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2021

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Impediments To Mathematical Creativity: Fixation And Flexibility In Proof Validation, Per Øystein Haavold Jan 2021

Impediments To Mathematical Creativity: Fixation And Flexibility In Proof Validation, Per Øystein Haavold

The Mathematics Enthusiast

Mathematical techniques in proof writing can be narrowed down to specific proof styles. Simply put, proofs can be direct or indirect- the latter using the Law of the Excluded Middle from logic as well as the axiom of Choice, to prove existence of mathematical objects. However, the thinking skills involved in writing indirect proofs are prone to errors, especially from novice proof writers such as prospective teachers. Creativity in mathematics entails the use of both direct and indirect approaches to determine the validity of a statement. In this article, I shed some light on this relationship, by reporting on some …

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The Academic Community’S Perceptions Of The Two-Column Proof, Jeffrey Pair, Susanne Strachota, Rashmi Singh Jan 2021

The Academic Community’S Perceptions Of The Two-Column Proof, Jeffrey Pair, Susanne Strachota, Rashmi Singh

The Mathematics Enthusiast

Our research team surveyed members of the mathematics education scholarly community to gain insight into the community’s perceptions of the two-column proof and its role in high school geometry. We created an email survey, which we sent to email addresses gathered from public lists of conference participants and speakers from recent mathematics education conferences. We asked study participants to describe the value of the two-column proof and discuss whether they would be in favor of eliminating it from the high school geometry curriculum. There was a wide range of diversity in the responses, and we present several themes that we …

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Unit Shapes And A Wealth Of Calculus Problems, Robert G. Donnelly, Alexander F. Thome Jan 2021

Unit Shapes And A Wealth Of Calculus Problems, Robert G. Donnelly, Alexander F. Thome

The Mathematics Enthusiast

For a given family of similar shapes, what we call a \unit shape" strongly analogizes the role of the unit circle within the family of all circles. Within many such families of similar shapes, we present what we believe is naturally and intrinsically unital about their unit shapes. We present a number of calculus problems related to extremal questions about collections of unit shapes, and we recapitulate some isoperimetric problems in terms of unit shapes. We close by presenting some problems (some of which are open) and by proffering perhaps a new perspective on the pi vs. t debate.

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Real Numbers As Infinite Decimals, Nicolas Fardin, Liangpan Li Jan 2021

Real Numbers As Infinite Decimals, Nicolas Fardin, Liangpan Li

The Mathematics Enthusiast

Stemming from an idea put forward by Loo-Keng Hua in 1962, this article describes an original way to perform arithmetic directly on infinite decimals. This approach leads to a new and elementary construction of the real number system via decimal representation. Based on the least upper bound property, a definition of trigonometric functions is also included, which settles an issue that Godfrey H. Hardy called \a fatal defect" in his Course of Pure Mathematics.

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Archimedes’ Works In Conoids As A Basis For The Development Of Mathematics, Kenton Ke Jan 2021

Archimedes’ Works In Conoids As A Basis For The Development Of Mathematics, Kenton Ke

The Mathematics Enthusiast

This paper explores Archimedes’ works in conoids, which are three dimensional versions of conic sections, and will discuss ideas that came up in Archimedes’ book On Conoids and Spheroids. In particular, paraboloids, or three dimensional parabolas, will be the primary focus, and a proof of one of the propositions is provided for a clearer understanding of how Archimedes proved many of his propositions. His main method is called method of exhaustion, with results justified by double contradiction. This paper will compare the ideas and problems brought up in On Conoids and Spheroids and how they relate to modern day calculus. …

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The History Of Bootstrapping: Tracing The Development Of Resampling With Replacement, Denise Lafontaine Jan 2021

The History Of Bootstrapping: Tracing The Development Of Resampling With Replacement, Denise Lafontaine

