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Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
How Reliable Are Shap Values When Trying To Explain Machine Learning Models, Jason Lawless
How Reliable Are Shap Values When Trying To Explain Machine Learning Models, Jason Lawless
Senior Honors Theses and Projects
With the rapid growth and application of machine learning and artificial intelligence models that can not be understood by humans, there is a growing movement calling for an increase in interpretability. There are numerous methods that attempt to explain these models that vary drastically in the process of evaluating models. In this paper, we investigate a local post-hoc method called SHAP. SHAP utilizes Shapley values from game theory to attribute an importance value to each input in a model at each datapoint. Shapley values can require significant computation time, especially as the number of inputs increases. In order to shorten …
Planning And Effects Of Equitable Teaching Practices In Emu Math 120 Class, Kyle Yapp
Planning And Effects Of Equitable Teaching Practices In Emu Math 120 Class, Kyle Yapp
Senior Honors Theses and Projects
The purpose of this project is to evaluate the effects of implementing Equitable Teaching practices in Math 120 Calculus 1. We used the EQUIP instrument in order to measure the amount of participation from each student. We used the X-PIPS-M instrument in order to get the students' responses to the class as well as have Dr. Ross reflect as a teacher. We used the MCOPP+ in order for Dr. Ross to reflect as a teacher. We also used the Calculus 1 Concept Inventory assessment in order to evaluate students' content knowledge growth during the course. We found that students responded …
Students’ Interpretations Of Categorical Data Using Dynamic Graphical Representations, Adam Eide
Students’ Interpretations Of Categorical Data Using Dynamic Graphical Representations, Adam Eide
Master's Theses and Doctoral Dissertations
Statistical association is an important concept in statistics. An exploratory study examined how students reason about statistical association utilizing graphical representations constructed with CODAP, a dynamic statistical graphing software. Task-based interviews were conducted with three 6th grade students prior to formal instruction. Students’ conceptions of a statistical relationship, proportional reasoning skill level, ability to interpret bivariate categorical graphs (particularly segmented bar graphs and two-way binned plots), and ability to identify association of two categorical variables were all investigated through interview tasks and responses to inquiry. Students were found to have developing proportional reasoning skills and struggled to correctly define and …
A Machine Learning Exploration Of Human Connectome Data, Katrina Prantzalos
A Machine Learning Exploration Of Human Connectome Data, Katrina Prantzalos
Senior Honors Theses and Projects
The intent of this project is to statistically examine the relationships between psychological traits, demographics, and physiological information provided by various brain scans. The Human Connectome Project dataset includes brain imaging data, demographics, and psychological data, from 1,206 individuals. Using this data, we performed exploratory data analysis, including an investigation of the distinctions in connectome data across participants with anxiety and/or depression as opposed to those without. Our aim was to predict the two mental disorders from given data via machine learning techniques such as Random Forest and Boosted Trees methods. Unfortunately, we were unable to reasonably predict anxiety or …
The Effects Of Gender And Ethnicity On Students' Perceptions Of Small-Group Learning In Collegiate Mathematics Courses, Layla Potts
Master's Theses and Doctoral Dissertations
Qualitative studies of students' perceptions on small-group work are limited, and few offer insights on the perceptions of women and minority students, for whom quantitative research suggests that small-group work is most beneficial. The aim of this research project is to conduct a qualitative analysis on the perceptions of women and minority students on their small-group learning experiences in collegiate mathematics courses. We conducted a Likert-scale survey of 114 Eastern Michigan University undergraduate students who were enrolled in a cross section of mathematics courses. The data were analyzed using statistical measures such as the frequency and modes of each response, …
Applications Of Laplace Transform, Andre Cocagne
Applications Of Laplace Transform, Andre Cocagne
Senior Honors Theses and Projects
