In this paper, our Founders Lab team members — Jacob Benevento, Sydney Evans, and Alec Whiteley — recount the year-long entrepreneurial journey that led to the creation and launch of our venture, Certified Circular. Certified Circular is a program that certifies on-campus events for implementing circular practices into their activities as well as off-campus businesses. The venture was formed in response to our group’s propelling question and industry selection, which called on us to create and market a venture within the ethical circular economy.

This thesis project has been conducted in accordance with The Founder’s Lab initiative which is sponsored by the W. P. Carey School of Business. This program groups three students together and tasks them with creating a business idea, conducting the necessary research to bring the concept to life, and exploring different aspects of business, with the end goal of gaining traction. The product we were given to work through this process with was Hot Head, an engineering capstone project concept. The Hot Head product is a sustainable and innovative solution to the water waste issue we find is very prominent in the United States. In order to bring the Hot Head idea to life, we were tasked with doing research on topics ranging from the Hot Head life cycle to finding plausible personas who may have an interest in the Hot Head product. This paper outlines the journey to gaining traction via a marketing campaign and exposure of our brand on several platforms, with a specific interest in website traffic. Our research scope comes from mainly primary sources like gathering opinions of potential buyers by sending out surveys and hosting focus groups. The paper concludes with some possible future steps that could be taken if this project were to be continued.

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.

With the rise of fast fashion and its now apparent effects on climate change, there is an evident need for change in terms of how we as individuals use our clothing and footwear. Our team has created Ray Fashion Inc., a sustainable footwear company that focuses on implementing the circular economy to reduce the amount of waste generated in shoe creation. We have designed a sandal that accommodates the rapid consumption element of fast fashion with a business model that promotes sustainability through a buy-back method to upcycle and retain our materials.

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.