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.

Dreadnought is a free-to-play multiplayer flight simulation in which two teams of 8 players each compete against one another to complete an objective. Each player controls a large-scale spaceship, various aspects of which can be customized to improve a player’s performance in a game. One such aspect is Officer Briefings, which are passive abilities that grant ships additional capabilities. Two of these Briefings, known as Retaliator and Get My Good Side, have strong synergy when used together, which has led to the Dreadnought community’s claiming that the Briefings are too powerful and should be rebalanced to be more in line with the power levels of other Briefings. This study collected gameplay data with and without the use of these specific Officer Briefings to determine the precise impact on gameplay. Linear correlation matrices and inference on two means were used to determine performance impact. It was found that, although these Officer Briefings do improve an individual player’s performance in a game, they do not have a consistent impact on the player’s team performance, and that these Officer Briefings are therefore not in need of rebalancing.

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.