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- Branch Mathematics and Statistics Faculty and Staff Publications (6)
- Senior Independent Study Theses (4)
- Electronic Theses, Projects, and Dissertations (2)
- Masters Theses & Doctoral Dissertations (2)
- Publications and Research (2)
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- Williams Honors College, Honors Research Projects (2)
- All HMC Faculty Publications and Research (1)
- Department of Mathematics Facuty Scholarship and Creative Works (1)
- Honors Projects (1)
- Honors Projects in Mathematics (1)
- Honors Theses (1)
- Journal of Humanistic Mathematics (1)
- Lisa D Humphreys (1)
- Ronald Greenberg (1)
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Articles 1 - 27 of 27
Full-Text Articles in Physical Sciences and 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 …
Mathematical Analysis Of An Sir Disease Model With Non-Constant Transmission Rate, Emma Bollinger, Tayler Valdez, Swarup Ghosh, Sunil Giri
Mathematical Analysis Of An Sir Disease Model With Non-Constant Transmission Rate, Emma Bollinger, Tayler Valdez, Swarup Ghosh, Sunil Giri
Student Research
- Epidemiology: A branch of medicine that studies causes, transmission, and control methods of diseases at the population level.
- Mathematical epidemiology deals with creating a model for a disease through the study of incidence and distribution of the disease throughout a population.
- Here, we have examined the behavior of a measles-like disease[2] that is characterized by a non-constant transmission rate.
Crocheting Mathematics Through Covid-19, Beyza C. Aslan
Crocheting Mathematics Through Covid-19, Beyza C. Aslan
Journal of Humanistic Mathematics
As it is often said, something good often comes out of most bad situations. The time I spent during COVID-19, at home and isolated with my two children, brought out one secret passion in me: crocheting. Not only did it help me pass the time in a sane and productive way, but also it gave me a new goal in life. It connected my math side with my artistic side. It gave me a new perspective to look at math, and helped me help others see math in a positive way.
Parametric Art, Shaun Pollard, Daanial Ahmad, Satyanand Singh
Parametric Art, Shaun Pollard, Daanial Ahmad, Satyanand Singh
Publications and Research
Lissajous curves, named after Jules Antoine Lissajous (1822-1880) are generated by the parametric equations ��=��������(����) and ��=��������(����) in its simplistic form. Others have studied these curves and their applications like Nathaniel Bowditch in 1815, and they are often referred to as Bowditch curves as well. Lissajous curves are found in engineering, mathematics, graphic design, physics, and many other backgrounds. In this project entitled “Parametric Art” this project will focus on analyzing these types of equations and manipulating them to create art. We will be investigating these curves by answering a series of questions that elucidate their purpose. Using Maple, which …
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. …
Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya
Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya
Department of Mathematics Facuty Scholarship and Creative Works
Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way to arrange information so …
A Mathematical Model Of Speeding, Jared Ott, Xavier Pérez Giménez
A Mathematical Model Of Speeding, Jared Ott, Xavier Pérez Giménez
Honors Theses
Crime is often regarded as nonsensical, impulsive, and irrational. These conjectures are pointed, though conversation about the pros and cons of crime does not happen often. People point to harsh fines, jail times, and life restrictions as their reason for judgement, stating that the trade-offs are far too unbalanced to participate in illicit activity. Yet, everyday people commit small crimes, sometimes based on hedonistic desires, other times based on a rational thought process.
Speeding seems to be one of those that almost all people commit at least once during their life. Our work hopes to make an incremental improvement on …
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.
Motion Planning For Educational Robots, Ronald I. Greenberg, Jeffery M. Karp
Motion Planning For Educational Robots, Ronald I. Greenberg, Jeffery M. Karp
Ronald Greenberg
This paper considers various simple ways of navigating in a 2-dimensional territory with a two-wheeled robot of a type typical in educational robotics. We determine shortest paths under various modes of operation and compare.
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 …
Creating Art Patterns With Math And Code, Boyan Kostadinov
Creating Art Patterns With Math And Code, Boyan Kostadinov
Publications and Research
The goal of this talk is to showcase some visualization projects that we developed for a 3-day Code in R summer program, designed to inspire the creative side of our STEM students by engaging them with computational projects that we developed with the purpose of mixing calculus level math and code to create complex geometric patterns. One of the goals of this program was to attract more minority and female students into applied math and computer science majors.
The projects are designed to be implemented using the high-level, open-source and free computational environment R, a popular software in industry for …
Catching Card Counters, Sarah French
Catching Card Counters, Sarah French
Honors Projects in Mathematics
The casino industry has been researched through a variety of disciplines including psychological gambling habits, technological advances, business strategies, and mathematical simulations. In the vast number of studies that have been conducted, there are few scholarly articles that focus on the specific aspect of card counting. The majority of games in the casino are designed to favor the “house”. This study focuses on the game of blackjack, in which players using a card counting strategy can tip the odds in their favor. A computer simulation was used to model the betting strategy of a card counter who would bet methodically. …
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 …
Collected Papers, Vol. V, Florentin Smarandache
Collected Papers, Vol. V, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Multiple Periodic Solutions For A Nonlinear Suspension Bridge Equation, Lisa Humphreys, P. Mckenna
Multiple Periodic Solutions For A Nonlinear Suspension Bridge Equation, Lisa Humphreys, P. Mckenna
Lisa D Humphreys
We investigate nonlinear oscillations in a fourth-order partial differential equation which models a suspension bridge. Previous work establishes multiple periodic solutions when a parameter exceeds a certain eigenvalue. In this paper, we use Leray Schauder degree theory to prove that if the parameter is increased further, beyond a second eigenvalue, then additional solutions are created.
An Amazing Mathematical Card Trick, Arthur T. Benjamin
An Amazing Mathematical Card Trick, Arthur T. Benjamin
All HMC Faculty Publications and Research
A magician gives a member of the audience 20 cards to shuffle. After the cards are thoroughly mixed, the magician goes through the deck two cards at a time, sometimes putting the two cards face to face, sometimes back to back, and sometimes in the same direction. Before dealing each pair of cards into a pile, he asks random members of the audience if the pair should be flipped over or not. He goes through the pile again four cards at a time and before each group of four is dealt to a pile, the audience gets to decide whether …
A Unifying Field In Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability And Statistics - 6th Ed., Florentin Smarandache
A Unifying Field In Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability And Statistics - 6th Ed., Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) “neutrosophy” – study of neutralities as an extension of dialectics; b) and its derivative “neutrosophic”, such as “neutrosophic logic”, “neutrosophic set”, “neutrosophic probability”, and “neutrosophic statistics” and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics. It was known to me his setting up in …
Collected Papers Vol. 1, Florentin Smarandache
Collected Papers Vol. 1, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Collected Papers Vol. Iii, Florentin Smarandache
Collected Papers Vol. Iii, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Collected Papers, Vol. 2, Florentin Smarandache
Collected Papers, Vol. 2, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache
Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.