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Articles 31 - 60 of 85
Full-Text Articles in Physical Sciences and Mathematics
Direct, Biomimetic Synthesis Of (+)-Artemone Via A Stereoselective, Organocatalytic Cyclization, Eric D. Nacsa, Brian C. Fielder, Shannon P. Wetzler, Veerasak Srisuknimit, Jonathan P. Litz, Mary J. Van Vleet, Kim Quach, David A. Vosburg
Direct, Biomimetic Synthesis Of (+)-Artemone Via A Stereoselective, Organocatalytic Cyclization, Eric D. Nacsa, Brian C. Fielder, Shannon P. Wetzler, Veerasak Srisuknimit, Jonathan P. Litz, Mary J. Van Vleet, Kim Quach, David A. Vosburg
All HMC Faculty Publications and Research
We present a four-step synthesis of (+)-artemone from (–)- linalool, featuring iminium organocatalysis of a doubly diastereoselective conjugate addition reaction. The strategy follows a proposed biosynthetic pathway, rapidly generates stereochemical complexity, uses no protecting groups, and minimizes redox manipulations.
Counting On R-Fibonacci Numbers, Arthur Benjamin, Curtis Heberle
Counting On R-Fibonacci Numbers, Arthur Benjamin, Curtis Heberle
All HMC Faculty Publications and Research
We prove the r-Fibonacci identities of Howard and Cooper using a combinatorial tiling approach.
Review: On Pairs Of Generalized And Hypergeneralized Projections In A Hilbert Space, Stephan Ramon Garcia
Review: On Pairs Of Generalized And Hypergeneralized Projections In A Hilbert Space, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
A Mathematician's Villanelle, Gizem Karaali
A Mathematician's Villanelle, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
The Cantor Trilogy, Harun Šiljak
The Cantor Trilogy, Harun Šiljak
Journal of Humanistic Mathematics
The Cantor trilogy is a mathematical dystopia featuring JHM as an important part of that world... at least to humans.
My Finite Field, Matthew Schroeder
My Finite Field, Matthew Schroeder
Journal of Humanistic Mathematics
A love poem written in the language of mathematics.
Prisoner's Dilemma, Raymond N. Greenwell
Prisoner's Dilemma, Raymond N. Greenwell
Journal of Humanistic Mathematics
No abstract provided.
Book Review: Love And Math: The Heart Of Hidden Reality By Edward Frenkel, Emily R. Grosholz
Book Review: Love And Math: The Heart Of Hidden Reality By Edward Frenkel, Emily R. Grosholz
Journal of Humanistic Mathematics
This review traces Edward Frenkel’s attempt to convey the excitement of mathematical research to a popular audience. In his expositions and explanations of his own research program, he shows how processes of mathematical discovery depend on the juxtaposition of various iconic and symbolic modes of representation as disparate fields of research are brought together in the service of problem solving. And he shows how crucial the encouragement of various older mathematicians was to his own development, as they guided his choice of problems, and served as inspiration.
Abscissas And Ordinates, David Pierce
Abscissas And Ordinates, David Pierce
Journal of Humanistic Mathematics
In the manner of Apollonius of Perga, but hardly any modern book, we investigate conic sections as such. We thus discover why Apollonius calls a conic section a parabola, an hyperbola, or an ellipse; and we discover the meanings of the terms abscissa and ordinate. In an education that is liberating and not simply indoctrinating, the student of mathematics will learn these things.
