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Gibbon's Guides: The Scholarly Reception Of Ammianus Marcellinus And Procopius Of Caesarea After The Decline And Fall Of The Roman Empire, Sarah J. Murtaugh

Scripps Senior Theses

This thesis explores the influence of Edward Gibbon's History of the Decline and Fall of the Roman Empire on modern scholarship about two ancient Roman historians, Ammianus Marcellinus and Procopius of Caesarea. It reveals that Gibbon's way of thinking about these historians, whom he referred to as his "guides," continues to shape scholarly discourse about them.

Working Title, Nathanael Thomas Little

CGU MFA Theses

(Working Title) is an exploration into the interaction of the idea spaces of installation art and the theme park, through Nate Little's narrative environment of Arboria. Plush Characters populate an environment that fills the gallery space.

Research, Character And Performance Process To Play The Role Of Eva In The Pomona College Theatre Department Fall 2012 Production Of Kindertransport, A Play By Diane Samuels, Roxanne D. Cook

Pitzer Senior Theses

This thesis paper presents the research and character development process that I undertook to play the role of Eva, in the Pomona College Fall 2012 production of Diane Samuels’ award winning play, Kindertransport. In the ten-months prior to the 1938 outbreak of World War II, nearly 10,000 predominately Jewish children from Germany, Austria, Czechoslovakia, and Poland were evacuated to Great Britain to escape the looming Holocaust. The program was given the name, Kindertransport (children’s transports) by German railway officials because only unaccompanied children under the age of 17 were allowed to leave. Once the Kinder arrived in England, host families …

Dab Shunt Spoor, Jen Grabarczyk

CGU MFA Theses

My work functions as an act of bearing witness. In it, I process consciousness, memory, narrative and time through the choreographed integration of cerebral representations and bodily movement. Through forms both strange and elegant, I seek to activate a viewer’s memory and consciousness–psychologically and corporeally.

From Profane To Divine: The Hegemonic Appropriation Of Pagan Imagery Into Eastern Christian Hymnody, Jordan Lippert

Scripps Senior Theses

Spanning the first seven centuries of Christianity, this paper explores how Eastern Christian and Byzantine hymn chant was developed alongside pagan and Jewish worship traditions around the Near East. Comparison of hymns by Christian composers such as St. Romanos the Melodist and pagan poetry reveals many similarities in the types of metaphorical imagery used in both religious expressions. Common in Christian hymn texts, well-known metaphors, like the “Light of God,” are juxtaposed with pagan mythological gods, such as Apollo and Helios. This paper attempts to explain how and why Christians appropriated and adopted ancient pagan imagery into the burgeoning musical …

A Refined Saddle Point Theorem And Applications, Harris Enniss

HMC Senior Theses

Under adequate conditions on $g$, we show the density in $L^2((0,\pi),(0,2\pi))$ of the set of functions $p$ for which \begin{equation*} u_{tt}(x,t)-u_{xx}(x,t)= g(u(x,t)) + p(x,t) \end{equation*} has a weak solution subject to \begin{equation*} \begin{aligned} u(x,t)&=u(x,t+2\pi)\\ u(0,t)&=u(\pi,t)=0. \end{aligned} \end{equation*}

To achieve this, we prove a Saddle Point Principle by means of a refined variant of the deformation lemma of Rabinowitz.

Generally, inf-sup techniques allow the characterization of critical values by taking the minimum of the maximae on some particular class of sets. In this version of the Saddle Point Principle, we introduce sufficient conditions for the existence of a saddle-structure which is …

Approval Voting Theory With Multiple Levels Of Approval, Craig Burkhart

HMC Senior Theses

Approval voting is an election method in which voters may cast votes for as many candidates as they desire. This can be modeled mathematically by associating to each voter an approval region: a set of potential candidates they approve. In this thesis we add another level of approval somewhere in between complete approval and complete disapproval. More than one level of approval may be a better model for a real-life voter's complex decision making. We provide a new definition for intersection that supports multiple levels of approval. The case of pairwise intersection is studied, and the level of agreement among …

Analysis Of Swarm Behavior In Two Dimensions, Louis Ryan

HMC Senior Theses

We investigate the steady state solutions that can exist for a two dimensional swarm of biological organisms, which have pairwise social interaction forces. The three steady states we investigate using a continuum model are a ribbon migrating swarm, a circular migrating swarm, and a milling swarm. We solve these numerically by reformulating the integral equation that arises from the continuum model as an energy minimization problem. For the ribbon migrating solution, we are able to determine an analytic solution from Carleman's equation which arises after an asymptotic expansion of the social interaction potential. Using this technique we are able to …

