In 1931 Gödel released his Incompleteness Theorem. His theorem was the opposite of what other mathematicians at the time wanted, but it was very influential to realize there is no perfectly complete formal systems. The incompleteness theorem is based of the idea that in a consistent system there are pieces that can not be proved or disproved, causing for incompleteness. The second part of that idea is that such a system can not prove that itself is consistent, which also makes it incomplete. I will verify theses proofs using a series of logic problems that show how a system is incomplete.
Sarah Curtiss, Brianna Meissner, Mari Tonsfeldt, Alexis Schwinghamer, and Sierra Wenning
When most people think of the flute, the traditional, classical flute sound comes to mind. This research delved into the study of contemporary, non-traditional sounds (extended techniques) because of the number of advantages that the study of extended techniques can provide to all aspects of flute playing. For example, certain techniques can strengthen the flexibility and control of the facial muscles, which helps with tone production, while other techniques can help to develop better awareness and control of intonation. Many extended techniques require different levels of breath control and more comprehensive physical strength, as well. In researching extended techniques, it is valuable and informative to consider the acoustic, pedagogical, and sonic factors and results.
This research is based on the Five Factors that were devised by Bill Connelly of SBNation. The Five Factors of football include Explosiveness, Efficiency, Field Position, Finishing Drives, and Turnovers. Each factor is composed of associated statistics that when put together make up the most important statistics in football. This research includes the analysis of all 857 FBS (the highest level of NCAA Division I football) games from the 2016 season. Data was analyzed through the use of an Excel spreadsheet. Five different statistics were looked at, each associated with one of the Five Factors. The statistics include Yards per Play, Success Rate, Average Starting Field Position, Points per Trip Inside the 40, and Turnover Margin. Game by game analysis of each statistic was conducted and the results were compiled together to help show the importance of each statistic and how each one impacted a team’s likelihood of winning. Trends were found that help show the impact that each statistic has on a football game; however, it is important to note that with so much variability in the game of football and how just about every statistic is dependent on other statistics, the results of this research will not always be consistent with individual game results.
Rayce Martin, Iraj Mamaghani, and Nikoloas Nikitas
Mitigating global climate change is a major contemporary topic of research and is of major interest to today’s societies. Developed countries the top contributors to the destruction of the climate with buildings in these countries being one of the reasons. Buildings in developed countries account for 20-40% of the total primary energy consumption. This high-energy consumption produces approximately 36% of the total CO2 emissions since fossil-fuels are the primary source of energy in almost all developed countries. To combat this, researchers have investigated wind energy harvesting technologies that produce electricity while also being considered “green”, or low carbon dioxide emitters. One of these technologies utilizes aeroelastic flutter to induce a current in conducting coil to produce electricity. This study examines a prototype that uses this principal with the intent to apply it in the built environment thus, offering a better alternative to conventional urban wind turbines.
From previous work in this area it was found that the inclination angle of these harvesters has not been evaluated. This study address this using a wind tunnel and a prototype while also attempting to characterize the motion of the fluttering membrane of the harvester. It is found that at non-perpendicular wind flows the voltage output of the conducting coils is decreased through all investigated windspeeds and is exaggerated in as speed increases. Analogies are discovered at Θ = -15° in which voltage dramatically decreases. It is also found that displacement and voltage increase as windspeed increases. Lower speeds produce more stable oscillations with higher speeds causing the oscillations to be unstable. The magnets tended to contact the conducting coil spool at higher windspeeds causing the instability.
Major League Baseball has been a catalyst for making decisions in sports and competition from a purely mathematical viewpoint. We have seen teams utilize unique on-field player alignments and roster-building strategies based on statistical observations and applications of math. This project examines the advantages Sabermetrics and analytics present within the sport. Untapped statistical categories that could further the success of teams in the future is also briefly discussed.
As a prospective math educator who will be teaching in the near future, I was concerned with the idea of preparing my future students for college math courses. I decided to research the effects of teaching students how to appropriately use problem solving strategies in math. My research led me towards looking at the benefits of students becoming better problem solvers and how teachers can implement problem solving into their daily lessons.
When this implementation is successful, students can become more independent with their learning, they are able to work and persevere through challenging problems, and they have a greater chance of being prepared for college math courses. The goal of problem solving is to create "Independent Learners." After conducting my research and discovering these benefits, I hope to implement problem solving strategies into my future classroom.
The dice game Farkle uses 6 six-sided dice and the objective of the game is to be the first person to score 10,000 points. The dice game involves rolling against the odds and possibly lose your running total points. Generating functions are used to determine the probability of various roll patterns and their expected values of points earned given the number of dice rolled. We are assuming the maximum Farkle score is attained for each roll for computations. The probability of rolling a Farkle for each case and the expected values are used as guidelines for decision-making during game play.
The UNDergraduate Showcase gives undergraduate students the opportunity to showcase their research via posters and oral presentations. The posters included in the collection have been recognized for their quality and preserved for future use. Students and faculty interested in participating in future showcases can find more information on the UNDergraduate Showcase website.
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