Claiming Impossible Bodies is a collection of poetry and collage exploring gender and sexuality through the lens of the vampire. For this project, I researched various representations of the vampires through folklore, classical and modern literature, film, and pop culture. The liminality of the vampire allows such figures to take different forms and identities, ranging from dark and grotesque creatures, such as the succubus or incubus from mythology, to modern sex-icons, like Edward Cullen from the Twilight Saga. Considering this wide range of performances by vampiric figures throughout history, the poems in this manuscript seek to deconstruct the binaries that vampires live between and expose the liminality in social norms that attempt to define our identities and shape our performances.

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 collection entitled “Poems on Home, Family, and the Self” is about the author’s role as a daughter to immigrant parents, who is finding her drive, and understanding where she comes from and how she will use that to find her purpose. The poems in this collection touch upon the author’s upbringing in Northern California, her transitioning relationship with her parents and her brother, as well as her experiences relative to her growth in Arizona. These pieces are greatly inspired by author Arundhati Roy and poet Li-Young Li. Specifically, the author is influenced by Li-Young Li’s approach to poetry – his commentary and storytelling of his life and his parents are objective, observatory, and allow the readers to make opinions for themselves. In this collection, the author aims to make statements about her family and upbringing and show the readers her new understanding of life and her ambitions.

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.