Gromov-Witten Theory Of Blowups Of Toric Threefolds, Dhruv Ranganathan

HMC Senior Theses

We use toric symmetry and blowups to study relationships in the Gromov-Witten theories of $\mathbb{P}^3$ and $\mathbb{P}^1\!\times\!\mathbb{P}^1\!\times\!\mathbb{P}^1$. These two spaces are birationally equivalent via the common blowup space, the permutohedral variety. We prove an equivalence of certain invariants on blowups at only points of $\mathbb{P}^3$ and $\mathbb{P}^1\!\times\!\mathbb{P}^1\!\times\!\mathbb{P}^1$ by showing that these invariants descend from the blowup. Further, the permutohedral variety has nontrivial automorphisms of its cohomology coming from toric symmetry. These symmetries can be forced to descend to the blowups at just points of $\mathbb{P}^3$ and $\mathbb{P}^1\!\times\!\mathbb{P}^1\!\times\!\mathbb{P}^1$. Enumerative consequences are discussed.

Flatterland: The Play, Kym Louie

HMC Senior Theses

This script is an adaptation of the popular science novel Flatterland: Like Flatland, Only More So by Ian Stewart. It brings new life to mathematical ideas and topics. By bringing math to the stage, concepts are presented in a more friendly and accessible manner. This play is intended to generate new interest in and expose new topics to an audience of nonmathematicians.

Counting Vertices In Isohedral Tilings, John Choi

HMC Senior Theses

An isohedral tiling is a tiling of congruent polygons that are also transitive, which is to say the configuration of degrees of vertices around each face is identical. Regular tessellations, or tilings of congruent regular polygons, are a special case of isohedral tilings. Viewing these tilings as graphs in planes, both Euclidean and non-Euclidean, it is possible to pose various problems of enumeration on the respective graphs. In this paper, we investigate some near-regular isohedral tilings of triangles and quadrilaterals in the hyperbolic plane. For these tilings we enumerate vertices as classified by number of edges in the shortest path …

Russian Mathematical Pedagogy In Reasoning Mind, Maia Valcarce

HMC Senior Theses

Reasoning Mind (RM) incorporates aspects of Russian mathematics pedagogy and curricula into its online math program. Our investigation identifies typical attributes of Russian pedagogy discussed in news articles and publications by Russian education experts, then determines how these attributes arise in RM. Analysis of RM's implementation of the characteristics reveals more successful inclusion of curricular attributes than classroom strategies. Thus, we outline classroom techniques that could be assimilated into RM to provide a more Russian learning experience along with students' exposure to Russian-style curricula.

Nonlinear Wave Equations And Solitary Wave Solutions In Mathematical Physics, Trevor Caldwell

HMC Senior Theses

In this report, we study various nonlinear wave equations arising in mathematical physics and investigate the existence of solutions to these equations using variational methods. In particular, we look for particle-like traveling wave solutions known as solitary waves. This study is motivated by the prevalence of solitary waves in applications and the rich mathematical structure of the nonlinear wave equations from which they arise. We focus on a semilinear perturbation of Maxwell's equations and the nonlinear Klein - Gordon equation coupled with Maxwell's equations. Physical ramifications of these equations are also discussed.

A Combinatorial Approach To $R$-Fibonacci Numbers, Curtis Heberle

HMC Senior Theses

In this paper we explore generalized “$r$-Fibonacci Numbers” using a combinatorial “tiling” interpretation. This approach allows us to provide simple, intuitive proofs to several identities involving $r$-Fibonacci Numbers presented by F.T. Howard and Curtis Cooper in the August, 2011, issue of the Fibonacci Quarterly. We also explore a connection between the generalized Fibonacci numbers and a generalized form of binomial coefficients.

Explorations Of The Aldous Order On Representations Of The Symmetric Group, Jack Newhouse

HMC Senior Theses

The Aldous order is an ordering of representations of the symmetric group motivated by the Aldous Conjecture, a conjecture about random processes proved in 2009. In general, the Aldous order is very difficult to compute, and the proper relations have yet to be determined even for small cases. However, by restricting the problem down to Young-Jucys-Murphy elements, the problem becomes explicitly combinatorial. This approach has led to many novel insights, whose proofs are simple and elegant. However, there remain many open questions related to the Aldous Order, both in general and for the Young-Jucys-Murphy elements.

