Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Claremont Colleges

Discipline
Keyword
Publication Year
Publication
Publication Type
File Type

Articles 1081 - 1110 of 2640

Full-Text Articles in Physical Sciences and Mathematics

An Exhibition Of Exponential Sums: Visualizing Supercharacters, Paula Burkhardt '16, Gabriel Currier '16, Stephan Ramon Garcia, Mathieu De Langis '15, Bob Lutz '13, Hong Suh '16 Jan 2015

An Exhibition Of Exponential Sums: Visualizing Supercharacters, Paula Burkhardt '16, Gabriel Currier '16, Stephan Ramon Garcia, Mathieu De Langis '15, Bob Lutz '13, Hong Suh '16

Pomona Faculty Publications and Research

We discuss a simple mathematical mechanism that produces a variety of striking images of great complexity and subtlety. We briefly explain this approach and present a selection of attractive images obtained using this technique.

Go to article

Model Spaces: A Survey, Stephan Ramon Garcia, William T. Ross Jan 2015

Model Spaces: A Survey, Stephan Ramon Garcia, William T. Ross

Pomona Faculty Publications and Research

This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.

Go to article

Exploring Algorithmic Musical Key Recognition, Nathan J. Levine Jan 2015

Exploring Algorithmic Musical Key Recognition, Nathan J. Levine

CMC Senior Theses

The following thesis outlines the goal and process of algorithmic musical key detection as well as the underlying music theory. This includes a discussion of signal-processing techniques intended to most accurately detect musical pitch, as well as a detailed description of the Krumhansl-Shmuckler (KS) key-finding algorithm. It also describes the Java based implementation and testing process of a musical key-finding program based on the KS algorithm. This thesis provides an analysis of the results and a comparison with the original algorithm, ending with a discussion of the recommended direction of further development.

Go to article

Elliptic Curves And The Congruent Number Problem, Jonathan Star Jan 2015

Elliptic Curves And The Congruent Number Problem, Jonathan Star

CMC Senior Theses

In this paper we explain the congruent number problem and its connection to elliptic curves. We begin with a brief history of the problem and some early attempts to understand congruent numbers. We then introduce elliptic curves and many of their basic properties, as well as explain a few key theorems in the study of elliptic curves. Following this, we prove that determining whether or not a number n is congruent is equivalent to determining whether or not the algebraic rank of a corresponding elliptic curve En is 0. We then introduce L-functions and explain the Birch and …

Go to article

Applications Of Monte Carlo Methods In Statistical Inference Using Regression Analysis, Ji Young Huh Jan 2015

Applications Of Monte Carlo Methods In Statistical Inference Using Regression Analysis, Ji Young Huh

CMC Senior Theses

This paper studies the use of Monte Carlo simulation techniques in the field of econometrics, specifically statistical inference. First, I examine several estimators by deriving properties explicitly and generate their distributions through simulations. Here, simulations are used to illustrate and support the analytical results. Then, I look at test statistics where derivations are costly because of the sensitivity of their critical values to the data generating processes. Simulations here establish significance and necessity for drawing statistical inference. Overall, the paper examines when and how simulations are needed in studying econometric theories.

Go to article

One-Bit Compressive Sensing With Partial Support Information, Phillip North Jan 2015

One-Bit Compressive Sensing With Partial Support Information, Phillip North

CMC Senior Theses

This work develops novel algorithms for incorporating prior-support information into the field of One-Bit Compressed Sensing. Traditionally, Compressed Sensing is used for acquiring high-dimensional signals from few linear measurements. In applications, it is often the case that we have some knowledge of the structure of our signal(s) beforehand, and thus we would like to leverage it to attain more accurate and efficient recovery. Additionally, the Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization. Indeed, the field of One-Bit Compressive Sensing aims to recover a signal from measurements reduced to only their sign-bit. This …

Go to article

An Exposition And Calibration Of The Ho-Lee Model Of Interest Rates, Benjamin I. Lawson Jan 2015

An Exposition And Calibration Of The Ho-Lee Model Of Interest Rates, Benjamin I. Lawson

CMC Senior Theses

The purpose of this paper is to create an easily understandable version of the Ho-Lee interest rate model. The first part analyzes the model in detail, and the second part calibrates it to demonstrate how it can be applied to real market data.

