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Articles 421 - 450 of 2641

Full-Text Articles in Physical Sciences and Mathematics

Using Mathematical Equations To Communicate And Think About Karma, Kien H. Lim, Christopher Yakes Jan 2021

Using Mathematical Equations To Communicate And Think About Karma, Kien H. Lim, Christopher Yakes

Journal of Humanistic Mathematics

Two equations are presented in this article to communicate a particular understanding of karma. The first equation relates future experiences to past and present actions. Although the equation uses variables and mathematical symbols such as the integral sign and summation symbol, it reads more like a literal translation of an English sentence. Based on the key idea in the first equation, a second equation is then created to highlight the viability of using math to communicate concepts that are not readily quantifiable. Analyzing such equations can stimulate thinking, enhance understanding of spiritual concepts, raise issues, and uncover tensions between our …

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Real-World Modelling To Increase Mathematical Creativity, Robert Weinhandl, Zsolt Lavicza Jan 2021

Real-World Modelling To Increase Mathematical Creativity, Robert Weinhandl, Zsolt Lavicza

Journal of Humanistic Mathematics

Modelling could be characterised as one of the core activities in mathematics education. However, when learning and teaching mathematics, mathematical modelling is mostly used to apply and deepen mathematical knowledge and competencies. Our educational study aims to explore how mathematical modelling, using real objects and high-quality mathematical technologies, could be utilised to acquire mathematical knowledge and competencies, and how learners could creatively use their existing knowledge. To discover the potential of mathematical modelling using real objects and high-quality mathematical technologies to acquire mathematical knowledge and competencies, and to stimulate learners' creativity, first, we combined cognitive and creative spirals and mathematical …

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A Heart-Centered Stance: Receptivity To Algebra Teachers’ And Students’ Multidimensional Experiences, Nicole L. Fonger Jan 2021

A Heart-Centered Stance: Receptivity To Algebra Teachers’ And Students’ Multidimensional Experiences, Nicole L. Fonger

Journal of Humanistic Mathematics

The algebra classroom in urban public high schools in the United States is a complex space, ripe with many challenges and opportunities. In this paper I introduce the notion of a heart-centered stance for the teacher and the educator, and a method of engaging in creative expression for reflection and introspection toward individual change in the rich context of the high school algebra classroom. My evolving relationships with two high school algebra teachers, observations of their classrooms, as well as my own self-study and professional growth, are incorporated into this paper as I introduce and exemplify two tenets of a …

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A Holistic Mathematics Curriculum Revision: An Adelphi University Case Study, Salvatore J. Petrilli Jan 2021

A Holistic Mathematics Curriculum Revision: An Adelphi University Case Study, Salvatore J. Petrilli

Journal of Humanistic Mathematics

Join me as I take you on a journey with the faculty of the Department of Mathematics and Computer Science at Adelphi University during our two-year re-envisioning and implementation of our mathematics curriculum. From the beginning this involved a data-driven initiative that naturally led to the revisions. Here I describe in detail the process that our department followed. In closing I end with some recommendations for interesting research directions in the field of mathematics education.

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The Prime Number Theorem As A Capstone In A Complex Analysis Course, Stephan Ramon Garcia Jan 2021

The Prime Number Theorem As A Capstone In A Complex Analysis Course, Stephan Ramon Garcia

Journal of Humanistic Mathematics

We present a detailed proof of the prime number theorem suitable for a typical undergraduate- or graduate-level complex analysis course. Our presentation is particularly useful for any instructor who seeks to use the prime number theorem for a series of capstone lectures, a scaffold for a series of guided exercises, or as a framework for an inquiry-based course. We require almost no knowledge of number theory, for our aim is to make a complete proof of the prime number theorem widely accessible to complex analysis instructors and their students. In particular, we highlight the potential pitfalls and subtleties that may …

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Mathematical Representations In Magazine Advertisements: Have The Messages Changed In A Decade?, Jennifer Hall Jan 2021

Mathematical Representations In Magazine Advertisements: Have The Messages Changed In A Decade?, Jennifer Hall

