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Barrett, The Honors College Thesis/Creative Project Collection


Barrett, the Honors College accepts high performing, academically engaged students and works with them in collaboration with all of the other academic units at Arizona State University. All Barrett students complete a thesis or creative project, supervised and defended in front of a faculty committee. The thesis or creative project allows students to explore an intellectual interest and produce an original piece of scholarly research. The thesis or creative project is a student’s opportunity to explore areas of academic interest with greater intensity than is possible in a single course. It is also an opportunity to engage with professors, nationally recognized in their fields and specifically interested and committed to working with honors students. This work provides tangible evidence of a student’s research, writing and creative skills to graduate schools and/or prospective employers.


Date Range
2012 2018


A Guide to Financial Mathematics is a comprehensive and easy-to-use study guide for students studying for the one of the first actuarial exams, Exam FM. While there are many resources available to students to study for these exams, this study is free to the students and offers an approach to the material similar to that of which is presented in class at ASU. The guide is available to students and professors in the new Actuarial Science degree program offered by ASU. There are twelve chapters, including financial calculator tips, detailed notes, examples, and practice exercises. Included at the end of ...

Contributors
Dougher, Caroline Marie, Milovanovic, Jelena, Boggess, May, et al.
Created Date
2015-05

A semi-implicit, fourth-order time-filtered leapfrog numerical scheme is investigated for accuracy and stability, and applied to several test cases, including one-dimensional advection and diffusion, the anelastic equations to simulate the Kelvin-Helmholtz instability, and the global shallow water spectral model to simulate the nonlinear evolution of twin tropical cyclones. The leapfrog scheme leads to computational modes in the solutions to highly nonlinear systems, and time-filters are often used to damp these modes. The proposed filter damps the computational modes without appreciably degrading the physical mode. Its performance in these metrics is superior to the second-order time-filtered leapfrog scheme developed by Robert ...

Contributors
Burke, Lee Matthew Moore, Moustaoui, Mohamed, Kostelich, Eric, et al.
Created Date
2016-05

A numerical study of wave-induced momentum transport across the tropopause in the presence of a stably stratified thin inversion layer is presented and discussed. This layer consists of a sharp increase in static stability within the tropopause. The wave propagation is modeled by numerically solving the Taylor-Goldstein equation, which governs the dynamics of internal waves in stably stratified shear flows. The waves are forced by a flow over a bell shaped mountain placed at the lower boundary of the domain. A perfectly radiating condition based on the group velocity of mountain waves is imposed at the top to avoid artificial ...

Contributors
Cole, Alexandra Shea, Moustaoui, Mohamed, Kostelich, Eric, et al.
Created Date
2017-05

My Barrett Honors Thesis Paper synthesizes three components of my Thesis Project, which demonstrates the process of developing strong research from the beginning stage of investigation of a problem to implementation of an intervention to address that problem. Specifically, I engaged in research on the topic of mathematics and students with autism spectrum disorders (ASD). My review of the literature demonstrated a current dearth in the knowledge on effective interventions in math for this population of students. As part of my project, I developed and implemented an intervention to address the problem and help improve the knowledge base in the ...

Contributors
Cleary, Shannon Taylor, Barnett, Juliet, Farr, Wendy, et al.
Created Date
2015-12

Pierre de Fermat, an amateur mathematician, set upon the mathematical world a challenge so difficult it took 357 years to prove. This challenge, known as Fermat's Last Theorem, has many different ways of being expressed, but it simply states that for $n > 2$, the equation $x^n + y^n = z^n$ has no nontrivial solution. The first set of attempts of proofs came from mathematicians using the essentially elementary tools provided by number theory: the notable mathematicians were Leonhard Euler, Sophie Germain and Ernst Kummer. Kummer was the final mathematician to try to use essentially elementary number theory as the ...

Contributors
Boyadjian, Hoveeg Krikor, Bremner, Andrew, Jones, John, et al.
Created Date
2016-12

Mathematics education, defined briefly by both students’ understanding and teacher instruction, is a cause for concern in the United States. A 1998 comprehensive study conducted by The Third International Mathematics and Science Study (TIMSS) shows that preadolescent mathematics education is comparatively less effective in this country than it is in other countries. The purposes of the present investigation were to understand why mathematics education has its short-comings in the United States, to analyze the most effective ways to help middle grade students learn mathematics, and to examine instructional methods for improving student understanding. The focus is on effective instructional methods ...

Contributors
Patel, Jay Narendra, Brass, Amber, White, Darcy, et al.
Created Date
2013-05

This paper focuses on the Szemerédi regularity lemma, a result in the field of extremal graph theory. The lemma says that every graph can be partitioned into bounded equal parts such that most edges of the graph span these partitions, and these edges are distributed in a fairly uniform way. Definitions and notation will be established, leading to explorations of three proofs of the regularity lemma. These are a version of the original proof, a Pythagoras proof utilizing elemental geometry, and a proof utilizing concepts of spectral graph theory. This paper is intended to supplement the proofs with background information ...

Contributors
Byrne, Michael John, Czygrinow, Andrzej, Kierstead, Hal, et al.
Created Date
2015-05

Cancer modeling has brought a lot of attention in recent years. It had been proven to be a difficult task to model the behavior of cancer cells, since little about the ”rules” a cell follows has been known. Existing models for cancer cells can be generalized into two categories: macroscopic models which studies the tumor structure as a whole, and microscopic models which focus on the behavior of individual cells. Both modeling strategies strive the same goal of creating a model that can be validated with experimental data, and is reliable for predicting tumor growth. In order to achieve this ...

Contributors
Han, Zimo, Motsch, Sebastien, Moustaoui, Mohamed, et al.
Created Date
2016-12

The dissipative shallow-water equations (SWE) possess both real-world application and extensive analysis in theoretical partial differential equations. This analysis is dominated by modeling the dissipation as diffusion, with its mathematical representation being the Laplacian. However, the usage of the biharmonic as a dissipative operator by oceanographers and atmospheric scientists and its underwhelming amount of analysis indicates a gap in SWE theory. In order to provide rigorous mathematical justification for the utilization of these equations in simulations with real-world implications, we extend an energy method utilized by Matsumura and Nishida for initial value problems relating to the equations of motion for ...

Contributors
Kofroth, Collin Michael, Jones, Don, Smith, Hal, et al.
Created Date
2017-05

Identifying associations between genotypes and gene expression levels using next-generation technology has enabled systematic interrogation of regulatory variation underlying complex phenotypes. Understanding the source of expression variation has important implications for disease susceptibility, phenotypic diversity, and adaptation (Main, 2009). Interest in the existence of allele-specific expression in autosomal genes evolved with the increased awareness of the important role that variation in non-coding DNA sequences can play in determining phenotypic diversity, and the essential role parent-of-origin expression has in early development (Knight, 2004). As new implications of high-throughput sequencing are conceived, it is becoming increasingly important to develop statistical methods tailored ...

Contributors
Malenica, Ivana, Craig, David, Rosenberg, Michael, et al.
Created Date
2012-12