Physical Sciences and Mathematics Commons^™

Digital Game-Based Approach To Math Learning For Students, Gul Ayaz, Katherine Smith

Modeling, Simulation and Visualization Student Capstone Conference

Mathematics is an important subject that is pervasive across many disciplines. It is also a subject that has proven to be challenging to both teach and learn. Students face many challenges with learning math such as a lack of motivation and anxiety. To address these challenges, game-based learning has become a popular approach to stimulate students and create a more positive classroom environment. It can serve as an alternative or supplement to traditional teaching and can better engage students while developing a positive attitude toward learning. The use of games in a classroom can create a more exciting and engaging …

The History Of The Enigma Machine, Jenna Siobhan Parkinson

History Publications

The history of the Enigma machine begins with the invention of the rotor-based cipher machine in 1915. Various models for rotor-based cipher machines were developed somewhat simultaneously in different parts of the world. However, the first documented rotor machine was developed by Dutch naval officers in 1915. Nonetheless, the Enigma machine was officially invented following the end of World War I by Arthur Scherbius in 1918 (Faint, 2016).

Applying Expansive Framing To An Integrated Mathematics-Computer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway

Publications

In this research report for the National Council of Teachers of Mathematics 2022 Research Conference, we discuss the theory of Expansive Framing and its application to an interdisciplinary mathematics-computer science curricular unit.

A Computer Programming Intervention For Second Grade Math Students, Eric B. Bagley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The multiplication algorithms taught to elementary students are made to help students find answers quickly, but why the algorithm works and how it relates to multiplication is not widely known. For example, one intuitive meaning of multiplication is that of iterated, or, repeated, addition. In this paper, we look at the ways a visual, block-based, programming activity uses the concept of iteration to help second-graders learn multiplication. The results of the study observing second-grade students use visual programming and iteration to setup and solve multiplication story problems. We found that generally students enjoyed these activities and found them helpful during …

The Executive’S Guide To Getting Ai Wrong, Jerrold Soh

Asian Management Insights

It’s all math. Really.

A New Metaphor: How Artificial Intelligence Links Legal Reasoning And Mathematical Thinking, Melissa E. Love Koenig, Colleen Mandell

Marquette Law Review

Artificial intelligence’s (AI’s) impact on the legal community expands exponentially each year. As AI advances, lawyers have more powerful tools to enhance their ability to research and analyze the law, as well as to draft contracts and other legal documents. Lawyers are already using tools powered by AI and are learning to shift their methodologies to take advantage of these enhancements. To continue to grow into their shifting role, lawyers should understand the relationship between AI, mathematics, and legal reasoning.

Local-Global Results On Discrete Structures, Alexander Lewis Stevens

Electronic Theses and Dissertations

Local-global arguments, or those which glean global insights from local information, are central ideas in many areas of mathematics and computer science. For instance, in computer science a greedy algorithm makes locally optimal choices that are guaranteed to be consistent with a globally optimal solution. On the mathematical end, global information on Riemannian manifolds is often implied by (local) curvature lower bounds. Discrete notions of graph curvature have recently emerged, allowing ideas pioneered in Riemannian geometry to be extended to the discrete setting. Bakry- Émery curvature has been one such successful notion of curvature. In this thesis we use combinatorial …

Fourth-Dimensional Education In Virtual Reality, Jesse P. Hamlin-Navias

Senior Projects Spring 2022

This project was driven by an interest in mathematics, visualization, and the budding field of virtual reality. The project aimed to create virtual reality software to allow users to interact and play with three-dimensional representations of four-dimensional objects. The chosen representation was a perspective projection. Much like three-dimensional shapes cast two-dimensional shadows, four-dimensional shapes cast three-dimensional shadows. Users of the software developed in this project could interact and experiment with these three-dimensional shadows using hand controlled inputs. The hypothesis put forward is that virtual reality is currently the best medium to teach three-dimensional and four-dimensional geometry.

Highlights Generation For Tennis Matches Using Computer Vision, Natural Language Processing And Audio Analysis, Alon Liberman

Senior Independent Study Theses

This project uses computer vision, natural language processing and audio analysis to automatize the highlights generation task for tennis matches. Computer vision techniques such as camera shot detection, hough transform and neural networks are used to extract the time intervals of the points. To detect the best points, three approaches are used. Point length suggests which points correspond to rallies and aces. The audio waves are analyzed to search for the highest audio peaks, which indicate the moments where the crowd cheers the most. Sentiment analysis, a natural language processing technique, is used to look for points where the commentators …

Stroke Clustering And Fitting In Vector Art, Khandokar Shakib

Senior Independent Study Theses

Vectorization of art involves turning free-hand drawings into vector graphics that can be further scaled and manipulated. In this paper, we explore the concept of vectorization of line drawings and study multiple approaches that attempt to achieve this in the most accurate way possible. We utilize a software called StrokeStrip to discuss the different mathematics behind the parameterization and fitting involved in the drawings.