Journal of Humanistic Mathematics

Although people's ideas about mathematics and mathematicians often develop from their school and home experiences, such ideas also are influenced by interactions with popular media. In this article, I report on findings from a study in which I analyzed magazine advertisements for representations of mathematics and mathematicians. Data collection took place in two phases, approximately a decade apart. In each phase, I reviewed a year’s worth of issues in each of six diverse, popular magazines for mathematical representations in advertisements. The frequency of mathematical advertisements decreased from Phase 1 to Phase 2, but the initial frequency was already extremely low, …

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Peer Motivation: Getting Through Math Together, Jessica Mean, Wes Maciejewski Jan 2021

Peer Motivation: Getting Through Math Together, Jessica Mean, Wes Maciejewski

Journal of Humanistic Mathematics

Students have a complex relationship with mathematics. Some love it, but more often than not, the feelings are less favorable. These feelings can lead to decreased motivation which makes it difficult for students to engage with the subject as the semester progresses. Instructors also have difficulty addressing this waning motivation. In this paper, we claim peers are better able to connect with the students and this can be leveraged to better motivate students. We present an approach to having peers motivate their students. These peer interactions integrated with a mandatory mathematics course might improve students’ motivation.

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In How Many Days Will He Meet His Wife?, Dipak Jadhav Jan 2021

In How Many Days Will He Meet His Wife?, Dipak Jadhav

Journal of Humanistic Mathematics

In how many days will he meet his wife? This is a question asked at the end of each of two problems embedded in the verses of the last chapter of the Vyavahāra-gaṇita (‘Mathematics of Transaction’) of Rājāditya of 12th century. He infuses elegance in those two problems by choosing the charming idea of a husband’s meeting with his wife after their quarrel. This paper not only presents the algorithms offered by Rājāditya to solve them on their own terms as well as on modern terms and discusses the historicity of the categories of those two problems but also …

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Raise The (Proportion) Bar!, Michael Waters Jan 2021

Raise The (Proportion) Bar!, Michael Waters

Journal of Humanistic Mathematics

This article, drawing mainly on references to teacher preparation textbooks, proposes proportion bars as a somewhat novel graphical approach to solving simple (direct) proportion problems and to illustrate the advantages of such an approach, which include accessibility with materials at early grade levels, allowance of students to better develop number sense and estimation, facilitation of setting up proportions, allowance for conceptual understanding and motivation of the procedure for solving direct proportions, assistance with part-to-part and part-to whole comparisons, and drawing of connections among mathematical topics. The emphasis is on teaching with understanding, rather than procedural knowledge.

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“It’S All For The Best”: Optimization In The History Of Science, Judith V. Grabiner Jan 2021

“It’S All For The Best”: Optimization In The History Of Science, Judith V. Grabiner

Journal of Humanistic Mathematics

Many problems, from optics to economics, can be solved mathematically by finding the highest, the quickest, the shortest—the best of something. This has been true from antiquity to the present. Why did we start looking for such explanations, and how and why did we conclude that we could productively do so? In this article we explore these questions and tell a story about the history of optimization. Scientific examples we use to illustrate our story include problems from ancient optics, and more modern questions in optics and classical mechanics, drawing on ideas from Newton’s and Leibniz’s calculus and from the …

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Humanistic Stem: From Concept To Course, Debra T. Bourdeau, Beverly L. Wood Jan 2021

Humanistic Stem: From Concept To Course, Debra T. Bourdeau, Beverly L. Wood

Journal of Humanistic Mathematics

Blending perspectives from the humanities and STEM fosters the creativity of all students. The culturally implicit dichotomy between the two meta-disciplines can be overcome with carefully designed courses and programs intent on doing so. The why and how of doing so through an online course is described with qualitative evidence of the success. Future plans for a full slate of such course and a virtual community are discussed.

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Ahab's Arithmetic: The Mathematics Of Moby-Dick, Sarah B. Hart Jan 2021

Ahab's Arithmetic: The Mathematics Of Moby-Dick, Sarah B. Hart

Journal of Humanistic Mathematics

In this article we explore mathematical allusions in Herman Melville’s novel Moby-Dick. We argue that both the quantity and sophistication of these allusions are evidence for Melville’s high level of mathematical knowledge and ability. We discuss some of the most compelling mathematical imagery, as well as giving background on the several mathematicians and mathematics books mentioned in the novel. We also include some biographical details supporting the assertion that Melville had an unusually good mathematical education.

