Bias In Monte Carlo Simulations Due To Pseudo-Random Number Generator Initial Seed Selection,
2011
Beaumont Health System
Bias In Monte Carlo Simulations Due To Pseudo-Random Number Generator Initial Seed Selection, Jack C. Hill, Shlomo S. Sawilowsky
Theoretical and Behavioral Foundations of Education Faculty Publications
Pseudo-random number generators can bias Monte Carlo simulations of the standard normal probability distribution function with initial seeds selection. Five generator designs were initial-seeded with values from 10000HEX to 1FFFFHEX, estimates of the mean were calculated for each seed, the distribution of mean estimates was determined for each generator and simulation histories were graphed for selected seeds.
Rated Extremal Principles For Finite And Infinite Systems,
2011
Wayne State University
Rated Extremal Principles For Finite And Infinite Systems, Hung M. Phan, Boris S. Mordukhovich
Mathematics Research Reports
In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the core geometric theory of variational analysis. We present their applications to calculus and optimality conditions for problems with infinitely many constraints.
A Multiple Regression Analysis Of Personality’S Impact On Actuarial Exam Performance,
2011
Bryant University
A Multiple Regression Analysis Of Personality’S Impact On Actuarial Exam Performance, Matthew Ciaffone
Honors Projects in Mathematics
Existing literature indicates that there is some connection between personality and both academic and work-related performance. The author's intent for the research described herein is to explore this connection for students majoring in actuarial mathematics with regard to their performance on actuarial certification exams. Specifically, using the five-factor model of personality, the author seeks to predict the number of attempts required to pass the first two exams in the process (Exam 1/P - probability; Exam 2/FM - financial mathematics) using measures of the five dimensions of the five-factor model (openness to experience, conscientiousness, extraversion, agreeableness, and emotional stability) through regression …
Factors Related To Math Performance And Potential Benefits Of One-On-One Instruction,
2011
Bryant University
Factors Related To Math Performance And Potential Benefits Of One-On-One Instruction, Amanda Zagame
Honors Projects in Mathematics
This fall 2010 study of Bryant University students enrolled in freshman-level math courses considered factors related to college-level math performance, including gender, math self-efficacy, math anxiety, and utilization of professors’ office hours and/or tutoring center services. Female students at Bryant reported lower levels of math self-efficacy and higher levels of math anxiety, both of which research has shown to be negatively correlated with test scores. The use of one-on-one instruction was expected to provide a potential counterweight to this equation. Results from the 287 initial and 229 final surveys administered in this study did not support this hypothesis. This phenomenon …
Group Actions And Divisors On Tropical Curves,
2011
Harvey Mudd College
Group Actions And Divisors On Tropical Curves, Max B. Kutler
HMC Senior Theses
Tropical geometry is algebraic geometry over the tropical semiring, or min-plus algebra. In this thesis, I discuss the basic geometry of plane tropical curves. By introducing the notion of abstract tropical curves, I am able to pass to a more abstract metric-topological setting. In this setting, I discuss divisors on tropical curves. I begin a study of $G$-invariant divisors and divisor classes.
Continued Fractions: A New Form,
2011
Harvey Mudd College
Continued Fractions: A New Form, Donald Lee Wiyninger Iii
HMC Senior Theses
While the traditional form of continued fractions is well-documented, a new form, designed to approximate real numbers between 1 and 2, is less well-studied. This report first describes prior research into the new form, describing the form and giving an algorithm for generating approximations for a given real number. It then describes a rational function giving the rational number represented by the continued fraction made from a given tuple of integers and shows that no real number has a unique continued fraction. Next, it describes the set of real numbers that are hardest to approximate; that is, given a positive …
Third And Fourth Binomial Coefficients,
2011
Harvey Mudd College
Third And Fourth Binomial Coefficients, Arthur T. Benjamin, Jacob N. Scott '11
All HMC Faculty Publications and Research
While formulas for the sums of kth binomial coefficients can be shown inductively or algebraically, these proofs give little insight into the combinatorics involved. We prove formulas for the sums of 3rd and 4th binomial coefficients via purely combinatorial arguments.
