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Articles 1 - 11 of 11
Full-Text Articles in Other Applied Mathematics
Mathematics Behind Machine Learning, Rim Hammoud
Mathematics Behind Machine Learning, Rim Hammoud
Electronic Theses, Projects, and Dissertations
Artificial intelligence (AI) is a broad field of study that involves developing intelligent
machines that can perform tasks that typically require human intelligence. Machine
learning (ML) is often used as a tool to help create AI systems. The goal of ML is
to create models that can learn and improve to make predictions or decisions based on given data. The goal of this thesis is to build a clear and rigorous exposition of the mathematical underpinnings of support vector machines (SVM), a popular platform used in ML. As we will explore later on in the thesis, SVM can be implemented …
Sum Of Cubes Of The First N Integers, Obiamaka L. Agu
Sum Of Cubes Of The First N Integers, Obiamaka L. Agu
Electronic Theses, Projects, and Dissertations
In Calculus we learned that Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …
Modeling Community Resource Management: An Agent-Based Approach, Maya M. Lapp
Modeling Community Resource Management: An Agent-Based Approach, Maya M. Lapp
Senior Independent Study Theses
As the human population continues increasing rapidly and climate change accelerates, resource depletion is becoming an international problem. Community-based natural resource management (CBNRM) has been suggested as a method to conserve resources while simultaneously empowering traditionally marginalized communities. Because classical equation-based modeling methods fail to capture the complexity of CBNRM, Agent-Based Modeling (ABM) has emerged as a primary method of modeling these systems. In this investigation, we conduct a sensitivity analysis and thorough evaluation of an existing ABM of community forest management. We then modify the original model by providing a new enforcement mechanism that improves the validity of both …
The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas
The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas
Honors Projects
In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time and …
Simulations And Queueing Theory: The Effects Of Randomly Bypassing Security, Emily Ortmann
Simulations And Queueing Theory: The Effects Of Randomly Bypassing Security, Emily Ortmann
Masters Theses & Doctoral Dissertations
We discuss queueing theory in the setting of airport security and customs. By developing queueing simulations based on mathematical models, we explore a variety of questions related to optimal queue design with respect to efficiency, feasibility, priority, and other prescribed/variable constraints.
Simulations And Queueing Theory: The Effects Of Priority And Vip Thresholds, Laura Schuck
Simulations And Queueing Theory: The Effects Of Priority And Vip Thresholds, Laura Schuck
Masters Theses & Doctoral Dissertations
Everyone has experienced waiting in lines, whether it is at the airport, the grocery store, or somewhere in-between. By developing queueing simulations based on mathematical models of airport security and customs, we explore a variety of questions related to optimal queue design with respect to efficiency, feasibility, priority, and other prescribed/variable constraints.
Sports Analytics With Computer Vision, Colby T. Jeffries
Sports Analytics With Computer Vision, Colby T. Jeffries
Senior Independent Study Theses
Computer vision in sports analytics is a relatively new development. With multi-million dollar systems like STATS’s SportVu, professional basketball teams are able to collect extremely fine-detailed data better than ever before. This concept can be scaled down to provide similar statistics collection to college and high school basketball teams. Here we investigate the creation of such a system using open-source technologies and less expensive hardware. In addition, using a similar technology, we examine basketball free throws to see whether a shooter’s form has a specific relationship to a shot’s outcome. A system that learns this relationship could be used to …
Inclusion Of Blocking Power For A Complete Voting Power Analysis In The Imf, Shiwani Varal
Inclusion Of Blocking Power For A Complete Voting Power Analysis In The Imf, Shiwani Varal
Senior Independent Study Theses
The International Monetary Fund (IMF) calculates the voting power of a country by dividing the total of one member's votes by the total of all members' votes. This method of calculating the power of a state judges power as voting weight. However, voting weights are the total number of votes a country has in an institution, while voting power is the influence a country has on a policy decision. A better approach to calculate this voting power within an institution is by using voting power indices. However, literature only calculates the winning power, while voting power is defined as the …
Using Mathematical Research Methods To Solve A Problem In Music Theory Instruction, Specifically, The Teaching Of Secondary Dominant Chords, Angela Ulrich
Williams Honors College, Honors Research Projects
The mathematical method for research is used to find a solution to a problem in music theory: understanding and identifying secondary dominant chords. By reviewing and assessing the teaching methods of university professors and theory textbooks, and comparing those findings with student reviews, a new method for teaching the concept is developed. The proposed system incorporates aural, visual, and kinetic exercises to serve every learner. The literature review and sample unit plan are followed by a possible procedure for testing the effectiveness of the new method.
Subgroups Of Finite Wreath Product Groups For P=3, Jessica L. Gonda
Subgroups Of Finite Wreath Product Groups For P=3, Jessica L. Gonda
Williams Honors College, Honors Research Projects
Let M be the additive abelian group of 3-by-3 matrices whose entries are from the ring of integers modulo 9. The problem of determining all the normal subgroups of the regular wreath product group P=Z9≀(Z3 × Z3) that are contained in its base subgroup is equivalent to the problem of determining the subgroups of M that are invariant under two particular endomorphisms of M. In this thesis we give a partial solution to the latter problem by implementing a systematic approach using concepts from group theory and linear algebra.
Optimal Placement Of Family Planning Centers, Kiera Dobbs
Optimal Placement Of Family Planning Centers, Kiera Dobbs
Senior Independent Study Theses
This project investigates and begins to solve the problem of access to family planning services in the United States. We research and implement methods in Operations Research to optimize the location of publicly funded family planning centers in the United States by minimizing travel distance. The solution begins with a designated number of family planning centers for the country. An apportionment integer programming algorithm is then exercised to allocate centers to all the states based on population, percent of population in poverty, and state square mileage. At the state level, we use apportionment again to distribute centers to counties. At …