The Mathematics Enthusiast

Sampling is one of the most fundamental concepts in statistics, as the quality and accuracy of the statistical inferences made, heavily depend on the method used to obtain the sample and the sample’s ability to represent the population of inference. Despite being a simple concept, sampling presents researchers with many challenges. Generally, due to monetary and time constraints, researchers must take a smaller sample size than they would ideally use. Using statistics from these small samples, estimates for population parameters can be made, typically in the form of a confidence interval. However, the validity of these confidence intervals depends on …

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Beauty Is In The Blind Spot Of The Beholder, Ron Aharoni Jan 2021

Beauty Is In The Blind Spot Of The Beholder, Ron Aharoni

The Mathematics Enthusiast

The paper addresses the time-old question of what is beauty. A rather ambitious, if not to say presumptuous, endeavour. But I do not aim high – I do not claim to get anywhere near unearthing the secret. Rather, I will use examples from mathematics, poetry, music and chess to substantiate one thesis: that the elusory character of beauty is not incidental. Its defiance of definition is part of its essence. The aesthetic sensation requires unawareness of its precise origin. Beauty is felt when some order is perceived, that is not fully comprehended. The order is too complex, or well hidden, …

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Variations On Convergence Criteria, Reinhard Oldenburg Jan 2021

Variations On Convergence Criteria, Reinhard Oldenburg

The Mathematics Enthusiast

The didactical idea of variation is exemplified with examples from convergence of series. This yields a new convergence test similar to the root test.

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Rednecks, Hillbillies, And White Trash In The Living Room: A Rhetorical Analysis Of Reality Television's Construction Of Appalachian Regional Identity, Bradlee Elizabeth Hartman Jan 2021

Rednecks, Hillbillies, And White Trash In The Living Room: A Rhetorical Analysis Of Reality Television's Construction Of Appalachian Regional Identity, Bradlee Elizabeth Hartman

Senior Independent Study Theses

Reality television is one of America’s guiltiest pleasures because it lets us peer into the lives of people who are both similar to and different from us. However, the narratives we see on the small screen are far from innocent; in fact, reality television plays a large role in directing how we make sense of the world and our place within it. To that end, this study examines how MTV’s reality television series, Buckwild, constructs a particular view of Appalachian regional identity. This study utilizes ideological criticism to uncover how MTV engages in continued stereotyping of Appalachian people. Specifically, my …

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Black Outside: A Film Exploring Black People’S Relationships With Outdoor Spaces, Zoie Bills Jan 2021

Black Outside: A Film Exploring Black People’S Relationships With Outdoor Spaces, Zoie Bills

Senior Independent Study Theses

Spending time in nature is regarded as a great way to have fun and improve one’s mental or physical health. Black people are largely underrepresented in public parks and other outdoor spaces. My film explores the lack of Black presence in outdoor spaces in an effort to promote Black people’s usage of these places. I used interviews with students, environmental activists, and my own family in order to explore the scholarly, structural, cultural, and personal factors that impact Black folks’ engagement with the outdoors. The interviews revealed several major takeaways including that Black people have historical roots in outdoor spaces …

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Option Implied Volatility's Predictability On Monthly Stock Returns, Hung T. Dao Jan 2021

Option Implied Volatility's Predictability On Monthly Stock Returns, Hung T. Dao

Senior Independent Study Theses

Since the trading of options is based on underlying stocks, it is reasonable to assume that information from the options market can be used to explain the returns in the stock market. Our independent study investigates the relationship between options implied volatility and stock returns. Previous studies have found significant results in using implied volatility in predicting stock returns. This paper provides a discussion of such studies, the theoretical framework for the research topic, and the Black-Scholes model, which is famous for its application in implied volatility calculation. Monthly returns of 20 large US firms are regressed against implied volatility …

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Whose Line Is It Anyway? Rhetoric, Pathology, And The Jewish Race In Late Victorian England, Stephanie G. Pokras Jan 2021

Whose Line Is It Anyway? Rhetoric, Pathology, And The Jewish Race In Late Victorian England, Stephanie G. Pokras