On Implementing And Testing The Rsa Algorithm, Kien Trung Le

Senior Independent Study Theses

In this work, we give a comprehensive introduction to the RSA cryptosystem, implement it in Java, and compare it empirically to three other RSA implementations. We start by giving an overview of the field of cryptography, from its primitives to the composite constructs used in the field. Then, the paper presents a basic version of the RSA algorithm. With this information in mind, we discuss several problems with this basic conception of RSA, including its speed and some potential attacks that have been attempted. Then, we discuss possible improvements that can make RSA runs faster and more secure. On the …

Non-Local Approximation Properties, Kira Pierce

Fall Showcase for Research and Creative Inquiry

This project concerns the approximation properties of a given set where X is a scattered sequence and Ï•(x) = 1/x* ln(1 + x^2 ). Similar approximation sets are commonly used in interpolation problems and are especially helpful due to their Fourier representation. For our work, we will work to prove the following theorem.

Excursions In Summation, Brock Erwin

Fall Showcase for Research and Creative Inquiry

Using polynomials from series representation of functions to approximate other functions on the closed interval from [-1,1].

Computational Thinking In Mathematics And Computer Science: What Programming Does To Your Head, Al Cuoco, E. Paul Goldenberg

Journal of Humanistic Mathematics

How you think about a phenomenon certainly influences how you create a program to model it. The main point of this essay is that the influence goes both ways: creating programs influences how you think. The programs we are talking about are not just the ones we write for a computer. Programs can be implemented on a computer or with physical devices or in your mind. The implementation can bring your ideas to life. Often, though, the implementation and the ideas develop in tandem, each acting as a mirror on the other. We describe an example of how programming and …

Cross-Model Parameter Estimation In Epidemiology, Julia R. Fitzgibbons

Honors Theses and Capstones

No abstract provided.

Statistical And Machine Learning Approaches To Depressive Disorders Among Adults In The United States: From Factor Discovery To Prediction Evaluation, Minhwa Lee

Senior Independent Study Theses

According to the National Institutes of Mental Health (NIMH), depressive disorders (or major depression) are considered one of the most common and serious health risks in the United States. Our study focuses on extracting non-medical factors of depressive disorders diagnosis, such as overall health states, health risk behaviors, demography, and healthcare access, using the Behavioral Risk Factor Surveillance System (BRFSS) data set collected by the Centers for Disease Control and Prevention (CDC) in 2018.

We set the two objectives of our study about depressive disorders diagnosis in the United States as follows. First, we aim to utilize machine learning algorithms …

Computational Simulation And Analysis Of Neuroplasticity, Madison E. Yancey

Browse all Theses and Dissertations

Homeostatic synaptic plasticity is the process by which neurons alter their activity in response to changes in network activity. Neuroscientists attempting to understand homeostatic synaptic plasticity have developed three different mathematical methods to analyze collections of event recordings from neurons acting as a proxy for neuronal activity. These collections of events are from control data and treatment data, referring to the treatment of neuron cultures with pharmacological agents that augment or inhibit network activity. If the distribution of control events can be functionally mapped to the distribution of treatment events, a better understanding of the biological processes underlying homeostatic synaptic …

Virtual Temari: Artistically Inspired Mathematics, Carl Giuffre, Lee Stemkoski

Journal of Humanistic Mathematics

Technology can be a significant aide in understanding and appreciating geometry, beyond theoretical considerations. Both fiber art and technology have been employed as a significant aide and an inspiring vessel in education to explore geometry. The Japanese craft known as temari, or "hand-balls", combines important artistic, spiritual, and familial values, and provides one such approach to exploring geometry. Mathematically, the artwork of temari may be classified based on whether they are inspired by polyhedra and discrete patterns or by periodic functional curves. The resulting designs of these categories provide an ancient vantage for displaying spherical patterns. We illustrate a …

Fern Or Fractal... Or Both?, Christina Babcock

Research and Scholarship Symposium Posters

Fractals are series of self similar sets and can be found in nature. After researching the Barnsley Fern and the iterated function systems using to create the fractal, I was able to apply what I learned to create a fractal shell. This was done using iterated function systems, matrices, random numbers, and Python coding.

A Cool Brisk Walk Through Discrete Mathematics, Stephen Davies

Computer Science Articles

A Cool Brisk Walk Through Discrete Mathematics - and its companion site "allthemath" - are completely-and-forever-free-and-open-source educational materials dedicated to the mathematics that budding computer science practitioners actually need to know. They feature the fun and addictive teaching of award-winning lecturer Dr. Stephen Davies of the University of Mary Washington in Fredericksburg, Virginia!

A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler

Senior Independent Study Theses

Santorini is a two player combinatorial board game. Santorini bears resemblance to the graph theory game of Geography, a game of moving and deleting vertices on a graph. We explore Santorini with game theory, complexity theory, and artificial intelligence. We present David Lichtenstein’s proof that Geography is PSPACE-hard and adapt the proof for generalized forms of Santorini. Last, we discuss the development of an AI built for a software implementation of Santorini and present a number of improvements to that AI.

