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Articles 1141 - 1170 of 2640

Full-Text Articles in Physical Sciences and Mathematics

The Importance Of Being Creative, Dennis Callahan Feb 2014

The Importance Of Being Creative, Dennis Callahan

The STEAM Journal

Dennis Callahan is a graduate student in Materials Science at Caltech and also is an advisor to The STEAM Journal. He has created many types of scientific art, and his images have twice consecutively won first place at Caltech's "Art of Science" competition.

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A Better Way To Restore Wildfire-Burned Forests, Char Miller Feb 2014

A Better Way To Restore Wildfire-Burned Forests, Char Miller

Pomona Faculty Publications and Research

No abstract provided.

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Arnold Diffusion, Florin Diacu Jan 2014

Arnold Diffusion, Florin Diacu

Journal of Humanistic Mathematics

No abstract provided.

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Game Theory Meets The Humanities And Both Win Or Book Review: Game Theory And The Humanities: Bridging Two Worlds, By Steven J. Brams, Karl-Dieter Crisman Jan 2014

Game Theory Meets The Humanities And Both Win Or Book Review: Game Theory And The Humanities: Bridging Two Worlds, By Steven J. Brams, Karl-Dieter Crisman

Journal of Humanistic Mathematics

This review discusses Brams' wide-ranging book Game Theory and the Humanities and gives some basic examples of the methodology and style, including how the Theory of Moves contributes to understanding such games.

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Promoting Active Studying: The Study Challenge, Christopher K. Storm, Salvatore Petrilli, Susan Petry Jan 2014

Promoting Active Studying: The Study Challenge, Christopher K. Storm, Salvatore Petrilli, Susan Petry

Journal of Humanistic Mathematics

We explore using a “Study Challenge” to help students become active studiers in mathematics courses. We describe how a Study Challenge works and how we implemented it in calculus and differential equations courses. We discuss qualitative reactions from students who accepted the Study Challenge, which suggest that this might be a useful tool for students’ to add to their examination preparation toolbox. Finally, we offer some suggestions for implementing a Study Challenge within the mathematics classroom.

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What Is So Negative About Negative Exponents?, Geoffrey D. Dietz Jan 2014

What Is So Negative About Negative Exponents?, Geoffrey D. Dietz

Journal of Humanistic Mathematics

While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that …

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Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta Jan 2014

Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta

Journal of Humanistic Mathematics

Benjamin Banneker, farmer, mathematician, astronomer, and scientist, is known for his mathematical puzzles, ephemeris calculations, almanacs, his wooden clock, land surveying work, and famous letter on human rights. However, as a naturalist, his scientific and systematic observations of the cicadas are less known. In this paper we publicize Banneker’s naturalistic study of the seventeen-year periodic cycle of the cicada and make available the original handwritten document of his observations. We also introduce the audience of this journal to an intriguing natural problem involving prime numbers.

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Improving Equity And Education: Why And How, Patricia Clark Kenschaft Jan 2014

Improving Equity And Education: Why And How, Patricia Clark Kenschaft

Journal of Humanistic Mathematics

Progress is possible. When I graduated from college, only 5\% of the new U.S. doctorates in mathematics went to women; now it is about 30\%. There is of course room (and need) for more progress. This paper begins with an account of my research about women and black mathematicians. The latter group claimed that racial equality can be achieved only when better elementary school mathematics education is available to all children in this country. That motivated me to lead a seven-year, grant-supported program to work with elementary school teachers and children in nine New Jersey districts, including Newark, Paterson, and …

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An Introduction To Fourier Analysis With Applications To Music, Nathan Lenssen, Deanna Needell Jan 2014

An Introduction To Fourier Analysis With Applications To Music, Nathan Lenssen, Deanna Needell

Journal of Humanistic Mathematics

In our modern world, we are often faced with problems in which a traditionally analog signal is discretized to enable computer analysis. A fundamental tool used by mathematicians, engineers, and scientists in this context is the discrete Fourier transform (DFT), which allows us to analyze individual frequency components of digital signals. In this paper we develop the discrete Fourier transform from basic calculus, providing the reader with the setup to understand how the DFT can be used to analyze a musical signal for chord structure. By investigating the DFT alongside an application in music processing, we gain an appreciation for …

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Liberal Arts Inspired Mathematics: A Report Or How To Bring Cultural And Humanistic Aspects Of Mathematics To The Classroom As Effective Teaching And Learning Tools, Anders K H Bengtsson Jan 2014

Liberal Arts Inspired Mathematics: A Report Or How To Bring Cultural And Humanistic Aspects Of Mathematics To The Classroom As Effective Teaching And Learning Tools, Anders K H Bengtsson