Strategic Treatment Interruptions During Imatinib Treatment Of Chronic Myelogenous Leukemia,
2011
California Polytechnic State University - San Luis Obispo
Strategic Treatment Interruptions During Imatinib Treatment Of Chronic Myelogenous Leukemia, Dana C. Paquin, Peter S. Kim, Peter P. Lee, Doron Levy
Mathematics
Although imatinib is an effective treatment for chronic myelogenous leukemia (CML), and nearly all patients treated with imatinib attain some form of remission, imatinib does not completely eliminate leukemia. Moreover, if the imatinib treatment is stopped, most patients eventually relapse (Cortes et al. in Clin. Cancer Res. 11:3425–3432, 2005). In Kim et al. (PLoS Comput. Biol. 4(6):e1000095, 2008), the authors presented a mathematical model for the dynamics of CML under imatinib treatment that incorporates the anti-leukemia immune response. We use the mathematical model in Kim et al. (PLoS Comput. Biol. 4(6):e1000095, 2008) to study and numerically simulate strategic treatment interruptions …
Deterministic And Stochastic Bellman's Optimality Principles On Isolated Time Domains And Their Applications In Finance,
2011
Western Kentucky University
Deterministic And Stochastic Bellman's Optimality Principles On Isolated Time Domains And Their Applications In Finance, Nezihe Turhan
Masters Theses & Specialist Projects
The concept of dynamic programming was originally used in late 1949, mostly during the 1950s, by Richard Bellman to describe decision making problems. By 1952, he refined this to the modern meaning, referring specifically to nesting smaller decision problems inside larger decisions. Also, the Bellman equation, one of the basic concepts in dynamic programming, is named after him. Dynamic programming has become an important argument which was used in various fields; such as, economics, finance, bioinformatics, aerospace, information theory, etc. Since Richard Bellman's invention of dynamic programming, economists and mathematicians have formulated and solved a huge variety of sequential decision …
Development Of Fractional Trigonometry And An Application Of Fractional Calculus To Pharmacokinetic Model,
2011
Western Kentucky University
Development Of Fractional Trigonometry And An Application Of Fractional Calculus To Pharmacokinetic Model, Amera Almusharrf
Masters Theses & Specialist Projects
No abstract provided.
Finding The Beat In Music: Using Adaptive Oscillators,
2011
Harvey Mudd College
Finding The Beat In Music: Using Adaptive Oscillators, Kate M. Burgers
HMC Senior Theses
The task of finding the beat in music is simple for most people, but surprisingly difficult to replicate in a robot. Progress in this problem has been made using various preprocessing techniques (Hitz 2008; Tomic and Janata 2008). However, a real-time method is not yet available. Methods using a class of oscillators called relay relaxation oscillators are promising. In particular, systems of forced Hopf oscillators (Large 2000; Righetti et al. 2006) have been used with relative success. This work describes current methods of beat tracking and develops a new method that incorporates the best ideas from each existing method and …
Markov Bases For Noncommutative Harmonic Analysis Of Partially Ranked Data,
2011
Harvey Mudd College
Markov Bases For Noncommutative Harmonic Analysis Of Partially Ranked Data, Ann Johnston
HMC Senior Theses
Given the result $v_0$ of a survey and a nested collection of summary statistics that could be used to describe that result, it is natural to ask which of these summary statistics best describe $v_0$. In 1998 Diaconis and Sturmfels presented an approach for determining the conditional significance of a higher order statistic, after sampling a space conditioned on the value of a lower order statistic. Their approach involves the computation of a Markov basis, followed by the use of a Markov process with stationary hypergeometric distribution to generate a sample.This technique for data analysis has become an accepted tool …
Verification Of Solutions To The Sensor Location Problem,
2011
Harvey Mudd College
Verification Of Solutions To The Sensor Location Problem, Chandler May
HMC Senior Theses
Traffic congestion is a serious problem with large economic and environmental impacts. To reduce congestion (as a city planner) or simply to avoid congested channels (as a road user), one might like to accurately know the flow on roads in the traffic network. This information can be obtained from traffic sensors, devices that can be installed on roads or intersections to measure traffic flow. The sensor location problem is the problem of efficiently locating traffic sensors on intersections such that the flow on the entire network can be extrapolated from the readings of those sensors. I build on current research …
Extending List Colorings Of Planar Graphs,
2011
Harvey Mudd College
Extending List Colorings Of Planar Graphs, Sarah Loeb
HMC Senior Theses