Senior Independent Study Theses

This thesis examines how both late Victorian Anglo-Jews and Gentiles used rhetoric of race science and Jewish pathology to encode lines of difference, as well as the relationship between these discourses. My first chapter analyzes the role of Gentile discourse of disease and disability as the foundation of late Victorian anti-Semitism. My second chapter focuses on Jewish ‘expert’ engagement with race science. In this chapter, I argue that contrary to the dominant historical narrative, not only was the Jewish community engaged with race science, but their scholarly conversations were dynamic and diverse. Ideas about race and pathology became central to …

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Reconsidering The Late Woodland: A Critical Reassessment Of Perception And Periodization In The Ohio Valley, 400-1000 Ce, Devin A. Henson Jan 2021

Reconsidering The Late Woodland: A Critical Reassessment Of Perception And Periodization In The Ohio Valley, 400-1000 Ce, Devin A. Henson

Senior Independent Study Theses

The Late Woodland period in eastern North America has traditionally been conceptualized as a cultural hiatus between the region’s Hopewell and Mississippian traditions. As a drastic (though not complete) reduction in the practices of monumental architecture and art produced with nonlocal materials occurred during this time, the end of the preceding Hopewell tradition (and its related Interaction Sphere) has been depicted as a “collapse” or “devolution” by multiple researchers. However, the Late Woodland also saw a rise in population, intensification of agriculture, and technological innovation. Although the combination of these factors and the period’s architectural and artistic reduction appear contradictory, …

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Resource Boom, Manufacturing Bust: The Dutch Disease And Deindustrialization In South America, Gabriel Melmed Jan 2021

Resource Boom, Manufacturing Bust: The Dutch Disease And Deindustrialization In South America, Gabriel Melmed

Senior Independent Study Theses

This thesis looks at the role of the 2003-2013 primary commodity boom in South American deindustrialization. I hypothesize that the boom has led to deindustrialization throughout the region because of the ‘Dutch disease,’ a process by which a boom in the natural resource sector causes the manufacturing sector to decline due to resource movement between sectors and real exchange rate appreciation. Using a panel dataset of 106 lower-middle and upper-middle income countries from 1995 to 2019, I analyze the extent to which a greater share of primary commodities in a country’s export basket has led to (a) lower manufacturing value …

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Monumentos A Dictadores: La Memoria Histórica Del Valle De Los Caídos Y El Museo Presidente Pinochet, Sofia Sequoia Biegeleisen Jan 2021

Monumentos A Dictadores: La Memoria Histórica Del Valle De Los Caídos Y El Museo Presidente Pinochet, Sofia Sequoia Biegeleisen

Senior Independent Study Theses

Este estudio independiente discute la teoría de la memoria historia en relación con dos casos de estudio: el Valle de los Caídos en España y el Museo Presidente Pinochet en Chile. El primer capítulo introduce textos que explican la importancia de la memoria histórica y establecen su utilidad para comprender una cultura. Esta información proporciona un contexto para entender las conexiones entre los casos de estudio y las populares narrativas históricas en España y Chile. El análisis del Valle discute la creación del monumento, su estilo arquitectónico y la influencia que la arquitectura tiene en el significado simbólico del sitio, …

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Foreign Election Interference And Hybrid Warfare, Jonathan Davies Jan 2021

Foreign Election Interference And Hybrid Warfare, Jonathan Davies

Senior Independent Study Theses

Election interference has long been a tool of foreign policy available to state actors but has recently risen in prominence as a result of Russia’s efforts to influence the 2016 presidential election in the United States. Although much has been written about election interference, most existing scholarship focuses on its use to promote a certain candidate or party. Hybrid warfare theory, which posits that modern conflict is increasingly characterized by the coordinated use of a wide range of tactics, provides a powerful alternative framework for understanding election interference. This Independent Study considers election interference through the lens of hybrid warfare …