Journal of Humanistic Mathematics

This is the report of a project on ways of teaching university-level mathematics in a humanistic way. The main part of the project recounted here involved a journey to the United States during the fall term of 2012 to visit several liberal arts colleges in order to study and discuss mathematics teaching. Several themes that came up during my conversations at these colleges are discussed in the text: the invisibility of mathematics in everyday life, the role of calculus in American mathematics curricula, the "is algebra necessary?'' discussion, teaching mathematics as a language, the transfer problem in learning, and the …

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Galileo And Aristotle's Wheel, Olympia Nicodemi Jan 2014

Galileo And Aristotle's Wheel, Olympia Nicodemi

Journal of Humanistic Mathematics

At the beginning of his last major work, Galileo tackles an old paradox, Aristotle's Wheel, in order to produce a model of the continuum that explains (at least to him) how line segments of different length could be put into a one-to-one correspondence. His argument seems like a playful digression. However, it is precisely this type of a one-to-one correspondence that he needs to support his work on free fall. In this article, we investigate how Galileo's model for the wheel paradox informs his work on free fall. We also examine some of the reasons his results on free fall---results …

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Paved With Good Intentions: Analysis Of A Randomized Block Kaczmarz Method, Deanna Needell, Joel A. Tropp Jan 2014

Paved With Good Intentions: Analysis Of A Randomized Block Kaczmarz Method, Deanna Needell, Joel A. Tropp

CMC Faculty Publications and Research

The block Kaczmarz method is an iterative scheme for solving overdetermined least-squares problems. At each step, the algorithm projects the current iterate onto the solution space of a subset of the constraints. This paper describes a block Kaczmarz algorithm that uses a randomized control scheme to choose the subset at each step. This algorithm is the first block Kaczmarz method with an (expected) linear rate of convergence that can be expressed in terms of the geometric properties of the matrix and its submatrices. The analysis reveals that the algorithm is most effective when it is given a good row paving …

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Paul Faulstich’S Reflective Review Of Susan A. Phillips’ Essay, Paul Faulstich Jan 2014

Paul Faulstich’S Reflective Review Of Susan A. Phillips’ Essay, Paul Faulstich

Pitzer Faculty Publications and Research

Paul Faulstich's review of Susan A. Phillips' essay titled, "Huerta del Valle: A New Nonprofit in a Neglected Landscape".

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Pitzer College Outback Preserve Restoration Project, Paul Faulstich Jan 2014

Pitzer College Outback Preserve Restoration Project, Paul Faulstich

Pitzer Faculty Publications and Research

A question we keep asking ourselves in environmental analysis at Pitzer College is whether it’s possible to create modern socionatural systems that are truly sustaining; that is, that avoid the features of contemporary systems in which the human factor dominates to the detriment of the environment. Any genuinely sustainable society must honor diversity— cultural and biological—and, at Pitzer, we’re committed to forging innovative directions for a healthy future. Toward this end, students, along with faculty and staff, have initiated a program of ecological restoration in the Pitzer College Outback Preserve.

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'Studio' Mathematics For Undergraduate Engineers, Lori Bassman, Darryl Yong Jan 2014

'Studio' Mathematics For Undergraduate Engineers, Lori Bassman, Darryl Yong

All Faculty Publications

Applied Mathematics for Engineering is a second year undergradu- ate mathematics requirement for engineering majors at Harvey Mudd College in Claremont, California since 2011. It has been jointly de- signed and taught by the engineering and mathematics departments. The class aims to help students develop confidence in their skill in applying mathematics to solve engineering problems and perseverance for complicated problems; to improve facility at previously learned mathematical skills and to incorporate new tools; and to develop strate- gic competence and better judgment on the correctness of solutions. This article describes the design principles used in creating the class and …

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Existence Of Positive Solutions For A Superlinear Elliptic System With Neumann Boundary Condition, Alfonso Castro, Juan C. Cardeño Jan 2014

Existence Of Positive Solutions For A Superlinear Elliptic System With Neumann Boundary Condition, Alfonso Castro, Juan C. Cardeño

All HMC Faculty Publications and Research

We prove the existence of a positive solution for a class of nonlin- ear elliptic systems with Neumann boundary conditions. The proof combines extensive use of a priori estimates for elliptic problems with Neumann boundary condition and Krasnoselskii's compression-expansion theorem

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The Apple Doesn’T Fall Far From The (Metric) Tree: Equivalence Of Definitions, Asuman Güven Aksoy, Sixian Jin Jan 2014

The Apple Doesn’T Fall Far From The (Metric) Tree: Equivalence Of Definitions, Asuman Güven Aksoy, Sixian Jin

CMC Faculty Publications and Research

In this paper we prove the equivalence of definitions for metric trees and for δ-Hperbolic spaces. We point out how these equivalences can be used to understand the geometric and metric properties of δ-Hperbolic spaces and its relation to CAT(κ) spaces.

