Biology is changing and becoming more quantitative. Research is creating new challenges that need to be addressed in education as well. New educational initiatives focus on combining laboratory procedures with mathematical skills, yet it seems that most curricula center on a single relationship between scientific knowledge and scientific method: that of the validity of knowledge claims, judged in terms of their consistency with data. Collecting data and obtaining results (however quantitative) are commonly part of science, but are not science itself. We envision that the operative use of the complete scientific method will play a critical role in providing the necessary underpinning for the integration of math and biology at various professional levels.

Bugelski and Sharlock (1952) credit McGeoch with saying that although the concept of mediation was an old one, it had generated more discussion than experimentation. Bugelski and Sharlock in commenting on McGeoch's statements had this to say, "The concept of mediation is of great potential value for the psychological analysis of learning, thinking, and insight." (Bugelski and Sharlock, 1952, p. 334) The views of Bugelski and Sharlock represent the current thinking in verbal learning circles relevant to the importance of mediation in symbolic forms of behavior. The experimental emphasis, at the present time, is upon the conditions underlying the process. With regard to the nature of mediation Jenkins has stated, The second task, I believe, is to press on in our experimental attack on the conditions of mediation: that is, we should attempt to discover how these implicit processes are acquired, how they are actuated, how they are inhibited, and in general, how they are employed by the subjects. (Jenkins, 1963, p. 212) One method by which the conditions of mediation may be discovered is to determine the relationship between this process and many other forms of intervening variables. In commenting on this latter point Mowrer has stated, "But no one, it seems, has addressed himself systematically to the question of the relation between intervening variables and mediators." (Mowrer, 1960, p. 68) These views of Jenkins and Mowrer on the direction experimentation should take in mediation suggest the need for the current study. The purpose of this study was to investigate the function of visual imagery, type of mediator and associative frequency in mediate association. The role of these factors was examined within an induced mediation paradigm of the form A- B, B-C, A-C.

The study was conducted to examine the importance of forage resources in limiting peak population density of black-tailed jackrabbits (Lepus californicus). The research design combined field studies of jackrabbit diet and vegetation impact with computer simulation of herbivore nutrition and population dynamics. The relationships between available forage, dietary intake, energy and protein balance and population changes were compared for high and low population density. Hypotheses tested were : (1) Dietary composition is unaffected by availability above 10 kg/ha; (2) Jackrabbits do not require more forage than is available at high population densities; (3) Dietary composition is not significantly different at high and low densities; (4) Dietary composition is not significantly different between sexes; (5) Nutritional balance of lactating females is not significantly altered at high density; and (6) Nutritional balance of females entering the breeding season is not significantly altered at high density. The field studies were designed to measure dietary preference by the jackrabbits, the availability of herbage, and utilization of selected plant species. Jackrabbits ate nearly all forage types available but primarily consumed dominant shrubs in fall and winter, suffrute scents in fall and winter, grasses in spring and summer, and forbs in summer. There was no significant difference between dietary composition or preference rating among density periods or sexes. Dietary percentage of preferred forage species was directly related to availability above 10 kg/ha. Jackrabbits removed an average of 30 to 40 percent of individual plants of Kochia americana, but only browsed on 5 toll percent of all available plants. Total removal of Kochiastanding crop averaged only 3.7 percent. The model used in the simulation studies incorporated relationships involving existence, activity and production (growth, gestation and lactation) requirements to estimate forage requirements. Intake and requirements affect energy and protein balance which are related to body weight changes and production. Model mortality rates are modified by nutritional deficiency as a fraction of the requirements. The following conclusions resulted from model simulations. Forage requirements are less than 1 percent of available forage, even at high population density. Nutritional balance of lactating females was unaffected by observed diets or population density. Nutritional balance of females entering the breeding season is unaffected by diet but may be affected by early breeding date or large litter sfze. Individual nutritional response and its interaction with food does not cause significant change in population mortality rates. Nutritional deficiency may contribute to mortality, particularly during lactation or winter periods, but these effects are independent of population density.