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Whitewashing V. Blackwashing: Structural Racism And Anti-Racist Praxis In Hollywood Cinema, Alyssa M. Smith Jan 2021

Whitewashing V. Blackwashing: Structural Racism And Anti-Racist Praxis In Hollywood Cinema, Alyssa M. Smith

Senior Independent Study Theses

When a discussion about whitewashing arises, there are often claims that “blackwashing,” the practice of replacing a traditionally White character or role with a Black actor, is the same issue. Much is known about whitewashing and how damaging it is to represent People of Color in film with White actors, however, blackwashing is a recent term to describe what is more often called “colorblind casting.” This study aims to dissect how whitewashing and blackwashing differ, as well as discuss how blackwashing succumbs to the racist history of the Hollywood film industry despite its attempt at leading a brighter future for …

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Now You See Me — Now You Don’T: An Investigation Of Hair Alterations Effects On Face Identification In Own- And Other-Race Faces, Maresa A. Tate Jan 2021

Now You See Me — Now You Don’T: An Investigation Of Hair Alterations Effects On Face Identification In Own- And Other-Race Faces, Maresa A. Tate

Senior Independent Study Theses

No abstract provided.

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Two Sides Of The Same Coin: Vergil And Ovid's Clashing Portrayals Of Individual And Group Identity, Dante G. King Jan 2021

Two Sides Of The Same Coin: Vergil And Ovid's Clashing Portrayals Of Individual And Group Identity, Dante G. King

Senior Independent Study Theses

This independent study examines Vergil’s Aeneid and Ovid’s Heroides and Metamorphoses with regard to Aeneas and Turnus as analogues for Roman citizens and Italic provincials respectively. As this project is primarily concerned with textual investigation, philological analysis of Vergil and Ovid’s texts takes center stage and is supplemented by contemporary material evidence and secondary scholarship in foundation narratology, identity, and political theory. So, whereas Vergil characterizes Aeneas as a dominant hero destined to found a new home for his people, the proto-Roman Trojans, and Turnus as a rebellious but ultimately ineffectual Italic monarch, Ovid presents the former as a detestable …

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The Application Of Machine Learning In Analyzing Organic Compounds From Nmr Spectral Data, Nicole Maia Powell Jan 2021

The Application Of Machine Learning In Analyzing Organic Compounds From Nmr Spectral Data, Nicole Maia Powell

Senior Independent Study Theses

Nuclear magnetic resonance (NMR) is used in organic chemistry to identify unknown organic compounds. The data obtained from an NMR spectrometer are typically shown in the form of a spectrum, which is then analyzed by an analytical chemist. The action of analyzing a spectrum, especially one of a large and complex molecule, is a long and tedious process. In this project, Python is used to implement hierarchical clustering on NMR data obtained from an NMR spectrometer at the College of Wooster to explore its application in NMR analysis. MATLAB is used to build a decision tree from the same data, …

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Helen Of Troy? A Reexamination Of Helen's Speech In The Iliad, Erin A. Robichaud Jan 2021

Helen Of Troy? A Reexamination Of Helen's Speech In The Iliad, Erin A. Robichaud

Senior Independent Study Theses

In most interpretations, Helen of Troy’s beauty makes her a vain, promiscuous, and dangerous woman. This is the Helen that patriarchal societies have written into existence and passed on to later generations, but it is not the Helen that appears in the Iliad. This thesis argues that Helen’s voice makes her a perceptive and powerful strategist. On different occasions, Helen adopts the speech patterns of various social groups represented in Homeric society in order to assume their identity. She builds a Trojan and a Greek persona as a means to protect herself from the trauma she experiences during the …

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La Isla Silenciada: A Study On Puerto Rican Attitudes Towards The U.S. Federal Government’S Response To Hurricane Maria And Its Impact On Puerto Rico’S Status, Lizbeth Acevedo Jan 2021