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On Approximation Schemes And Compactness, Asuman Güven Aksoy, Jose M. Almira Jan 2014

On Approximation Schemes And Compactness, Asuman Güven Aksoy, Jose M. Almira

CMC Faculty Publications and Research

We present an overview of some results about characterization of compactness in which the concept of approximation scheme has had a role. In particular, we present several results that were proved by the second author, jointly with Luther, a decade ago, when these authors were working on a very general theory of approximation spaces. We then introduce and show the basic properties of a new concept of compactness, which was studied by the first author in the eighties, by using a generalized concept of approximation scheme and its associated Kolmogorov numbers, which generalizes the classical concept of compactness.

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Small Zeros Of Quadratic Forms Outside A Union Of Varieties, Wai Kiu Chan, Lenny Fukshansky, Glenn R. Henshaw Jan 2014

Small Zeros Of Quadratic Forms Outside A Union Of Varieties, Wai Kiu Chan, Lenny Fukshansky, Glenn R. Henshaw

CMC Faculty Publications and Research

Let be a quadratic form in variables defined on a vector space over a global field , and be a finite union of varieties defined by families of homogeneous polynomials over . We show that if contains a nontrivial zero of , then there exists a linearly independent collection of small-height zeros of in , where the height bound does not depend on the height of , only on the degrees of its defining polynomials. As a corollary of this result, we show that there exists a small-height maximal totally isotropic subspace of the quadratic space such that is not …

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Well-Rounded Zeta-Function Of Planar Arithmetic Lattices, Lenny Fukshansky Jan 2014

Well-Rounded Zeta-Function Of Planar Arithmetic Lattices, Lenny Fukshansky

CMC Faculty Publications and Research

We investigate the properties of the zeta-function of well-rounded sublattices of a fixed arithmetic lattice in the plane. In particular, we show that this function has abscissa of convergence at s=1 with a real pole of order 2, improving upon a result of Stefan Kühnlein. We use this result to show that the number of well-rounded sublattices of a planar arithmetic lattice of index less than or equal to N is O(N log N) as N → ∞. To obtain these results, we produce a description of integral well-rounded sublattices of a fixed planar integral well-rounded lattice and investigate convergence …

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On The Geometry Of Cyclic Lattices, Lenny Fukshansky, Xun Sun Jan 2014

On The Geometry Of Cyclic Lattices, Lenny Fukshansky, Xun Sun

CMC Faculty Publications and Research

Cyclic lattices are sublattices of ZN that are preserved under the rotational shift operator. Cyclic lattices were introduced by D.~Micciancio and their properties were studied in the recent years by several authors due to their importance in cryptography. In particular, Peikert and Rosen showed that on cyclic lattices in prime dimensions, the shortest independent vectors problem SIVP reduces to the shortest vector problem SVP with a particularly small loss in approximation factor, as compared to general lattices. In this paper, we further investigate geometric properties of cyclic lattices. Our main result is a counting estimate for the number of well-rounded …

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Metamorphism Of Cretaceous Standstones By Natural Coal-Fires, San Rafael Swell, Utah, Alexa R. Zilberfarb Jan 2014

Metamorphism Of Cretaceous Standstones By Natural Coal-Fires, San Rafael Swell, Utah, Alexa R. Zilberfarb

Scripps Senior Theses

Underground coal fires commonly metamorphose or melt surrounding rocks at temperatures exceeding 1000°C. Numerous “baked” sandstone clinker deposits occur in the Cretaceous sedimentary rocks exposed in the San Rafael Swell, UT. This study examines clinker in three main localities: 1) East Carbon, UT, 2) Helper, UT, and 3) Emery, UT. The extent of pyrometamorphism in these areas is variably developed, but reached high enough temperature in Helper, UT to initiate melting and the production of paralavas. These paralavas were examined compositionally and mineralogically to determine melting conditions, peak temperatures, and mobility of different metals as a result of pyrometamorphism. X-ray …

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Wetlands And Greenhouse Gas Fluxes: Causes And Effects Of Climate Change – A Meta-Analysis, Robert E. Ventura Jan 2014

Wetlands And Greenhouse Gas Fluxes: Causes And Effects Of Climate Change – A Meta-Analysis, Robert E. Ventura

Pomona Senior Theses

Climate change is one of the largest problems facing this generation. Anthropogenically caused increases of greenhouse gas emissions is a significant culprit to this problem. Although the obvious problems such as cars, industry, and urbanism garnish a significant amount of the criticism, natural sources such as wetlands are also beginning to contribute to this issue. This is becoming increasingly significant as wetlands shift from being sinks of greenhouse gases to becoming sources as various anthropogenic impacts, including global warming itself, begin to affect the health of the wetlands. The aim of this project is to look at four common types …