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The one-way analysis of variance (ANOVA) is mainly based on several assumptions and can be used to compare the means of two or more independent groups of a factor. To relax the normality assumption in one-way ANOVA, recent studies have considered exponential distortion or tilt of a reference distribution. The reason for the exponential distortion was not investigated before; thus the main objective of the study is to closely examine the reason behind it. In doing so, a new generalized semi-parametric approach for one-way ANOVA is introduced. The proposed method not only compares the means but also variances of any type of distributions. Simulation studies show that proposed method has favorable performance than classical ANOVA. The method is demonstrated on meteorological radar data and credit limit data. The asymptotic distribution of the proposed estimator was determined in order to test the hypothesis for equality of one sample multivariate distributions. The power comparison of one sample multivariate distributions reveals that there is a significant power improvement in the proposed chi-square test compared to the Hotelling's T-Square test for non normal distributions. A bootstrap paradigm is incorporated for testing equidistributions of multiple samples. As far as power comparison simulations for multiple large samples are considered, the proposed test outperforms other existing parametric, nonparametric and semi-parametric approaches for non normal distributions.

The aim of this thesis is to examine the connection between the Riemannhypothesis and the distribution of prime numbers. We first derive theanalytic continuation of the zeta function and prove some of its propertiesusing a functional equation. Results from complex analysis such asJensen’s formula and Hadamard factorization are introduced to facilitatea deeper investigation of the zeros of the zeta function. Subsequently, therelation between these zeros and the asymptotic distribution of primesis rendered explicit: they determine the error term when the prime-counting function π(x) is approximated by the logarithmic integral li(x).We show that this absolute error is O(x exp(−c√log x) ) and that the Riemannhypothesis implies the significantly improved upper bound O(√x log x).

Aquatic plants (macrophytes) are important components of freshwater ecosystems and serve numerous purposes, physical and biological, that help to structure aquatic communities. Although macrophytes represent an essential component of stable aquatic communities, invasive macrophytes may negatively alter ecosystem properties. Non-native, invasive species have been identified as a major cause of biodiversity loss and the increasing prevalence of invasive species has prompted studies to help understand their impacts and to conserve biodiversity. Studying mechanisms of invasion also gives insight into how communities are structured and assembled. This study examined mechanisms that contribute to macrophyte invasion. First, I reviewed literature concerning mechanisms of macrophyte invasion. Mechanisms identified with this review were then placed within the context of the invasion process and potential taxonomic biases were discussed. Second, a set of classic invasion hypotheses were tested, including biotic resistance, disturbance, and stress, using mixed-effects models on survey data collected from twenty-nine lakes across the United States. Finally, using the same survey data, I performed an observational test of Darwin’s Naturalization Hypothesis at a small (point) and large (lake) scale for two highly invasive macrophytes, Potamogeton crispus and Myriophyllum spicatum. Results of the first study indicated that many invasion mechanisms have been tested with fully aquatic macrophytes with varied levels of support. In addition, there is likely a taxonomic bias depending on geographic location of the invaded area. The second study indicated that biotic interaction, disturbance, and stress interact, often in non-linear ways to influence probability of an invasive species occurring at a location. However, models containing these variables explained a relatively low percentage of variation in probabilities. Finally, there was no support for Darwin’s naturalization hypothesis at either a point or lake scale. Future research should continue the search for mechanisms that allow introduced species to establish. It is likely that general principles do not exist, at least among comparisons across ecosystem types. However, ecologists should continue to search for general patterns within definable ecosystem units to increase understanding about factors contributing to invasibility.

In this thesis I propose an interpretation of Plato's middle period dialectic. I contend that the method of such dialectic has two components, the doctrine of recollection and the method of hypothesis, and that the two are intimately related. In contrast to the orthodox interpretation, which ignores recollection and sees the method of hypothesis as essentially deductive, I suggest that the discovery of knowledge occurs from the recollection of a pre-natal vision of reality (the world of forms), where such recollection is stimulated by dialectical questioning. Recollection is gradual and uncertain. The direction of the dialectical questioning is itself guided by one's intuition, or (incomplete) recollection of reality at the time, thus providing a progressive interaction between recollection and the method of dialectical questioning, reasoning by hypothesis. In this way, one builds a provisional picture of reality, where the prime relation between hypotheses about such reality is one of coherence. The true dialectician will not only develop a complete and coherent picture of reality, but will ultimately verify the accuracy of this picture upon apprehension of the unhypothetical first principle, the form of the good. / Thesis / Master of Arts (MA)

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