Go to article

The Future Of Squaw Valley And Alpine Meadows, Brian Friel Jan 2015

The Future Of Squaw Valley And Alpine Meadows, Brian Friel

Pomona Senior Theses

This paper examines the ongoing conflict between Squaw Valley Ski Holdings and the local Tahoe community and analyzes this conflict within the greater historical context of ski resort consolidation and development across the Western United States.

Go to article

Ensuring Our Future Or Sowing The Seeds Of Our Own Destruction? Crop Insurance And Water Use In Texas, Michael Shapiro Jan 2015

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.

Go to article

Bridging The Blue-Green Divide: The Role Of Environmental Ngos In Tackling Environmental Problems In Taiwan, Yttrium Sua Jan 2015

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 …

Go to article

Looking Beyond Fossil Fuel Divestment: Combating Climate Change In Higher Education, Robin Xu Jan 2015

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 …

Go to article

Combinatorial Proofs Of Fibonomial Identities, Arthur Benjamin, Elizabeth Reiland Dec 2014

Combinatorial Proofs Of Fibonomial Identities, Arthur Benjamin, Elizabeth Reiland

All HMC Faculty Publications and Research

We provide a list of simple looking identities that are still in need of combinatorial proof.

Go to article

Review: Crystal Bases Of Q-Deformed Kac Modules Over The Quantum Superalgebras Uq(Gl(Mln)), Gizem Karaali Aug 2014

Review: Crystal Bases Of Q-Deformed Kac Modules Over The Quantum Superalgebras Uq(Gl(Mln)), Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Go to article

Op-Ed: Solve This Math Problem: The Gender Gap, Francis Su Aug 2014

Op-Ed: Solve This Math Problem: The Gender Gap, Francis Su

All HMC Faculty Publications and Research

Women may not face such blatant impediments to doing math and science today. But Mirzakhani's achievement aside, we are still a long way from adequately recognizing the outstanding work of women.

Go to article

Math Talk: Preparing Your Conference Presentation, Gizem Karaali Aug 2014

Math Talk: Preparing Your Conference Presentation, Gizem Karaali

Pomona Faculty Publications and Research

If you are a typical reader of this blog, then you recently wrapped up your finals week and then dutifully made a summer plan. And then came the summer. Your plan may have involved working on a manuscript, preparing for a qualifying exam or a new course coming up in the fall, drafting a grant proposal, learning a new language (human or machine), eating kale in four different forms, and perhaps some fun times under the sun. Some, like me, also made plans to travel to conferences and give talks. Gearing up to get ready for my first conference of …

Go to article

Exponential Decay Of Reconstruction Error From Binary Measurements Of Sparse Signals, Richard Baraniuk, Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters Aug 2014

Exponential Decay Of Reconstruction Error From Binary Measurements Of Sparse Signals, Richard Baraniuk, Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters

CMC Faculty Publications and Research

Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem—e.g., in determining the relationship between genetics and the presence or absence of a disease—or they may be a result of extreme quantization. A recent influx of literature has suggested that using prior signal information can greatly improve the ability to reconstruct a signal from binary measurements. This is exemplified by onebit compressed sensing, which takes the compressed sensing model but assumes that only the sign of each measurement is retained. It has recently been shown that the number of one-bit measurements …

Go to article

Four Quotient Set Gems, Stephan Ramon Garcia, Michael Someck '14, Bob Lutz '13, Bryan Brown '15, Michael Dairyko '13 Aug 2014

Four Quotient Set Gems, Stephan Ramon Garcia, Michael Someck '14, Bob Lutz '13, Bryan Brown '15, Michael Dairyko '13

Pomona Faculty Publications and Research

Our aim in this note is to present four remarkable facts about quotient sets. These observations seem to have been overlooked by the MONTHLY, despite its intense coverage of quotient sets over the years.