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You Can Always Count On Word Problems, Mark Huber, Gizem Karaali Jan 2021

You Can Always Count On Word Problems, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

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Front Matter Jan 2021

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

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Carbon Policy Implementation: A Country-Level Analysis Of Carbon Tax Vs. Cap And Trade, Paris Mccaw Jan 2021

Carbon Policy Implementation: A Country-Level Analysis Of Carbon Tax Vs. Cap And Trade, Paris Mccaw

CMC Senior Theses

Climate change is arguably the greatest issue faced by this generation. Mitigation requires an informed and motivated global effort in order to be effective. This paper examines the relationship between emissions from 1980-2020 along with relevant covariates, and carbon policy status, specifically a carbon tax and a cap and trade. An analysis of how the implementation of carbon policies impacts emissions helps to determine the most effective and efficient way to combat climate change. I first run a regression of covariates with emissions and find statistically significant factors that influence emissions: meat production, population, intellectual property charges, and infant deaths. …

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Multifractional Brownian Motion And Its Applications To Factor Analysis On Consumer Confidence Index, Christopher Box Jan 2021

Multifractional Brownian Motion And Its Applications To Factor Analysis On Consumer Confidence Index, Christopher Box

CMC Senior Theses

This thesis aims at introducing a new way to model time series objects in statistics using multifractional processes. It provides a detailed review of Brownian motion, fractional Brownian motion and extends the above 2 models to multifractional processes. To demonstrate a successful application to the real world, we perform pattern analysis on consumer confidence and household spending behavior. The analysis is conducted through investigating the local Holder regularity of the consumer confidence index and household expenditure. In the analysis, we first model consumer confidence index and household expenditure with a multifractional stochastic processes. We then use the index, pointwise Holder …

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Uncovering Object Categories In Infant Views, Naiti S. Bhatt Jan 2021

Uncovering Object Categories In Infant Views, Naiti S. Bhatt

Scripps Senior Theses

While adults recognize objects in a near-instant, infants must learn how to categorize the objects in their visual environments. Recent work has shown that egocentric head-mounted camera videos contain rich data that illuminate the infant experience (Clerkin et al., 2017; Franchak et al., 2011; Yoshida & Smith, 2008). While past work has focused on the social information in view, in this work, we aim to characterize the objects in infants’ at-home visual environments by modifying modern computer vision models for the infant view. To do so, we collected manual annotations of objects that infants seemed to be interacting within a …

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A Gender And Race Theoretical And Probabilistic Analysis Of The Recent Title Ix Policy Changes, Jordan Wellington Jan 2021

A Gender And Race Theoretical And Probabilistic Analysis Of The Recent Title Ix Policy Changes, Jordan Wellington

Scripps Senior Theses

On May 6th, 2020, after extensive public comment and review, the Department of Education published the final rule for the new Title IX regulations, which took effect in schools on August 14th. Title IX is the nearly fifty year old piece of the Education Amendments that prohibits sexual discrimination in federally funded schools. Several of these changes, such as the inclusion of live hearings and cross examination of witnesses, have been widely criticized by victims’ rights advocates for potentially retraumatizing victims of sexual assault and discouraging students from pursuing a Title IX claim. While the impact of the new regulations …

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Using Nmr Spectroscopy And Computational Chemistry To Confirm The Structure Of Novel Antibiotic Nocamycin O, Stephanie Lewis Jan 2021

Using Nmr Spectroscopy And Computational Chemistry To Confirm The Structure Of Novel Antibiotic Nocamycin O, Stephanie Lewis

CMC Senior Theses

In recent years, many medically promising antibiotics have been discovered in nature, especially in insect-microbe symbioses. One of the better-studied examples of this kind of defensive relationship is that of fungus-growing ants and the antibiotic-producing Actinobacteria. These bacteria produce several defensive chemicals with myriad uses, including one antibiotic that inhibits the growth of several bacterial strains, including other Actinobacteria. This antibiotic (known as nocamycin O) is a promising candidate for medicinal use due to its similarities to bacterial RNA polymerase inhibitors tirandamycin and streptolydigin, which inhibit several human pathogens. The determination of the structure of nocamycin O will be an …

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Feature Investigation For Stock Returns Prediction Using Xgboost And Deep Learning Sentiment Classification, Seungho (Samuel) Lee Jan 2021

Feature Investigation For Stock Returns Prediction Using Xgboost And Deep Learning Sentiment Classification, Seungho (Samuel) Lee