Many students of the sciences who must have background in mathematics take courses up to, and including, differential equations. In this course, one of the topics covered is the Laplace transform. Coming to prominence in the late 20th century after being popularized by a famous electrical engineer, knowledge on how to do the Laplace transform has become a necessity for many fields. While it is discussed and examples are given of how it is used, none of its applications are explored in depth in a class like differential equations. As such, this project seeks to showcase some of the …
An Analysis Of Charles Fefferman's Proof Of The Fundamental Theorem Of Algebra, Kyle O. Linford
An Analysis Of Charles Fefferman's Proof Of The Fundamental Theorem Of Algebra, Kyle O. Linford
Senior Honors Theses and Projects
Many peoples' first exploration into more rigorous and formalized mathematics is with their early explorations in algebra. Much of their time and effort is dedicated to finding roots of polynomials-a challenge that becomes more increasingly difficult as the degree of the polynomials increases, especially if no real number roots exist. The Fundamental Theorem of Algebra is used to show that there exists a root, particularly a complex root, for any nth degree polynomial. After struggling to prove this statement for over 3 centuries, Carl Friedrich Gauss offered the first fairly complete proof of the theorem in 1799. Further proofs of …
Characterizing The Properties Of Specific Binomial Coefficients In Congruence Relations, Tyler Robert Russ
Characterizing The Properties Of Specific Binomial Coefficients In Congruence Relations, Tyler Robert Russ
Master's Theses and Doctoral Dissertations
The number theoretic conjecture we examine in this paper originates when trying to construct a characterizable generating set for the complex cobordism polynomial ring. To date there is no efficient, universal method for characterizing such a generating set. Wilfong conjectures that smooth projective toric varieties can act as these generators [7]. Toric varieties are related to polytopes by a bijective correspondence. Studying the combinatorial structure of these polytopes is much more manageable than studying properties of toric varieties directly. This gives rise to the number theoretic conjecture considered here. A proof of this number theoretic conjecture would in turn prove …
Image Reconstruction Through Polyfiltered Variation Minimization, Michael Hagen
Image Reconstruction Through Polyfiltered Variation Minimization, Michael Hagen
Master's Theses and Doctoral Dissertations
There has been considerable interest in reconstruction of remotely sensed imagery from incomplete frequency measurements for some time now. Given the nature of the collection process, it may be that portions of the spectrum are either missing or corrupted such that one is left with an incomplete representation of the original image. The advances in both the theory and available software for sparse signal reconstruction through function minimization make it an attractive approach for recreating the missing frequency data. It is the aim of this thesis to generalize the reconstruction technique known as Total Variation (TV) minimization from a signal …
Examining The Accuracy Of The Normal Approximation To The Poisson Random Variable, Wesley Jacob Rich
Examining The Accuracy Of The Normal Approximation To The Poisson Random Variable, Wesley Jacob Rich
Master's Theses and Doctoral Dissertations
Because the Poisson distribution is discrete, it is sometimes useful to use the continuous normal distribution as an approximation. In doing so, determining the accuracy of the approximation is important. Some issues of interest include: knowing how the error depends on the Poisson parameter, knowing when the approximation overestimates or underestimates the distribution, bounding the magnitude of the error, and determining if the approximation can be improved. This paper addresses these issues by examining how two types of absolute error measurements are affected by variations in the Poisson parameter; changes in the relative error are also examined. Generally, the error …
Problem Solving In The Fourth Grade Classroom, Lisa Lefevre
Problem Solving In The Fourth Grade Classroom, Lisa Lefevre
Senior Honors Theses and Projects
No abstract provided.
A Model For Radiation Interactions With Matter, Carrie Beck
A Model For Radiation Interactions With Matter, Carrie Beck
Senior Honors Theses and Projects
The intent of this project is to derive a realistic mathematical model for radiation interactions with matter. The model may be solved analytically, but I will also employ two computational methods, a finite difference method and a stochastic (Monte Carlo) method to gain insight into the physical process and to test the numerical techniques. Radiation interactions with matter constitute a large number of important scientific, industrial, and medical applications. This project will derive a model for the interaction of radiation with matter, which might allow one to compare different designs for shielding. It is also applicable in atmospheric physics in …