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Fast Algorithms For Analyzing Partially Ranked Data, Matthew Mcdermott Jan 2014

Fast Algorithms For Analyzing Partially Ranked Data, Matthew Mcdermott

HMC Senior Theses

Imagine your local creamery administers a survey asking their patrons to choose their five favorite ice cream flavors. Any data collected by this survey would be an example of partially ranked data, as the set of all possible flavors is only ranked into subsets of the chosen flavors and the non-chosen flavors. If the creamery asks you to help analyze this data, what approaches could you take? One approach is to use the natural symmetries of the underlying data space to decompose any data set into smaller parts that can be more easily understood. In this work, I describe …

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A Volumetric Study Of Aqueous Butanol Solutions, Priyanka P. Chary Jan 2014

A Volumetric Study Of Aqueous Butanol Solutions, Priyanka P. Chary

Scripps Senior Theses

Alcohol molecules consist of two distinct regions: a polar, hydrophilic alcohol group, and an aliphatic hydrocarbon chain. These regions interact with solvent water molecules in different ways. While the alcohol group acts as a solvent structure breaker by hydrogen bonding with nearby water molecules, the hydrophobic carbon chain acts instead as a solvent structure maker and causes the surrounding water molecules to align themselves in a Clathrate structure. The presence of these two contrasting solute-solvent interactions affects the properties of the solution, among them the molar volume. The partial molar volume of the alcohol is analyzed with respect to three …

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Let's Not Eat Alone: A Search For Food Security Justice, Emma Shorr Jan 2014

Let's Not Eat Alone: A Search For Food Security Justice, Emma Shorr

Pitzer Senior Theses

The food justice movement has taken off in recent years. Despite its call for justice in the food system, it has been critiqued as being inaccessible to people who need food the most. The food system marginalizes women, minorities, and low-income people, making these groups the most at risk for food insecurity. Solutions to food insecurity come from both government and non-governmental avenues. This thesis calls for a merger of solutions to food insecurity and food justice in food security justice, and assesses the ability of solutions to food insecurity to confront issues of injustice. Community-based solutions currently have the …

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Symmetries Of Embedded Complete Bipartite Graphs, Erica Flapan, Nicole Lehle '09, Blake Mellor, Matt Pittluck, Xan Vongsathorn '09 Jan 2014

Symmetries Of Embedded Complete Bipartite Graphs, Erica Flapan, Nicole Lehle '09, Blake Mellor, Matt Pittluck, Xan Vongsathorn '09

Pomona Faculty Publications and Research

We characterize which automorphisms of an arbitrary complete bipartite graph Kn,m can be induced by a homeomorphism of some embedding of the graph in S3.

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Topological Symmetry Groups Of Small Complete Graphs, Erica Flapan, Dwayne Chambers Jan 2014

Topological Symmetry Groups Of Small Complete Graphs, Erica Flapan, Dwayne Chambers

Pomona Faculty Publications and Research

Topological symmetry groups were originally introduced to study the symmetries of non-rigid molecules, but have since been used to study the symmetries of any graph embedded in R3. In this paper, we determine for each complete graph Kn with n ≤ 6, what groups can occur as topological symmetry groups or orientation preserving topological symmetry groups of some embedding of the graph in R3.

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Mathematical And Physical Aspects Of Complex Symmetric Operators, Stephan Ramon Garcia, Emil Prodan, Mihai Putinar Jan 2014

Mathematical And Physical Aspects Of Complex Symmetric Operators, Stephan Ramon Garcia, Emil Prodan, Mihai Putinar

Pomona Faculty Publications and Research

Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, C-selfadjoint extensions of C-symmetric unbounded operators, resolvent estimates, reality of spectrum, bases of C-orthonormal vectors, and conjugate-linear symmetric operators. The main results are complemented by a variety of natural examples arising in field theory, quantum physics, and complex variables.

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Using Topology To Explore Mathematics Education Reform, Carling Sugarman Jan 2014

Using Topology To Explore Mathematics Education Reform, Carling Sugarman

HMC Senior Theses

Mathematics education is a constant topic of conversation in the United States. Many attempts have been made historically to reform teaching methods and improve student results. Particularly, past ideas have emphasized problem-solving to make math feel more applicable and enjoyable. Many have additionally tackled the widespread problem of “math anxiety” by creating lessons that are more discussion-based than drill-based to shift focus from speed and accuracy. In my project, I explored past reform goals and some added goals concerning students' perceptions of mathematics. To do so, I created and tested a pilot workshop in topology, a creative and intuitive field, …

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