Approval Voting In Box Societies, Patrick Eschenfeldt

HMC Senior Theses

Under approval voting, every voter may vote for any number of canditates. To model approval voting, we let a political spectrum be the set of all possible political positions, and let each voter have a subset of the spectrum that they approve, called an approval region. The fraction of all voters who approve the most popular position is the agreement proportion for the society. We consider voting in societies whose political spectrum is modeled by $d$-dimensional space ($\mathbb{R}^d$) with approval regions defined by axis-parallel boxes. For such societies, we first consider a Tur&#aacute;n-type problem, attempting to find the maximum …

Uniquely Solvable Puzzles And Fast Matrix Multiplication, Palmer Mebane

HMC Senior Theses

In 2003 Cohn and Umans introduced a new group-theoretic framework for doing fast matrix multiplications, with several conjectures that would imply the matrix multiplication exponent $\omega$ is 2. Their methods have been used to match one of the fastest known algorithms by Coppersmith and Winograd, which runs in $O(n^{2.376})$ time and implies that $\omega \leq 2.376$. This thesis discusses the framework that Cohn and Umans came up with and presents some new results in constructing combinatorial objects called uniquely solvable puzzles that were introduced in a 2005 follow-up paper, and which play a crucial role in one of the $\omega …

Searching Stars For A Moving Hider, Jennifer Iglesias

HMC Senior Theses

In a search game, a seeker searches for a hider in some space. The seeker wishes to find the hider as quickly as possible, and the hider wishes to avoid capture as long as possible. In this paper, I will focus on the case where the search space is a star, and the only information the seeker has is the speed of the hider. I will provide algorithms for some cases where the seeker is guaranteed to find the hider and prove optimality for some of these cases. Also, I will look at some cases where the hider can avoid …

Detecting Covert Members Of Terrorist Networks, Alice Paul

HMC Senior Theses

Terrorism threatens both international peace and security and is a national concern. It is believed that terrorist organizations rely heavily on a few key leaders and that destroying such an organization's leadership is essential to reducing its influence. Martonosi et al. (2011) argues that increasing the amount of communication through a key leader increases the likelihood of detection. If we model a covert organization as a social network where edges represent communication between members, we want to determine the subset of members to remove that maximizes the amount of communication through the key leader. A mixed-integer linear program representing this …

Algebraic Methods For Log-Linear Models, Aaron Pribadi

HMC Senior Theses

Techniques from representation theory (Diaconis, 1988) and algebraic geometry (Drton et al., 2008) have been applied to the statistical analysis of discrete data with log-linear models. With these ideas in mind, we discuss the selection of sparse log-linear models, especially for binary data and data on other structured sample spaces. When a sample space and its symmetry group satisfy certain conditions, we construct a natural spanning set for the space of functions on the sample space which respects the isotypic decomposition; these vectors may be used in algorithms for model selection. The construction is explicitly carried out for the case …

Switching Between Cooperation And Competition In Social Selection, August Guang

HMC Senior Theses

Roughgarden et al. (2006) proposed a theory called social selection as a behavioral game theoretic model for sexual reproduction that incorporates both competition and cooperation in 2006. Players oscillate between playing competitively to maximize their individual fitness, leading to a Nash Competitive Equilibrium, and playing cooperatively to maximize a team fitness function, leading to a Nash Bargaining Solution. Roughgarden et al. (2006) gives rates of change for both the competitive state and the cooperative state, but does not explain her rates or how to switch between the states in sufficient detail.

We test and rederive the rates, critiquing an assumption …

'I Am Rooted, But I Flow': Virginia Woolf And 20th Century Thought, Emily Lauren Hanna

Scripps Senior Theses

My thesis is about Virginia Woolf’s novels, Mrs. Dalloway, The Waves, and To the Lighthouse. I examine these novels in relation to the theories of Henri Bergson, William James, and Sigmund Freud, and the groundwork of Modernism. I relate Woolf's use of water imagery and stream of consciousness technique to Bergson’s theory of “la durée,” or psychological, subjective time, James’ “stream of consciousness” theory in psychology, and Freud’s theory of the “oceanic” feeling of religious experience.