The Symbolic And Mathematical Influence Of Diophantus's Arithmetica, Cyrus Hettle
The Symbolic And Mathematical Influence Of Diophantus's Arithmetica, Cyrus Hettle
Journal of Humanistic Mathematics
Though it was written in Greek in a center of ancient Greek learning, Diophantus's Arithmetica is a curious synthesis of Greek, Egyptian, and Mesopotamian mathematics. It was not only one of the first purely number-theoretic and algebraic texts, but the first to use the blend of rhetorical and symbolic exposition known as syncopated mathematics. The text was influential in the development of Arabic algebra and European number theory and notation, and its development of the theory of indeterminate, or Diophantine, equations inspired modern work in both abstract algebra and computer science. We present, in this article, a selection of problems …
Love Games: A Game-Theory Approach To Compatibility, Kerstin Bever, Julie Rowlett
Love Games: A Game-Theory Approach To Compatibility, Kerstin Bever, Julie Rowlett
Journal of Humanistic Mathematics
In this note, we present a compatibility test with a rigorous mathematical foundation in game theory. The test must be taken separately by both partners, making it difficult for either partner alone to control the outcome. To introduce basic notions of game theory we investigate a scene from the film "A Beautiful Mind" based on John Nash's life and Nobel-prize-winning theorem. We recall this result and reveal the mathematics behind our test. Readers may customize and modify the test for more accurate results or to evaluate interpersonal relationships in other settings, not only romantic. Finally, we apply Dyson's and Press's …
On The Persistence And Attrition Of Women In Mathematics, Katrina Piatek-Jimenez
On The Persistence And Attrition Of Women In Mathematics, Katrina Piatek-Jimenez
Journal of Humanistic Mathematics
The purpose of this study was to investigate what motivates women to choose mathematics as an undergraduate major and to further explore what shapes their future career goals, paying particular attention to their undergraduate experiences and their perceptions of the role of gender in these decisions. A series of semi-structured, individual interviews were conducted with twelve undergraduate women mathematics majors who were attending either a large public university or a small liberal arts college. This study found that strong mathematical identities and enjoyment of mathematics heavily influenced their decisions to major in mathematics. At the career selection stage, these women …
Probing The Inverted Classroom: A Study Of Teaching And Learning Outcomes In Engineering And Mathematics, Nancy K. Lape, Rachel Levy, Darryl Yong
Probing The Inverted Classroom: A Study Of Teaching And Learning Outcomes In Engineering And Mathematics, Nancy K. Lape, Rachel Levy, Darryl Yong
All HMC Faculty Publications and Research
Flipped classrooms have started to become commonplace on university campuses. Despite the growing number of flipped courses, however, quantitative information on their effectiveness remains sparse. Active learning is a mode of instruction that focuses the responsibility of learning on learners. Multiple studies have shown that active learning leads to better student outcomes. Given that instructors in flipped classrooms are generally able to create more opportunities for students to apply or practice course material, we hypothesized that students in a flipped classroom would exhibit more learning compared to students in an unflipped class. This case study describes our research comparing …
Acceptance-Rejection Sampling With Hierarchical Models, Christian A. Ayala
Acceptance-Rejection Sampling With Hierarchical Models, Christian A. Ayala
CMC Senior Theses
Hierarchical models provide a flexible way of modeling complex behavior. However, the complicated interdependencies among the parameters in the hierarchy make training such models difficult. MCMC methods have been widely used for this purpose, but can often only approximate the necessary distributions. Acceptance-rejection sampling allows for perfect simulation from these often unnormalized distributions by drawing from another distribution over the same support. The efficacy of acceptance-rejection sampling is explored through application to a small dataset which has been widely used for evaluating different methods for inference on hierarchical models. A particular algorithm is developed to draw variates from the posterior …
The Future Of Ios Development: Evaluating The Swift Programming Language, Garrett Wells
The Future Of Ios Development: Evaluating The Swift Programming Language, Garrett Wells
CMC Senior Theses
Swift is a new programming language developed by Apple for creating iOS and Mac OS X applications. Intended to eventually replace Objective-C as Apple’s language of choice, Swift needs to convince developers to switch over to the new language. Apple has promised that Swift will be faster than Objective-C, as well as offer more modern language features, be very safe, and be easy to learn and use. In this thesis I test these claims by creating an iOS application entirely in Swift as well as benchmarking two different algorithms. I find that while Swift is faster than Objective-C, it does …
On The Characterization Of Prime Sets Of Polynomials By Congruence Conditions, Arvind Suresh
On The Characterization Of Prime Sets Of Polynomials By Congruence Conditions, Arvind Suresh
CMC Senior Theses
This project is concerned with the set of primes modulo which some monic, irreducible polynomial over the integers has a root, called the Prime Set of the polynomial. We completely characterise these sets for degree 2 polynomials, and develop sufficient machinery from algebraic number theory to show that if the Galois group of a monic, irreducible polynomial over the integers is abelian, then its Prime Set can be written as the union of primes in some congruence classes modulo some integer.