Go to article

Near Oracle Performance And Block Analysis Of Signal Space Greedy Methods, Raja Giryes, Deanna Needell Jul 2014

Near Oracle Performance And Block Analysis Of Signal Space Greedy Methods, Raja Giryes, Deanna Needell

CMC Faculty Publications and Research

Compressive sampling (CoSa) is a new methodology which demonstrates that sparse signals can be recovered from a small number of linear measurements. Greedy algorithms like CoSaMP have been designed for this recovery, and variants of these methods have been adapted to the case where sparsity is with respect to some arbitrary dictionary rather than an orthonormal basis. In this work we present an analysis of the so-called Signal Space CoSaMP method when the measurements are corrupted with mean-zero white Gaussian noise. We establish near-oracle performance for recovery of signals sparse in some arbitrary dictionary. In addition, we analyze the block …

Go to article

Jhm Contents Word Puzzle, Robert Haas Jul 2014

Jhm Contents Word Puzzle, Robert Haas

Journal of Humanistic Mathematics

This is a word-search puzzle based on the contents page of the previous (Volume 4 Issue 1-January 2014) issue of the Journal of Humanistic Mathematics.

Go to article

The Physicist's Basement, Nora Culik Jul 2014

The Physicist's Basement, Nora Culik

Journal of Humanistic Mathematics

No abstract provided.

Go to article

Jeffery's Equation, Sandra J. Stein Jul 2014

Jeffery's Equation, Sandra J. Stein

Journal of Humanistic Mathematics

No abstract provided.

Go to article

The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried Jul 2014

The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried

Journal of Humanistic Mathematics

Teachers and students of mathematics often view history of mathematics as just mathematics as they know it, but in another form. This view is based on a misunderstanding of the nature of history of mathematics and the kind of knowledge it attempts to acquire. Unfortunately, it can also lead to a deep sense of disappointment with the history of mathematics itself, and, ultimately, a misunderstanding of the historical nature of mathematics. This kind of misunderstanding and the disappointment following from it--both raised to the level of resentment--run through the paper "A Critique of the Modern Consensus in the Historiography of …

Go to article

A Critique Of The Modern Consensus In The Historiography Of Mathematics, Viktor Blåsjö Jul 2014

A Critique Of The Modern Consensus In The Historiography Of Mathematics, Viktor Blåsjö

Journal of Humanistic Mathematics

The history of mathematics is nowadays practiced primarily by professional historians rather than mathematicians, as was the norm a few decades ago. There is a strong consensus among these historians that the old-fashioned style of history is “obsolete,” and that “the gains in historical understanding are incomparably greater” in the more “historically sensitive” works of today. I maintain that this self-congratulatory attitude is ill-founded, and that the alleged superiority of modern historiographical standards ultimately rests on a dubious redefinition of the purpose of history rather than intrinsic merit.

Go to article

How Do I Love Thee? Let Me Count The Ways For Syllabic Variation In Certain Poetic Forms, Mike Pinter Jul 2014

How Do I Love Thee? Let Me Count The Ways For Syllabic Variation In Certain Poetic Forms, Mike Pinter

Journal of Humanistic Mathematics

The Dekaaz poetic form, similar to haiku with its constrained syllable counts per line, invites a connection between poetry and mathematics. Determining the number of possible Dekaaz variations leads to some interesting counting observations. We discuss two different ways to count the number of possible Dekaaz variations, one using a binary framework and the other approaching the count as an occupancy problem. The counting methods described are generalized to also count variations of other poetic forms with syllable counts specified, including haiku. We include Dekaaz examples and suggest a method that can be used to randomly generate a Dekaaz variation.

Go to article

Fields In Math And Farming, Susan D'Agostino Jul 2014

Fields In Math And Farming, Susan D'Agostino

Journal of Humanistic Mathematics

A young woman’s search for a a contemplative, insightful experience leads her from farming to mathematics.