La Isla Silenciada: A Study On Puerto Rican Attitudes Towards The U.S. Federal Government’S Response To Hurricane Maria And Its Impact On Puerto Rico’S Status, Lizbeth Acevedo

Senior Independent Study Theses

Puerto Rico’s ongoing economic crisis and the inadequate emergency response to the devastation of Hurricane Maria are deeply tied to the island’s neo-colonial political arrangement with the United States. The two-principle alternative political arrangements—statehood and independence—are the subject of vigorous ongoing debate both on the U.S. mainland and the island. However, the results of periodic plebiscites on the island are often poor indicators of the island residents’ true preferences on the matter because they are often subject to politicization and abstention campaigns. Therefore, I use a survey with a representative sample of island residents conducted in the aftermath of Hurricane …

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The Ghosts Of Grief: An Exploration Of Gothic Influence In 2010s Horror Cinema, Halen Gifford Jan 2021

The Ghosts Of Grief: An Exploration Of Gothic Influence In 2010s Horror Cinema, Halen Gifford

Senior Independent Study Theses

The purpose of this project is to examine gothic influences in contemporary horror cinema of the 2010s. To fulfill this purpose, the study employs comparative film analysis methods to analyze The Babadook (2014), The Invitation (2015), and Crimson Peak (2015) in order to identify intertextual gothic references in the cinematography, mise en scène, and narratives of the films. Specifically, this project examines the haunted house trope in the horror genre as characterized by the presence of ghosts and the personification of the setting. Through this analysis, four common themes emerged: “Houses with Personality,” “Tragic Losses,” “Memories and Ghosts,” and “Isolation.” …

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Political Identity Rules: Support Of Renewable Energy Jobs And Attitudes On Soil Conservation In Northeastern Ohio, Leah H. Jorn Jan 2021

Political Identity Rules: Support Of Renewable Energy Jobs And Attitudes On Soil Conservation In Northeastern Ohio, Leah H. Jorn

Senior Independent Study Theses

The purpose of this study was to look at the support of a proposed Act and renewable energy jobs as it paired with endorsement from elite Republicans. This was tested across political groups but mainly focuses on Republican responses. The hypothesis was that with elite endorsement Republican approval will increase for both the Act and renewable energy jobs. This study also focuses on attitudes of local farmers in Northeastern Ohio on soil conservation and how Republican values and identity politics affect this. This was studied through both a survey of approximately 450 people and through archival work. The results indicate …

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"The Refugees Are Better Off Than We Are": Evaluating The Impact Of Syrian Refugees On Jordanian Labor Markets, Maggie Dougherty Jan 2021

"The Refugees Are Better Off Than We Are": Evaluating The Impact Of Syrian Refugees On Jordanian Labor Markets, Maggie Dougherty

Senior Independent Study Theses

This thesis analyses the labor market impacts associated with hosting Syrian refugees in Jordan through the Syrian conflict. We provide a critical analysis of the sentiment that ‘the refugees are better off than we are.’ This sentiment derives from the perception that the poor economic conditions are the fault of refugees, because they take jobs from native citizens, or because of the international humanitarian aid that refugees receive. We suggest that this perception is a ‘false narrative’ which does not accurately describe the many causes of economic hardships in Jordan, thereby misplacing blame on refugees. The article analyzes the structural …

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“Sisters Are Doin’ It For Themselves”: Creating A Financial Literacy Workshop For College-Aged Women On The Relationship Among Spending, Saving, And Investing, Lesley Chinery Jan 2021

“Sisters Are Doin’ It For Themselves”: Creating A Financial Literacy Workshop For College-Aged Women On The Relationship Among Spending, Saving, And Investing, Lesley Chinery