The Knapsack Subproblem Of The Algorithm To Compute The Erdos-Selfridge Function, Brianna Sorenson

Undergraduate Honors Thesis Collection

This thesis summarizes the methodology of a new algorithm to compute the Erdos-Selfridge function which uses a wheel sieve, shows that a knapsack algorithm can be used to minimize the work needed to compute these values by selecting a subset of rings for use in the wheel, and compares the results of several different knapsack algorithms in this particular scenario.

Cheat Detection Using Machine Learning Within Counter-Strike: Global Offensive, Harry Dunham

Senior Independent Study Theses

Deep learning is becoming a steadfast means of solving complex problems that do not have a single concrete or simple solution. One complex problem that fits this description and that has also begun to appear at the forefront of society is cheating, specifically within video games. Therefore, this paper presents a means of developing a deep learning framework that successfully identifies cheaters within the video game CounterStrike: Global Offensive. This approach yields predictive accuracy metrics that range between 80-90% depending on the exact neural network architecture that is employed. This approach is easily scalable and applicable to all types of …

Predicting Stag And Hare Hunting Behaviors Using Hidden Markov Model, Rex Bringula, Ma. Mercedes T. Rodrigo

Department of Information Systems & Computer Science Faculty Publications

In this paper, we used Hidden Markov Model (HMM) to describe the gaming behaviors of students and whether they will exhibit “stag” or “hare” hunting behavior in a mobile game for mathematics learning. We found that there is a 99% probability that the students will stay either as stag or hare hunters. Our results also suggest that they would choose arithmetic problems involving addition. These game behaviors are not beneficial to learning because they are only exhibiting mathematical skills they already know. The results of the study show that stag and hare hunters have unique traits that separate the one …

Nonsupereulerian Graphs With Large Size, Paul A. Catlin, Zhi-Hong Chen

Zhi-Hong Chen

No abstract provided.

Data Mining And Machine Learning To Improve Northern Florida’S Foster Care System, Daniel Oldham, Nathan Foster, Mihhail Berezovski

Beyond: Undergraduate Research Journal

The purpose of this research project is to use statistical analysis, data mining, and machine learning techniques to determine identifiable factors in child welfare service records that could lead to a child entering the foster care system multiple times. This would allow us the capability of accurately predicting a case’s outcome based on these factors. We were provided with eight years of data in the form of multiple spreadsheets from Partnership for Strong Families (PSF), a child welfare services organization based in Gainesville, Florida, who is contracted by the Florida Department for Children and Families (DCF). This data contained a …

Integrating Mathematics And Educational Robotics: Simple Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal, Sara T. Greenberg

George K. Thiruvathukal

This paper shows how students can be guided to integrate elementary mathematical analyses with motion planning for typical educational robots. Rather than using calculus as in comprehensive works on motion planning, we show students can achieve interesting results using just simple linear regression tools and trigonometric analyses. Experiments with one robotics platform show that use of these tools can lead to passable navigation through dead reckoning even if students have limited experience with use of sensors, programming, and mathematics.

Using Neural Networks To Classify Pdes, Julia Balukonis, Sabrina Fuller, Haley Rosso

Mathematics & Computer Science Student Scholarship

Major: Mathematics
Minor: Computer Science and Film

Faculty Mentor: Dr. Lynette Boos, Mathematics and Computer Science

We designed two neural networks that can learn how to classify three different types of partial differential equations (PDEs). Our data consists of numerical solutions to three categories of PDEs: Burger’s, Diffusion, and Transport equations. Using TensorFlow and the Keras library, we performed two tasks – the first a binary classification of Burger’s and Diffusion equation data, and the second a multi-label classification incorporating the Transport Equations as well. Our binary classification network requires vector labels to perform efficiently. Furthermore, our tertiary classification network …

Interview Of Stephen Andrilli, Ph.D., Stephen Francis Andrilli Ph.D., Jane Highley

All Oral Histories

Stephen Francis Andrilli was born in August 1952 in Bryn Mawr, PA. He was born to Francis and Leatrice Andrilli. Dr. Andrilli is the oldest of four children; his three sisters are Carol (now Carol Strosser), Patricia (now Patricia Kempczynski), and Barbara (now Barbara Parkes). Aside from a few years of living in Gettysburg, Dr. Andrilli has lived in the Philadelphia area for most of his life. He attended St. Jerome School, where he finished 8th grade. He then attended LaSalle College High School, where he graduated in 1969 at age 16. He entered La Salle University (formerly La Salle …

Integrating Mathematics And Educational Robotics: Simple Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal, Sara T. Greenberg

Computer Science: Faculty Publications and Other Works

This paper shows how students can be guided to integrate elementary mathematical analyses with motion planning for typical educational robots. Rather than using calculus as in comprehensive works on motion planning, we show students can achieve interesting results using just simple linear regression tools and trigonometric analyses. Experiments with one robotics platform show that use of these tools can lead to passable navigation through dead reckoning even if students have limited experience with use of sensors, programming, and mathematics.