Barrett, The Honors College Thesis/Creative Project Collection

Over the course of 2020, individuals and organizations were thrown various unprecedented obstacles that necessitated flexibility, empathy, and understanding. Many organizations were forced to reevaluate their financial status, their purpose, and how they could provide for their employees. The COVID-19 pandemic meant that most companies had to introduce a ‘work from home’ policy, drastically decreasing the face-to-face contact that employees had with each other and leadership. The virus, coupled with the social and political unrest in the U.S. in the wake of the Black Lives Matter movement and the 2020 presidential election, inspired many companies to reframe their organization and redefine their goals.<br/> The B2B (business-to-business) Marketing Agency, The Mx Group, is preparing for a change in leadership, with the current Chief Executive Officer and Founder stepping down, being replaced by the President of the company. The company plans to execute the transition in the spring of 2022, allowing them the rest of 2021 to plan for the change, catering to employees’ individual and the company’s collective needs. It was also prompted by factors such as the COVID-19 pandemic to reevaluate the values that it upholds as an organization, coinciding with the change in leadership. Leaders of the company are actively encouraging employees to engage with these values by recognizing when a colleague performs in alignment with a value.<br/> In reframing their organization, The Mx Group has a significant opportunity to uniquely position itself in the industry. Lee G. Bolman and Terrence E. Deal (2017) introduced four frames: human resources, symbolic, structural, and political, as a way to guide a transformative application of leadership and management in business. Analyzed from these perspectives, The Mx Group can utilize contemporary ideas to efficiently and effectively seize its opportunity of embedding new values and a change in leadership.

Optimal foraging theory provides a suite of tools that model the best way that an animal will <br/>structure its searching and processing decisions in uncertain environments. It has been <br/>successful characterizing real patterns of animal decision making, thereby providing insights<br/>into why animals behave the way they do. However, it does not speak to how animals make<br/>decisions that tend to be adaptive. Using simulation studies, prior work has shown empirically<br/>that a simple decision-making heuristic tends to produce prey-choice behaviors that, on <br/>average, match the predicted behaviors of optimal foraging theory. That heuristic chooses<br/>to spend time processing an encountered prey item if that prey item's marginal rate of<br/>caloric gain (in calories per unit of processing time) is greater than the forager's<br/>current long-term rate of accumulated caloric gain (in calories per unit of total searching<br/>and processing time). Although this heuristic may seem intuitive, a rigorous mathematical<br/>argument for why it tends to produce the theorized optimal foraging theory behavior has<br/>not been developed. In this thesis, an analytical argument is given for why this<br/>simple decision-making heuristic is expected to realize the optimal performance<br/>predicted by optimal foraging theory. This theoretical guarantee not only provides support<br/>for why such a heuristic might be favored by natural selection, but it also provides<br/>support for why such a heuristic might a reliable tool for decision-making in autonomous<br/>engineered agents moving through theatres of uncertain rewards. Ultimately, this simple<br/>decision-making heuristic may provide a recipe for reinforcement learning in small robots<br/>with little computational capabilities.

This thesis is a supplement textbook designed with ASU’s MAT 370, or more generally, a course in introductory real analysis (IRA). With research in the realms of mathematics textbook creation and IRA pedagogy, this supplement aims to provide students or interested readers an additional presentation of the materials. Topics discussed include the real number system, some topology of the real line, sequences of real numbers, continuity, differentiation, integration, and the Fundamental Theorem of Calculus. Special emphasis was placed on worked examples of proven results and exercises with hints at the end of every chapter. In this respect, this supplement aims to be both versatile and self-contained for the different mathematics skill levels of readers.