Number Theory and the Queen of Mathematics

Geometry is an integral component of secondary mathematics curriculum. From my experience in a mathematics teacher preparation program, I have seen a real push to connect geometry to other areas of mathematics. Secondary geometry can often be presented without clear or any connections to other areas of mathematics. One main purpose of this paper is to explore geometry and its rightful connection to other areas of mathematics, specifically number theory. Such strong emphasis is placed on drawing connections to number theory because of its intrinsic value in enhancing understanding of mathematical concepts. Learning number theory has positive ramifications for students, making the transition from arithmetic to an introduction to algebra. It helps “students develop better understandings of the abstract conceptual structure of whole numbers and integers,” and it has important algebraic characteristics, which relate to variables and mathematical reasoning (Campbell & Zazkis, 2006, p.28). Another purpose of this paper is to explore not only number theory as it relates to geometry, but also the basic history of number theory. Number theory has a beauty, accessibility, history, formal and cognitive nature, and intrinsic merits all to its own (Campbell & Zazkis, 2006, p. 13). For the sake of all the intrigue of number theory, I have a desire to learn more about it to fuel my own pursuit of a better understanding of effectively teaching mathematics, but also to use it to encourage and engage students in their personal pursuit of mathematical understanding

What A Waste! A Secondary Environmental Science Unit On Waste Reduction And Management

This writing serves as an introductory unit to waste management and reduction to be used in a high school urban environmental education classroom. The research question for this capstone was, does teaching environmental science through waste reduction and management in an urban classroom affect student engagement and connection? The research outlined in this paper explores and examines the concept of an urban classroom environment, the importance of teaching environmental science, and tools and materials to incorporate a unit on waste into an environmental science course. The paper goes on to explain the importance of educating students about the waste crisis and explores ways to increase engagement when it comes to waste reduction in their communities. This topic was chosen due to its extreme relatability to students who reside in a metropolitan or urban area. It contains immediately applicable content that would serve to enrich a current curriculum or aid in developing a new one

Modeling My Mother? An Exploration of the Relationship between a Mother's Occupational Status and Her Daughter's Career Aspirations

Thesis advisor: Sara MoormanThis research looks at the ways in which mothers influence their daughter’s educational achievements and occupational aspirations. The goal is to determine whether the Role-Model Hypothesis or Grades Hypothesis explains the relationship more. According to the literature, the Role-Model Hypothesis is based on ideas of socialization and gender-role stereotypes while the Grades Hypothesis is based on the idea of transmission of social capital, which improves test scores. In order to test these hypotheses, a series of multinomial logistic regression models were run on the responses of a sample of 7,716 female students and their mothers to the Educational Longitudinal Study, (ELS) 2002, Base Year. The results provide evidence in support of the Grades Hypothesis. A mother with higher educational attainment and a more prestigious occupation is more likely to have a daughter with higher test scores, with higher test scores leading to higher expectations and aspirations by the daughter. Implications of this finding include suggestions for the need for action, policy changes, and the decline in the importance of gender theory in influencing aspirations.Thesis (BA) — Boston College, 2013.Submitted to: Boston College. College of Arts and Sciences.Discipline: College Honors Program.Discipline: Sociology Honors Program.Discipline: Sociology

Variability Time Scales of TeV Blazars Observed in the ASCA Continuous Long-Look X-ray Monitoring

Three uninterrupted, long (lasting respectively 7, 10, and 10 days) ASCA observations of the well-studied TeV-bright blazars Mrk 421, Mrk 501 and PKS 2155-304 all show continuous strong X-ray flaring. Despite the relatively faint intensity states in 2 of the 3 sources, there was no identifiable quiescent period in any of the observations. Structure function analysis shows that all blazars have a characteristic time scale of ~ a day, comparable to the recurrence time and to the time scale of the stronger flares. On the other hand, examination of these flares in more detail reveals that each of the strong flares is not a smooth increase and decrease, but exhibits substructures of shorter flares having time scales of ~10 ks. We verify via simulations that in order to explain the observed structure function, these shorter flares ("shots") are unlikely to be fully random, but in some way are correlated with each other. The energy dependent cross-correlation analysis shows that inter-band lags are not universal in TeV blazars. This is important since in the past, only positive detections of lags were reported. In this work, we determine that the sign of a lag may differ from flare to flare; significant lags of both signs were detected from several flares, while no significant lag was detected from others. However, we also argue that the nature of the underlying component can affect these values. The facts that all flares are nearly symmetric and that fast variability shorter than the characteristic time scale is strongly suppressed, support the scenario where the light crossing time dominates the variability time scales of the day-scale flares.Comment: 29 pages, 12 figures, accepted for publication in Ap

Male Tibetan Macaques’ (Macaca Thibetana) Choice of Infant Bridging Partners

Adult male Tibetan (Macaca thibetana), Barbary (M. sylvanus), and stump-tailed macaques (M. arctoides) engage in bridging, a ritualized infant-handling behavior. Previous researchers found a bias toward the use of male infants for this behavior, but its function is debated. Explanations include three hypotheses: paternal care, mating effort, and agonistic buffering. We studied a group of habituated, provisioned Tibetan macaques to test whether adult males’ affiliative relationships with females predicted their use of an infant for bridging. We also examined biases for sex, age, and individual in males’ choice of bridging infant. We collected data via all occurrences, focal animal, and scan methods, from August to September 2011 at the Valley of the Wild Monkeys, China. We found that male infants were significantly preferred over females for bridging, but of three male infants in the group, only one was used by all males, while one male infant was used less often than expected. Adult males had females they were significantly more likely to be proximate to and/or to groom, but these corresponded to the mother of the bridging infant for only one male. Our results are most consistent with the agonistic buffering hypothesis: lower-ranked males used the alpha male’s preferred bridging infant in an attempt to regulate their interactions with the alpha

Tourist Behavior and Decibel Levels Correlate with Threat Frequency in Tibetan Macaques (Macaca thibetana) at Mt. Huangshan, China

Tourism is a common component of management practices directed toward endangered species and habitats, but few studies have explored the potential stressors that may occur to nonhumans as objects of tourism. We examined the impact that tourists have on provisioned, habituated Tibetan macaques (Macaca thibetana). Data were collected during August 2005 at the Valley of the Wild Monkeys (VWM), Mt. Huangshan, China. From a tourist viewing platform, we measured tourist densities, behaviors (for example, foot, hand, and mouth noises; mimicking monkeys; throwing objects or food), and decibel levels. Frequencies of monkey threats in the provisioning area of their range were recorded. The tourists\u27 collective behaviors correlated with monkey threats (Pearson\u27s correlations; r=0.391, p=0.014), as did decibel levels on the viewing platform (r=0.334, p=0.038). No relationship between tourist density and monkey threats, or between particular tourist behaviors and monkey threats, was significant. Based on these results, we recommend park staff be trained on how to discourage noise often associated with tourists and regulate prohibited tourist behaviors, such as feeding the monkeys. Enforcement of park rules will decrease chances that tourist-monkey interactions at VWM will escalate into situations where injuries occur, as has happened at some other macaque tourism sites. Finally, we suggest the development of tourist education materials