Compressive Sensing With Redundant Dictionaries And Structured Measurements, Felix Krahmer, Deanna Needell, Rachel Ward
Compressive Sensing With Redundant Dictionaries And Structured Measurements, Felix Krahmer, Deanna Needell, Rachel Ward
CMC Faculty Publications and Research
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary D. This problem is now understood to be well-posed and efficiently solvable under suitable assumptions on the measurements and dictionary, if the number of measurements scales roughly with the sparsity level. One sufficient condition for such is the D-restricted isometry property (D-RIP), which asks that the sampling matrix approximately preserve the norm of all signals which are sufficiently sparse in D. While many classes of random matrices are known to satisfy such conditions, such matrices …
One-Bit Compressive Sensing With Partial Support, Phillip North, Deanna Needell
One-Bit Compressive Sensing With Partial Support, Phillip North, Deanna Needell
CMC Faculty Publications and Research
The Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization, as is exemplified by the so-called one-bit compressed sensing framework which aims to recover a signal from measurements reduced to only their sign-bit. In applications, it is often the case that we have some knowledge of the structure of the signal beforehand, and thus would like to leverage it to attain more accurate and efficient recovery. This work explores avenues for incorporating such partial support information into the one-bit setting. Experimental results demonstrate that newly proposed methods of this work yield improved signal recovery …
On Lattices Generated By Finite Abelian Groups, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
On Lattices Generated By Finite Abelian Groups, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
CMC Faculty Publications and Research
This paper is devoted to the study of lattices generated by finite Abelian groups. Special species of such lattices arise in the exploration of elliptic curves over finite fields. In the case where the generating group is cyclic, they are also known as the Barnes lattices. It is shown that for every finite Abelian group with the exception of the cyclic group of order four these lattices have a basis of minimal vectors. Another result provides an improvement of a recent upper bound by M. Sha for the covering radius in the case of the Barnes lattices. Also discussed are …
Stability Of Ideal Lattices From Quadratic Number Fields, Lenny Fukshansky
Stability Of Ideal Lattices From Quadratic Number Fields, Lenny Fukshansky
CMC Faculty Publications and Research
We study semi-stable ideal lattices coming from real quadratic number fields. Specifically, we demonstrate infinite families of semi-stable and unstable ideal lattices of trace type, establishing explicit conditions on the canonical basis of an ideal that ensure stability; in particular, our result implies that an ideal lattice of trace type coming from a real quadratic field is semi-stable with positive probability. We also briefly discuss the connection between stability and well-roundedness of Euclidean lattices.
Height Bounds On Zeros Of Quadratic Forms Over Q-Bar, Lenny Fukshansky
Height Bounds On Zeros Of Quadratic Forms Over Q-Bar, Lenny Fukshansky
CMC Faculty Publications and Research
In this paper we establish three results on small-height zeros of quadratic polynomials over Q. For a single quadratic form in N ≥ 2 variables on a subspace of Q N , we prove an upper bound on the height of a smallest nontrivial zero outside of an algebraic set under the assumption that such a zero exists. For a system of k quadratic forms on an L-dimensional subspace of Q N , N ≥ L ≥ k(k+1) 2 + 1, we prove existence of a nontrivial simultaneous small-height zero. For a system of one or two inhomogeneous quadratic and …
Permutation Invariant Lattices, Lenny Fukshansky, Stephan Ramon Garcia, Xun Sun
Permutation Invariant Lattices, Lenny Fukshansky, Stephan Ramon Garcia, Xun Sun
CMC Faculty Publications and Research
We say that a Euclidean lattice in Rn is permutation invariant if its automorphism group has non-trivial intersection with the symmetric group Sn, i.e., if the lattice is closed under the action of some non-identity elements of Sn. Given a fixed element τ ∈ Sn, we study properties of the set of all lattices closed under the action of τ: we call such lattices τ-invariant. These lattices naturally generalize cyclic lattices introduced by Micciancio in [8, 9], which we previously studied in [1]. Continuing our investigation, we discuss some basic properties of permutation invariant lattices, in particular proving that the …
Spherical 2-Designs And Lattices From Abelian Groups, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
Spherical 2-Designs And Lattices From Abelian Groups, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
CMC Faculty Publications and Research
We consider lattices generated by finite Abelian groups. The main result says that such a lattice is strongly eutactic, which means the normalized minimal vectors of the lattice form a spherical 2-design, if and only if the group is of odd order or if it is a power of the group of order 2. This result also yields a criterion for the appropriately normalized minimal vectors to constitute a uniform normalized tight frame.
Ensuring Our Future Or Sowing The Seeds Of Our Own Destruction? Crop Insurance And Water Use In Texas, Michael Shapiro
Ensuring Our Future Or Sowing The Seeds Of Our Own Destruction? Crop Insurance And Water Use In Texas, Michael Shapiro
Pomona Senior Theses
Agriculture is the largest consumer of water in the United States. Policies that affect agriculture therefore have the potential to have a large effect on the overall use of water. Crop insurance is one such policy, which was found to significantly increase water use in the state of Texas. Much, but not all of this effect can be explained by an increase in planting density, and results vary widely by crop and by region.