CMC Senior Theses

This paper attempts to quantify predictive power of social media sentiment and financial data in stock prediction by utilizing a comprehensive set of stock-related fundamental and technical variables and social media sentiments. For conducting sentiment analysis, this study employs a pretrained finBERT model that provides three different sentiment classifications and respective softmax scores. Hence, the significance of these variables is evaluated with XGBoost regression and Shapley Additive exPlanations (SHAP) frameworks. Through investigating feature importance, this study finds that statistical properties of sentiment variables provide a stronger predictive power than a weighted sentiment score and that it is possible to quantify …

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A Detailed X-Ray Analysis Of The Cold Front In Relics Cluster A2163, Anne Poy Jan 2021

A Detailed X-Ray Analysis Of The Cold Front In Relics Cluster A2163, Anne Poy

CMC Senior Theses

Galaxy clusters are the largest gravitationally bound objects in the Universe. Studying them can teach us about how they merge and grow, which in turn provides unparalleled information about the history of the evolution of the Universe. X-ray observations of galaxy clusters have uncovered substructure in the hot, X-ray emitting gas known as the intracluster mediums (ICM). Substructure indicates that the ICM has been churned up, possibly by a significant off-axis merger event. This substructure includes cold fronts, sloshing spirals, and shocks. We present deep Chandra observations of the merging cluster Abell 2163. We investigate the global spectrum and find …

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An Evaluation Of Knot Placement Strategies For Spline Regression, William Klein Jan 2021

An Evaluation Of Knot Placement Strategies For Spline Regression, William Klein

CMC Senior Theses

Regression splines have an established value for producing quality fit at a relatively low-degree polynomial. This paper explores the implications of adopting new methods for knot selection in tandem with established methodology from the current literature. Structural features of generated datasets, as well as residuals collected from sequential iterative models are used to augment the equidistant knot selection process. From analyzing a simulated dataset and an application onto the Racial Animus dataset, I find that a B-spline basis paired with equally-spaced knots remains the best choice when data are evenly distributed, even when structural features of a dataset are known …

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Factory To Table: A Philosophic Analysis Of The Justice Or Lack Thereof Of Agricultural Markets, Will Carter Jan 2021

Factory To Table: A Philosophic Analysis Of The Justice Or Lack Thereof Of Agricultural Markets, Will Carter

CMC Senior Theses

How food is produced has dramatic consequences on how we live, our world’s justice, and the future of our planet. In a world increasingly driven by neoliberalism, agricultural markets have been incentivized to industrialize, globalize, and consolidate. This has resulted in the global dominance of a new type of agriculture, industrial agriculture, driven by the market logic of lowering costs and raising profits. Industrial agriculture has undoubtedly generated the profound benefit of cheaper, more plentiful food in much of the world. These favorable innovations lead many scholars to argue that free markets produce the most just and efficient arrangements for …

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On Properties Of Positive Semigroups In Lattices And Totally Real Number Fields, Siki Wang Jan 2021

On Properties Of Positive Semigroups In Lattices And Totally Real Number Fields, Siki Wang

CMC Senior Theses

In this thesis, we give estimates on the successive minima of positive semigroups in lattices and ideals in totally real number fields. In Chapter 1 we give a brief overview of the thesis, while Chapters 2 – 4 provide expository material on some fundamental theorems about lattices, number fields and height functions, hence setting the necessary background for the original results presented in Chapter 5. The results in Chapter 5 can be summarized as follows. For a full-rank lattice L ⊂ Rd, we are concerned with the semigroup L+ ⊆ L, which denotes the set of all vectors with nonnegative …

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Using Twitter Api To Solve The Goat Debate: Michael Jordan Vs. Lebron James, Jordan Trey Leonard Jan 2021

Using Twitter Api To Solve The Goat Debate: Michael Jordan Vs. Lebron James, Jordan Trey Leonard

CMC Senior Theses

Using a Twitter API, I gather and analyze tweets by performing sentiment analysis to solve the GOAT debate among professional athletes with the primary focus on comparing Michael Jordan and LeBron James. Athletes from the National Football League (NFL), the National Basketball Association (NBA), Major League Baseball (MLB), and the National Collegiate Athletic Association (NCAA) Division 1 Men's and Women's Basketball were selected to compare how sentiment polarity varies across sports. Sentiment polarity is measured by labeling text as "positive", "neutral", or "negative" which allows us to determine which athlete/sport is highly favored among the Twitter community when it comes …