Senior Independent Study Theses

The purpose of this study is to create a financial literacy workshop for college-aged women to increase understanding of the relationship among spending, saving, and investing. Utilizing relevant scholarship on gender and economics, the Elaboration Likelihood Model, and interviews with experts in economics and with facilitators of financial literacy workshops, I created a virtual workshop for college-aged women. This research found that successfully enabling both central and peripheral processing routes plays a significant role in attracting potential participants to workshops and in turn, cognitively engages them during workshops. Moreover, planners of workshops need to ensure consistent appealing messaging in communication …

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Peace Be With You: An Analysis Of The Effectiveness Of Interfaith Versus Single-Faith Peacebuilding Programming At Reducing Violence In Religious Conflict, Sydney Maureen Hanes Jan 2021

Peace Be With You: An Analysis Of The Effectiveness Of Interfaith Versus Single-Faith Peacebuilding Programming At Reducing Violence In Religious Conflict, Sydney Maureen Hanes

Senior Independent Study Theses

This study seeks to analyze the effectiveness of interfaith versus single-faith peacebuilding programming at reducing levels of violence in instances of violent religious conflict. After reviewing the literature, I used contact theory and constructivism to form my hypothesis that interfaith programming is more effective compared to single-faith programming at reducing violence. Using a mixed-methods approach, I conducted a most similar systems case study design to analyze the effectiveness of different forms of faith-based programming within the conflict in Northern Ireland. I also analyzed geographical data to test for relationships between the types of programming and conflict violence. Although there was …

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Corporate Pressure Makes Regime Diamonds: An Analysis Of The Impact Of Multinational Corporations On International Environmental Regime Effectiveness, Katie Harvey Jan 2021

Corporate Pressure Makes Regime Diamonds: An Analysis Of The Impact Of Multinational Corporations On International Environmental Regime Effectiveness, Katie Harvey

Senior Independent Study Theses

Despite the tendency for multinational corporations to overexploit natural resources and pollute the Earth, the immense power of capital in a globalizing world has presented a unique opportunity for corporations to become drivers for positive global environmental change. To make sense of this puzzle, this study asks how does an international environmental regime’s relationship to the economic marketplace impact its institutional and ecological effectiveness? Through a small-n case study, this project analyzes the historical context, market interactions, and regime outcomes of four distinct instances of global environmental governance: the stratospheric ozone regime, the climate change regime, the global oceanic regime, …

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A Case Of Mistaken (Ethnic) Identity: Rethinking Civil War Duration, Ethnic Saliency, Terrorism, And The Real Factors Discouraging Resolution, Angie Bittar Jan 2021

A Case Of Mistaken (Ethnic) Identity: Rethinking Civil War Duration, Ethnic Saliency, Terrorism, And The Real Factors Discouraging Resolution, Angie Bittar

Senior Independent Study Theses

The field of political violence has consistently emphasized understanding the way that civil wars end, with less emphasis placed on the circumstances which elicit extended civil war duration. This analysis shifts the focus of study on to the internal factors of civil war, following the question: What are the domestic factors of civil war that cause some wars to be more durable and resistant to resolution than others? Building off of several prominent theories within the field of political violence and the anthropological study of ethnic saliency, I hypothesize that civil wars that are characterized as identity based will be …

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Visit Which Scotland? Political Events Illuminating Two Competing Visions Of Re-Emerging Scottish Identity Since The Late Twentieth-Century, Erin W. Delaney Jan 2021

Visit Which Scotland? Political Events Illuminating Two Competing Visions Of Re-Emerging Scottish Identity Since The Late Twentieth-Century, Erin W. Delaney

Senior Independent Study Theses

Since the late twentieth century, Scotland has undergone a series of political changes. I argue that a consequence of these changes has been increased support for a separate national Scottish identity. By analyzing competing visions of this identity through the tourism industry and Gaelic revival, this IS shows the complexities of this move towards nationalism. While many scholars have analyzed the re-emergence of Scottish identity since 1707, the relationship between Gaelic revival efforts and the tourism industry have not been connected to show the complexities of this re-emerging Scottish identity. This IS draws on a vast array of interdisciplinary sources …

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