Effects Of Method And Context Of Note-Taking On Memory: Handwriting Versus Typing In Lecture And Textbook-Reading Contexts, Ian Schoen

Pitzer Senior Theses

Both electronic note-taking (typing) and traditional note-taking (handwriting) are being utilized by college students to retain information. The effects of the method of note-taking and note-taking context were examined to determine if handwriting or typing notes and whether a lecture context or a textbook-reading context influenced retention. Pitzer College and Scripps College students were assigned to either handwrite or type notes on a piece of academic material presented in either a lecture or textbook context and were given a test to assess their retention. The results demonstrated that there was a significant main effect for typing notes such that typing …

Spelling Gratitude: An Aesthetic Exploration, Lily Anna Burgess

Scripps Senior Theses

This thesis is founded in the positive psychological theory of gratitude, the experience of thankfulness and its benefits on both the individual and the community. My explorations via personal journaling, careful reflection, and engaging in craft, led me to cultivate a new definition for gratitude: present moment awareness. Using sheer fabric and the meditative act of embroidering, the language of gratitude was relearned and cultivated. My piece aims to incite further explorations in thanks.

Educating For Environmental Literacy In America's Public Schools, Annie L. Stoller-Patterson

Pomona Senior Theses

This paper explores how education for environmental literacy can be integrated into America's public school system. It investigates the benefits of environmental education and how green school buildings, sustainable cafeterias, school gardens and environmental education curriculum can be used to teach for environmental literacy at all grade levels. Includes sample lesson plan.

Analysis Of Biodiesel Quality Using Reversed Phase High-Performance Liquid Chromatography, Kellyann M. Murphy

Pomona Senior Theses

The alternative fuel biodiesel is produced from the transesterification of vegetable oils or animal fat to fatty acid methyl esters. Pomona has a reactor on campus that can be used to run this reaction and produce biodiesel. The use of biodiesel has been found to lower air pollutant and greenhouse gas emissions, but can be potentially harmful to the engines if it contains impurities. This paper proposes a method using high-performance liquid chromatography to test the quality of biodiesel. This method utilizes instrumentation and materials that are available in Pomona College's Chemistry Department, requires very little sample preparation, and is …

Bikeurious: A Transportation Reorientation, Aerienne Russell

Pomona Senior Theses

Since a young age, I have been interested in bicycling as a form of fun and fanciful recreation, but it wasn’t until the summer of 2011 that a serious shift occurred in my understanding of the bike as more than a mere machine. A spontaneous 700-mile journey redefined my relationship with travel, transcended my notions of transportation, and enabled me to better mediate myself within my environment. In writing about these experiences, I hope to offer some insight into how American culture currently frames transportation and how I hope the construction of a bike positive culture can instill social, environmental, …

Walking Los Angeles, Zoe R. Carlberg

Pomona Senior Theses

This paper is about my experience walking through Los Angeles County. My principal motivations were to explore what it means to be a pedestrian in an urban landscape that generally does not recognize walkers and to give value to often overlooked spaces. The paper includes a brief history of the Los Angeles region, methodology, an analysis of some other art projects that have been done about walking, and a vignette of the experience.

The Full Cost Of Renewables: Managing Wind Integration Costs In California, William Savage

Pomona Senior Theses

Wind power will be an important component of California's aggressive strategies to meet its greenhouse gas reduction targets by the year 2020. However, the costs of integrating wind power's variable and uncertain output are often ignored. I argue that California must take prudent action to understand, minimize, and allocate wind integration costs. A review of numerous studies suggests that for wind penetration levels below 20%, integration costs should remain modest. However, costs are heavily dependent on market structure, and I suggest numerous ways that California can optimize its market design to manage wind integration costs.

Subverting Socialist Realism: Vasily Grossman's Marginal Heroes, Maria Karen Whittle

Pomona Senior Theses

Soviet writer Vasilii Grossman has been renowned in the West as a dissident author of Life and Fate, which multiple sources, including The New York Times have called "arguably the greatest Russian novel of the 20th century." Grossman, however, was not a dissident, but an official state writer attempting to publish for a Soviet audience. Grossman's work was criticized by Soviets as being "too Jewish", while Jewish scholars have called it "not Jewish enough." And, despite his modern critical acclaim, little scholarship on Grossman exists. In my thesis, I explore these paradoxes. I argue that Grossman attempts to reinterpret traditional …