Bridging The Blue-Green Divide: The Role Of Environmental Ngos In Tackling Environmental Problems In Taiwan, Yttrium Sua
Bridging The Blue-Green Divide: The Role Of Environmental Ngos In Tackling Environmental Problems In Taiwan, Yttrium Sua
Pomona Senior Theses
This thesis attempts to provide a brief historical outline of the environmental movement in Taiwan and the unique political situation that has directly affected how the movement has progressed. Thereafter, it looks at some examples of environmental disputes that have occurred in recent years, paying special attention to the ways the environmental movement has interacted with the government. This provides the background to frame the analysis, which will shed light on the reasons for the current state of distrust and antagonistic interactions between the environmental movement and the government. Finally, the thesis evaluates whether such interactions with the government is …
Reforestation, Renewal, And The Cost Of Coal: Opposing A Manichean Worldview In Central Appalachia, Elizabeth R. Hansen
Reforestation, Renewal, And The Cost Of Coal: Opposing A Manichean Worldview In Central Appalachia, Elizabeth R. Hansen
Pomona Senior Theses
Surface coal mining is a major form of land change and environmental degradation in Central Appalachia. Traditional mine reclamation iresults in unmanaged, unproductive grasslands that fail to mitigate many of the environmental costs of coal mining and are of minimal use to communities. Forestry reclamation is an alternative reclamation tactic that has the potential to address both environmental and socioeconomic concerns in Central Appalachia. A case study of Laurel Fork Mine in Eastern Kentucky is included.
Discovery Islands, Earth Islands: The Theory And Practice Of Island Imagery In Environmental Thought, Naomi A. Bosch
Discovery Islands, Earth Islands: The Theory And Practice Of Island Imagery In Environmental Thought, Naomi A. Bosch
Pomona Senior Theses
Earth Island is a core metaphor of activist thought often applied in Environmental Analysis and related fields as a tool for thinking about the planet’s limited resources. It puts forth the claim that if only we thought of the earth as more like an island, we would better understand our connectivity to other living things and be drawn to develop better and more extensive practices of environmental stewardship. This thesis uses personal accounts of environmental life philosophies and political practices collected from residents of the Discovery Islands in British Columbia as a site for analytical comparison between the theory and …
Looking Beyond Fossil Fuel Divestment: Combating Climate Change In Higher Education, Robin Xu
Looking Beyond Fossil Fuel Divestment: Combating Climate Change In Higher Education, Robin Xu
Pomona Senior Theses
The young fossil fuel divestment movement is altering the landscape of climate change activism on US campuses. Student-run divestment campaigns are now pushing for institutions of higher education to withdraw their investments from the top 200 public fossil fuel companies. Despite student fervor, however, divestment has remained a controversial tactic for combating climate change. The first half of this thesis examines the stated motives of a selection of institutions that have officially agreed or declined to divest, and investigates the hypothesis that pushing for divestment alone will not achieve broad success because it does not appeal to a wide enough …
Innovation Or Inundation: The Political Economy Of Sea Level Rise In The San Francisco Bay Area, Nicole Quilliam
Innovation Or Inundation: The Political Economy Of Sea Level Rise In The San Francisco Bay Area, Nicole Quilliam
Pomona Senior Theses
Sea levels are rising around the world due to climate change and the rise in greenhouse gas emissions causing an environmental climate crisis. This thesis paper analyzes how sea level rise is affecting the San Francisco Bay Area. It walks through the geographical factors contribute to more severe impacts of sea level rise, potential adaptation strategies, and discusses the economic impacts and political challenges of protecting communities from sea level rise.
Geographic Relevance For Travel Search: The 2014-2015 Harvey Mudd College Clinic Project For Expedia, Inc., Hannah Long
Geographic Relevance For Travel Search: The 2014-2015 Harvey Mudd College Clinic Project For Expedia, Inc., Hannah Long
Scripps Senior Theses
The purpose of this Clinic project is to help Expedia, Inc. expand the search capabilities it offers to its users. In particular, the goal is to help the company respond to unconstrained search queries by generating a method to associate hotels and regions around the world with the higher-level attributes that describe them, such as “family- friendly” or “culturally-rich.” Our team utilized machine-learning algorithms to extract metadata from textual data about hotels and cities. We focused on two machine-learning models: decision trees and Latent Dirichlet Allocation (LDA). The first appeared to be a promising approach, but would require more resources …