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Information Prioritization: A Comparison Between Utility Maximizers And Probability Matchers, Yusuf Ismaeel Jan 2021

Information Prioritization: A Comparison Between Utility Maximizers And Probability Matchers, Yusuf Ismaeel

CMC Senior Theses

This thesis examines the differences between probability matchers and utility maximizers in their preferences for information sources in a lab environment. In this paper, we consider the best source of information to be the most connected one. We conducted several linear probability model type regressions along with logit regressions. Furthermore, we also attempted to control and fix any potential misclassifications in classifying the cognitive strategy by using instrumental variables. The results show that utility maximizers will almost always choose the most informed node. Probability matchers, on the other hand, do not exhibit such a behavior as the probability matching strategy …

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Random Matrix Theory: A Combinatorial Proof Of Wigner's Semicircle Law, Vanessa Wolf Jan 2021

Random Matrix Theory: A Combinatorial Proof Of Wigner's Semicircle Law, Vanessa Wolf

Scripps Senior Theses

A combinatorial proof of Wigner’s semicircle law for the Gaussian Unitary Ensemble (GUE) is presented using techniques from free probability. Motivating examples taken from the symmetric Bernoulli ensemble and the GUE show the distribution of eigenvalues of sample n x n matrices approaching Wigner’s semicircle as n get large. The concept of crossing and non-crossing pairings is developed, along with proofs of Wick’s Formula for real and complex Gaussians. It is shown that Wigner’s semicircle distribution has moments given by the Catalan numbers. Wick’s Formula and several additional lemmas (proved in sequence) lead to a "method of moments" proof that …

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Computationally Recovering Preferred Factorizations Of Quantum Hilbert Space, Louisa Cornelis Jan 2021

Computationally Recovering Preferred Factorizations Of Quantum Hilbert Space, Louisa Cornelis

Scripps Senior Theses

This thesis addresses the question of the preferred factorization of the quantum mechanical Hilbert Space into sub parts. Specifically, I computationally implement streamlined aspects of the recent “in principle” proposal of Carroll and Singh in their paper Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics. The goal is to link the selection of a preferred tensor product factorization to the appearance of quasi-classical behavior in this preferred factorization. Carroll and Singh quantify quasi-classical behavior through the criteria of “robustness” and “predictability” using the purity and pointer entropies. This work tests whether it is necessary to use both entropies …

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Using Augmented Reality As A Tool For Distance Learning Of Vsepr Theory, Isabelle Lopez Jan 2021

Using Augmented Reality As A Tool For Distance Learning Of Vsepr Theory, Isabelle Lopez

Scripps Senior Theses

Distance learning poses challenges in most academic settings, especially at the undergraduate laboratory level. Improving this mode of learning diminishes the impact of current events on young scientists’ development of foundational laboratory concepts. Our work explores the use of augmented reality (AR) in a laboratory setting. We developed a completely virtual valence shell electron pair repulsion (VSEPR) theory lab activity consistent with the goals of Keck Science Department’s Introduction to Chemistry course’s in-person VSEPR lab activity. We were able to maintain a hands-on learning experience for students while using a tool many students already own: an iPhone as an alternative …

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Influence Of Iceberg-Discharge Events On The Climate And Circulation Of The Central North Atlantic Ocean During The Last Glaciation, Ava Mcilvaine Jan 2021

Influence Of Iceberg-Discharge Events On The Climate And Circulation Of The Central North Atlantic Ocean During The Last Glaciation, Ava Mcilvaine

Scripps Senior Theses

The repeated occurrence of episodic iceberg-discharge events and abrupt climate change in the North Atlantic Ocean is well-documented for the late Quaternary period. However, much of the evidence for these periods known as Heinrich Events comes from the subpolar region, where deposition can be dominated by ice-rafted debris (IRD) and overwhelm other oceanographic and climatic indicators. Thus, the following analysis of coarse sediment from Integrated Ocean Drilling Program (IODP) Core Site U1313 (41°0.0'N, 32°57.42'W) evaluated ocean cooling related to ice-rafting, water mass migration, and climate change over the approximate last 100,000 years. Site U1313 is located near the North Atlantic …

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