In the study of list colorings of graphs, we assume each vertex of a graph has a specified list of colors from which it may be colored. For planar graphs, it is known that there is a coloring for any list assignment where each list contains five colors. If we have some vertices that are precolored, can we extend this to a coloring of the entire graph? We explore distance constraints when we allow the lists to contain an extra color. For lists of length five, we fix $W$ as a subset of $V(G)$ such that all vertices in $W$ …
Combinatorial Interpretations Of Fibonomial Identities,
2011
Harvey Mudd College
Combinatorial Interpretations Of Fibonomial Identities, Elizabeth Reiland
HMC Senior Theses
The Fibonomial numbers are defined by \[ \begin{bmatrix}n \\ k \end{bmatrix} = \frac{\prod_{i=n-k+1} ^{n} F_i}{\prod_{j=1}^{k} F_j} \] where $F_i$ is the $i$th Fibonacci number, defined by the recurrence $F_n=F_{n-1}+F_{n-2}$ with initial conditions $F_0=0,F_1=1$. In the past year, Sagan and Savage have derived a combinatorial interpretation for these Fibonomial numbers, an interpretation that relies upon tilings of a partition and its complement in a given grid.In this thesis, I investigate previously proven theorems for the Fibonomial numbers and attempt to reinterpret and reprove them in light of this new combinatorial description. I also present combinatorial proofs for some identities I did …
Operator Splitting Method And Applications For Semilinear Parabolic Partial Differential Equations,
2011
George Fox University
Operator Splitting Method And Applications For Semilinear Parabolic Partial Differential Equations, R. Corban Harwood
Faculty Publications - Department of Mathematics
This dissertation presents a redefined operator splitting method used in solving semilinear parabolic partial differential equations. As one such form, the reaction-diffusion equation is highly prevalent in mathematical modeling. Besides being physically meaningful as a separation of two distinct physical processes in this equation, operator splitting simplifies the solution method in several ways. The super-linear speed-up of computations is a rewarding simplification as it presents great benefits for large-scale systems. In solving these semilinear equations, we will develop a condition for oscillation-free methods, a condition independent of the usual stability condition. This numerical consideration is important to fully embody our …
The Impact Of Manipulatives On Learning In The Elementary And Middle School Mathematics Classroom,
2011
Bemidji State University
The Impact Of Manipulatives On Learning In The Elementary And Middle School Mathematics Classroom, Laura Dahl
Mathematics Graduate Theses
This paper is a review of research pertaining to the use of manipulatives in the elementary and middle school mathematics classrooms. It embodies the logic behind using manipulative materials in the classroom setting and the impact their use will have on student understanding and enjoyment for learning mathematical concepts. This research paper will identify the struggles and concerns of manipulative use along with the need of increased professional development and training for teachers to be better prepared for the daunting, yet rewarding challenges of successfully teaching mathematics.
Collecting, Analyzing And Interpreting Bivariate Data From Leaky Buckets: A Project-Based Learning Unit,
2011
Utah State University
Collecting, Analyzing And Interpreting Bivariate Data From Leaky Buckets: A Project-Based Learning Unit, Florence Funmilayo Obielodan
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Despite the significance and the emphasis placed on mathematics as a subject and field of study, achieving the right attitude to improve students‟ understanding and performance is still a challenge. Previous studies have shown that the problem cuts across nations around the world, both developing countries and developed alike. Teachers and educators of the subject have responsibilities to continuously develop innovative pedagogical approaches that will enhance students‟ interests and performance. Teaching approaches that emphasize real life applications of the subject have become imperative. It is believed that this will stimulate learners‟ interest in the subject as they will be able …
The Roller-Coaster Conjecture,
2011
Montclair State University
The Roller-Coaster Conjecture, Leslie A. Cheteyan
Theses, Dissertations and Culminating Projects
No abstract provided.
Polynomial Solutions To The Diophantine Equation X² + Y³ = 6912z²,
2011
Montclair State University
Polynomial Solutions To The Diophantine Equation X² + Y³ = 6912z², Emel Demirel
Theses, Dissertations and Culminating Projects
In this paper, I investigate polynomial solutions to the Diophantine equa tion, X² +Y³ = 6912Z², where X = g(x,y), Y = h(x,y) and Z = f(x,y) are polynomials with integer coefficients. The focus is on the greatest common di visors for the integer values of these polynomials when the polynomials f (x, y), g(x, y) and h(x, y) are relatively prime in Q[x, y]. However, for a fixed integer pair xo, Yo, the integer values f(x0,y0), g(x0, y0) and h(x0,y0) are not necessarily relatively prime in Z. I investigate the greatest common divisors (GCDs) of these three polynomial values …
