modified:
- 10/14/2020
- Date Created:
- March 28, 2011
- Rights Statement:
- In Copyright
- Resource Type:
- Research Paper
- Description:
- For a given system of linear equations L, the Rado number of the system is the least integer n for which every t-coloring of {1,...,n} contains a monochromatic solution of one of the equations in L, if such an integer exists. In this thesis, the 2-color disjunctive Rado numbers for the equations ax1 = x2 and bx1 + x2 = x3 are determined for more than half of all values of a and b.
- Subject:
- Mathematics
- Creator:
- Purcilly, Adam
- Contributor:
- Dr. Brian Hopkins, Thesis Advisor
- Owner:
- lsquillante@saintpeters.edu
- Publisher:
- Saint Peter's University
- Date Uploaded:
- 10/14/2020
- Date Modified:
- 10/14/2020
- Date Created:
- Spring 2013
- Rights Statement:
- In Copyright
- Resource Type:
- Research Paper
- Description:
- Does high payroll necessarily mean higher performance for all baseball statistics? Major League Baseball (MLB) is a league of different teams in different cities all across the United States, and those locations strongly influence the market of the team and thus the payroll. Year after year, a certain amount of teams, including the usual ones in big markets, choose to spend a great amount on payroll in hopes of improving their team and its player value output, but at times the statistics produced by these teams may not match the difference in payroll with other teams. This observation invites a few questions for investigation. • Are high-payroll teams actually seeing an improvement in results? • Are the results between high-payroll and non-high-payroll teams actually statistically different? • What statistics present the strongest relation with high payroll increase? • What statistics present the weakest relation with payroll increase? The questions and possibilities are endless, so those are just the beginning, but the purpose of this study is to answer the questions raised above and to investigate if high-payroll teams truly perform better, and then interpret what the results actually mean.
- Subject:
- Mathematics
- Creator:
- Lambrianou, Nicholas
- Contributor:
- Dr. Nicholas Kintos, Thesis Advisor
- Owner:
- lsquillante@saintpeters.edu
- Publisher:
- Saint Peter's University
- Date Uploaded:
- 10/14/2020
- Date Modified:
- 10/14/2020
- Date Created:
- April 2013
- Rights Statement:
- In Copyright
- Resource Type:
- Research Paper
- Description:
- Since the invention of the Rubik’s cube in the 1970s, mathematicians have been captivated with finding out the maximum number of moves needed to solve the Rubik’s cube optimally from any of the cube’s approximately 43 trillion possible positions. This value, known as God’s number, depends on the metric, which is the set of allowed moves. This thesis proposes a new “robotic turn metric” based on allowing antipodal faces of the cube to be turned simultaneously. Although human solvers cannot easily accomplish such moves, they are used by various robotic cube solvers, thus the name. We explore lower and upper bounds for God’s number in this metric and how it compares to God’s number in the Face Turn Metric and Quarter Turn Metric.
- Subject:
- Mathematics
- Creator:
- Hollingsworth, Nykosi
- Contributor:
- Dr. Brian Hopkins, Thesis Advisor
- Owner:
- lsquillante@saintpeters.edu
- Publisher:
- Saint Peter's University
- Date Uploaded:
- 10/14/2020
- Date Modified:
- 10/14/2020
- Date Created:
- April 28, 2015
- Rights Statement:
- In Copyright
- Resource Type:
- Research Paper
- Description:
- Game theory is used in a wide variety of applications. It is most notably used in economics but also has widespread applications in politics and biology. In this paper, we will only look at the economic and political applications of game theory in general and Steven J. Brams’ Theory of Moves (TOM) in particular. Brams uses numerous examples from politics, economics, and religion to illustrate the compatibility of TOM in real life issues as compared to the standard game theory. We will refer to these examples when appropriate. In the succeeding paragraphs and in other sections of this paper, we discuss how game theory, especially in its dynamic form, can be used to model real life situations.
- Subject:
- Mathematics
- Creator:
- Adhikari, Samik
- Contributor:
- Dr. Brian Hopkins, Thesis Advisor
- Owner:
- lsquillante@saintpeters.edu
- Publisher:
- Saint Peter's University
- Date Uploaded:
- 10/20/2020
- Date Modified:
- 10/20/2020
- Date Created:
- Spring 2011
- Rights Statement:
- In Copyright
- Resource Type:
- Research Paper
- Description:
- The purpose of this honors thesis is to serve as a call to research and action of both experts and current and future mathematics educators. Mathematics is a complicated, abstract, and beautiful field. Math is used in everyday life, whether or not it is recognized. However, the thought of partaking in any activity involving mathematics can cause stress and anxiety. Sometimes, this occurs in the classroom, but may also happen in everyday activities. Examples include calculating a tip or calculating interest on a loan. This phenomenon has been identified as Math Anxiety. Research has been done for many years to understand this complex concept, including its causes and effects on students and adults; however, there is so much that remains unknown. This study reviews the current literature on math anxiety in the classroom, both at the K-12 and undergraduate levels, to recognize the importance of identifying math anxiety. This research will come to form a tentative action plan for educators to help alleviate math anxiety for both their students and themselves.
- Subject:
- Mathematics and Education
- Creator:
- Goodman, Matthew
- Contributor:
- Dr. Jenna Cook, Thesis Advisor and Dr. John Hammett, Thesis Advisor
- Owner:
- lsquillante@saintpeters.edu
- Publisher:
- Saint Peter's University
- Date Uploaded:
- 06/14/2022
- Date Modified:
- 06/14/2022
- Date Created:
- Spring 2022
- Rights Statement:
- In Copyright
- Resource Type:
- Research Paper
- Description:
- The digraphs of permutation polynomials in the form ax^k+b and ax^k using the field Zp are being studied during this thesis. I will be testing to see how changes to constants, exponents, and coefficients affect the digraphs of these permutation polynomials. Using previous work from scholarly articles as well as my own experimentation with the effects of certain changes to polynomial functions, I have devised several theorems and lemmas that will increase the understanding of permutation polynomials.
- Subject:
- Mathematics
- Creator:
- Coombes, Christian
- Contributor:
- Dawn Nelson, Ph.D., Thesis Advisor
- Owner:
- lsquillante@saintpeters.edu
- Publisher:
- Saint Peter's University
- Date Uploaded:
- 06/13/2023
- Date Modified:
- 06/13/2023
- Date Created:
- Spring 2023
- Rights Statement:
- In Copyright
- Resource Type:
- Research Paper
- Description:
- Many people around the world have a special place in their hearts for music–but they cannot say the same for math. So much beauty can be experienced when listening to music, although what most do not realize is it comes from the special relationship music has with numbers and patterns. This study investigates how mathematics fits into something as creative and artistic as music. The way math is used to comprehend the basic components of music is explained, starting with how we perceive sound. The way our ears process the music affects which frequencies sound more pleasant when played together, and which do not. Timing matters a lot in music, as well. The repetition of beats and the patterns of rhythms combine and contribute to how a song sounds. The comprehension and appreciation of mathematics in music is the goal of this thesis, and to understand how music can be used as a tool to grasp the concepts in music.
- Subject:
- Mathematics
- Creator:
- Maravillas, Genesis
- Contributor:
- Nikolas Kintos, Ph.D., Thesis Advisor
- Owner:
- lsquillante@saintpeters.edu
- Publisher:
- Saint Peter's University
- Date Uploaded:
- 06/13/2023
- Date Modified:
- 06/13/2023
- Date Created:
- Spring 2023
- Rights Statement:
- In Copyright
- Resource Type:
- Research Paper