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Articles 31 - 41 of 41
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I Don't Play Chess: A Study Of Chess Piece Generating Polynomials, Stephen R. Skoch
I Don't Play Chess: A Study Of Chess Piece Generating Polynomials, Stephen R. Skoch
Senior Independent Study Theses
This independent study examines counting problems of non-attacking rook, and non-attacking bishop placements. We examine boards for rook and bishop placement with restricted positions and varied dimensions. In this investigation, we discuss the general formula of a generating function for unrestricted, square bishop boards that relies on the Stirling numbers of the second kind. We discuss the maximum number of bishops we can place on a rectangular board, as well as a brief investigation of non-attacking rook placements on three-dimensional boards, drawing a connection to latin squares.
Beyond Ss: An Analysis Of Alternative Risk Measures, Jai Kedia
Beyond Ss: An Analysis Of Alternative Risk Measures, Jai Kedia
Senior Independent Study Theses
Investors require a return from investing in stock securities that adequately compensate the investors for the risk level assumed. Therefore, any calculation of expected returns from a stock requires knowledge of the risk of the security. While there is no strong consensus on an ideal risk measure, traditionally risk has been conceptualized as volatility and is measured by the ß of the stock or portfolio. This paper hypothesizes that alternative risk measures such as higher order moments, size, leverage, and price-to-book value add explanatory power to the ß when predicting stock returns. Empirical analysis is conducted using both regression and …
Keeping Your Options Open: An Introduction To Pricing Options, Ryan F. Snyder
Keeping Your Options Open: An Introduction To Pricing Options, Ryan F. Snyder
Senior Independent Study Theses
An option is a contract which gives the holder of the option the right, but not the obligation, to buy or sell a given security at a given price, which is called the strike price. For example, suppose Yahoo stock is currently trading at $10 per share. A person could buy an option that gives him or her the ability to purchase shares of Yahoo stock for $12 in one year. If the price of Yahoo stock is greater than $12 in one year, the holder of the option will make money. However, he or she will not use the …
A Bayesian Model Of Fertility Decisions In Relationship To Female Labor Force Participation, Rebecca C. Wardrop
A Bayesian Model Of Fertility Decisions In Relationship To Female Labor Force Participation, Rebecca C. Wardrop
Senior Independent Study Theses
Due to the increasing number of women in the labor force, opportunity costs associated with labor force participation are becoming an important factor in fertility decisions. Further, these decisions are assumed to be dynamic as the opportunity costs change as a woman progresses through her career. A Bayesian statistical model , which allows the distribution of the likelihood of having children to be updated as information is gathered, lends itself to the dynamicity of the decision-making process. A generalized model for fertility decisions in terms of labor force participation is created. I also discuss potentials for implementation and furthering the …
Generalist And Specialist Pollination Syndromes: When Are They Favoured? A Theoretical Approach To Predict The Conditions Under Which A Generalist Or Specialist Pollination Syndrome Is Favoured., Tyler L. Poppenwimer
Generalist And Specialist Pollination Syndromes: When Are They Favoured? A Theoretical Approach To Predict The Conditions Under Which A Generalist Or Specialist Pollination Syndrome Is Favoured., Tyler L. Poppenwimer
Senior Independent Study Theses
No abstract provided.
Markov Chain Theory With Applications To Baseball, Cal D. Thomay
Markov Chain Theory With Applications To Baseball, Cal D. Thomay
Senior Independent Study Theses
The applications of Markov chains span a wide range of fields to which models have been designed and implemented to simulate random processes. Markov chains are stochastic processes that are characterized by their memoryless property, where the probability of the process being in the next state of the system depends only on the current state and not on any of the previous states. This property is known as the Markov property. This thesis paper will first introduce the theory of Markov chains, along with explaining two types of Markov chains that will be beneficial in creating a model for analyzing …
The Analytic Hierarchy Process: A Mathematical Model For Decision Making Problems, Giang Huong Nguyen
The Analytic Hierarchy Process: A Mathematical Model For Decision Making Problems, Giang Huong Nguyen
Senior Independent Study Theses
The ability to make the right decision is an asset in many areas and lines of profession including social work, business, national economics, and international security. However, decision makers often have difficulty choosing the best option since they might not have a full understanding of their preferences, or lack a systematic approach to solve the decision making problems at hand. The Analytic Hierarchy Process (AHP) provides a mathematical model that helps the decision makers arrive at the most logical choice, based on their preferences. We investigate the theory of positive, reciprocal matrices, which provides the theoretical justification of the method …
The Machete Number, David Freund
The Machete Number, David Freund
Senior Independent Study Theses
Knot theory is a branch of topology that deals with the structure and properties of links. Employing a variety of tools, including surfaces, graph theory, and polynomials, we develop and explore classical link invariants. From this foundation, we de fine two novel link invariants, braid height and machete number, and investigate their properties and connection to classical invariants.
Let's Get In The Mood: An Exploration Of Data Mining Techniques To Predict Mood Based On Musical Properties Of Songs, Sarah Smith-Polderman
Let's Get In The Mood: An Exploration Of Data Mining Techniques To Predict Mood Based On Musical Properties Of Songs, Sarah Smith-Polderman
Senior Independent Study Theses
This thesis explores the possibility of predicting the mood a song will evoke in a person based on certain musical properties that the song exhibits. First, I introduce the topic of data mining and establish its significant relevance in this day and age. Next, I explore the several tasks that data mining can accomplish, and I identify classification and clustering as the two most relevant tasks for mood prediction based on musical properties of songs. Chapter 3 introduces in detail two specific classification techniques: Naive Bayes Classification and k-Nearest Neighbor Classification. Similarly, Chapter 4 introduces two specific clustering techniques: …
The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods, Ruth A. Steinhour
The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods, Ruth A. Steinhour
Senior Independent Study Theses
Differential equations are vitally important in numerous scientific fields. Oftentimes, they are quite challenging to solve. This Independent Study examines one method for solving differential equations. Norwegian mathematician Sophus Lie developed this method, which uses groups of symmetries, called Lie groups. These symmetries map one solution curve to another. They can be used to determine a canonical coordinate system for a given differential equation. Writing the differential equation in terms of a different coordinate system can make the equation simpler to solve. This I.S. explores techniques for finding a canonical coordinate system and using it to solve a given differential …
Iteration Digraphs, Hannah Roberts
Iteration Digraphs, Hannah Roberts
Senior Independent Study Theses
No abstract provided.