Go to article

Being Reasonable: Using Brainteasers To Develop Reasoning Ability In Humanistic Mathematics Courses, Gary Stogsdill Jul 2014

Being Reasonable: Using Brainteasers To Develop Reasoning Ability In Humanistic Mathematics Courses, Gary Stogsdill

Journal of Humanistic Mathematics

Developing reasoning ability is often cited as one of the principal justifications of a mathematics requirement for liberal arts undergraduates. Humanistic math courses have become recognized as a paradigm for liberal arts mathematics, but such courses may not provide the opportunity to develop reasoning ability. The author describes his procedure for using brainteasers to promote reasoning in a humanistic math course for liberal arts undergraduates.

Go to article

Joining ``The Mathematician's Delirium To The Poet's Logic'': Mathematical Literature And Literary Mathematics, Rita Capezzi, Christine Kinsey Jul 2014

Joining ``The Mathematician's Delirium To The Poet's Logic'': Mathematical Literature And Literary Mathematics, Rita Capezzi, Christine Kinsey

Journal of Humanistic Mathematics

This paper describes our team-taught interdisciplinary mathematics and literature course, Mathematical Literature and Literary Mathematics, which invites students to consider Raymond Queneau's challenge: "Why shouldn't one demand a certain effort on the reader's part? Everything is always explained to him. He must eventually tire of being treated with such contempt.'' We study works by Berge, Borges, Calvino, Perec, Queneau, Robbe-Grillet and Stoppard, among others. From a literary critical perspective, the course highlights the play of language rather than the primacy of meaning. We choose texts where mathematical concepts are subjects or structuring elements of the literature, and ideally both. …

Go to article

Some Effects Of The Human Genome Project On The Erdős Collaboration Graph, Chris Fields Jul 2014

Some Effects Of The Human Genome Project On The Erdős Collaboration Graph, Chris Fields

Journal of Humanistic Mathematics

The Human Genome Project introduced large-scale collaborations involving dozens to hundreds of scientists into biology. It also created a pressing need to solve discrete mathematics problems involving tens of thousands of elements. In this paper, we use minimal path lengths in the Erdős Collaboration Graph between prominent individual researchers as a measure of the distance between disciplines, and we show that the Human Genome Project brought laboratory biology as a whole closer to mathematics. We also define a novel graph reduction method and a metric that emphasizes the robustness of collaborative connections between researchers; these can facilitate the analysis of …

Go to article

Linear Convergence Of Stochastic Iterative Greedy Algorithms With Sparse Constraints, Nam Nguyen, Deanna Needell, Tina Woolf Jul 2014

Linear Convergence Of Stochastic Iterative Greedy Algorithms With Sparse Constraints, Nam Nguyen, Deanna Needell, Tina Woolf

CMC Faculty Publications and Research

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to the solution within a specified tolerance. This generalized framework applies to problems such as sparse signal recovery in compressed sensing, low-rank matrix recovery, and co-variance matrix estimation, giving methods with provable convergence guarantees that often outperform their deterministic counterparts. We also analyze the settings where gradients and projections can only be computed approximately, and prove the methods are robust to these approximations. We include many numerical experiments which …

Go to article

Lattices From Elliptic Curves Over Finite Fields, Lenny Fukshansky, Hiren Maharaj Jul 2014

Lattices From Elliptic Curves Over Finite Fields, Lenny Fukshansky, Hiren Maharaj

CMC Faculty Publications and Research

In their well known book Tsfasman and Vladut introduced a construction of a family of function field lattices from algebraic curves over finite fields, which have asymptotically good packing density in high dimensions. In this paper we study geometric properties of lattices from this construction applied to elliptic curves. In particular, we determine the generating sets, conditions for well-roundedness and a formula for the number of minimal vectors. We also prove a bound on the covering radii of these lattices, which improves on the standard inequalities.

Go to article

First Prev Next Last