2009-2010 MICS Student Research
Bridging the Gap Between Hardware and Software
Mentor: Dr. Lori Carter
As it would be impossible to learn everything related to computers, students have been forced to choose a specialty. The students who study Computer Science have little or no knowledge regarding the physical hardware that comprises their main programming tool, the computer itself. On the other hand Engineering majors know little about what brings the hardware to life. This project will attempt to develop a series of labs using the Lego Mindstorms platform which will be a start at bridging the gap between Computer Science and Engineering. This platform affords the student a fun and relatively simple way to explore embedded real-time processors. The lack of a conventional operating system used with such processors brings Computer Science majors closer to the hardware, while the low level programming required brings Engineering majors a greater understanding of the software used to control the circuitry.
Qualitative Analysis of Systems of Ordinary Differential Equations
Mentor: Dr. Jesus Jimenez
Only a small subset of ordinary differential equations (ODEs) can be solved analytically. With the increasing availability of powerful computers, we have become accustomed to solving ODEs using a variety of numerical methods, and these methods can produce very good approximations for solutions, but they are only approximations. They can only give discrete solutions and they cannot be used to prove the properties of the system. These limitations are significant barriers to using numerical methods alone in an analysis of chaos, bifurcations, and limit cycles in systems of ODEs. This project is devoted to introducing the theory involved in a qualitative analysis of systems of ODEs. It begins by discussing the dynamics of selected two and three dimensional linear systems and the possible behavioral variants observed in these systems. The discussion then builds on the theory of linear systems to begin to understand the behavior of nonlinear systems. We approach the understanding of non-linear systems by examining the statements and results of the Hartman-Grobman, Poincare-Bendixson, and Poincare-Hopf theorems.
Constructing an Academic Predictive Model: Predicting the Academic Success of Incoming Freshmen After One Year of Undergraduate Education
Mentors: Dr. Maria Zack and Dr. Greg Crow
The current study aims to construct a predictive model by which undergraduate applicants can be ranked according to their potential to succeed in their first year at a four year undergraduate institution. The model considers such factors as the student’s high school grade point average, the academic strength of their high school, their standardized test scores, and the number of advanced placement credits received prior to high school graduation. The ability to accurately predict the academic success of incoming freshman after one year of undergraduate education will enable faculty and staff to provide appropriate support for at-risk students.
Searching for Patterns in Brunnian Links
Mentor: Dr. Catherine Crockett
A fundamental goal in knot theory is to distinguish one knot from another. This paper starts with an introduction to knot theory in order to build the foundation necessary for understanding the research done. This project seeks to indentify patterns and establish connections among subfamilies of Brunnian Links. Possible relationships among the colorability, crossing number, polynomial, and braid word are explored. These results add to the collective knowledge about this interesting family of links.
A Bayesian Decision Model to Play Rook
Mentor: Dr. Jeff McKinstry
Creating a computer opponent to play cards is difficult due to the elements of complexity and chance. In the card game rook, even without the element of chance, given a specific deal of the cards, there are as many as n!^4 possible ways for players to play the cards, where n is the number of cards in each person’s hand. When n is 9, there are 1.7 x 1022 potential permutations. Playing card games optimally is still an open problem.
Bayesian networks have recently been applied successfully to probabilistic decision making with uncertainty. The goal of this project is to try to design a Bayesian network to play rook well. The results will be compared to the optimal solution obtained from the MiniMax Algorithm, a standard game playing algorithm applied to games with perfect information.
An Analysis of Chapel Attendance
Mentors: Dr. Maria Zack and Dr. Greg Crow
According to its Mission Statement, “Point Loma Nazarene University exists to provide higher education in a vital Christian community where minds are engaged and challenged, character is modeled and formed, and service becomes an expression of faith.” It is not just an academic community but is instead a flurry of academia in the framework of a “vital Christian community” (Pointloma.edu). One of the institutionally implemented practices for fostering this Christian community is chapel. At PLNU, chapel offers an opportunity for students across the campus “to explore ways to align their hearts and minds to that of Christ” (Pointloma.edu). Since chapel is such an integral component to the Point Loma community, attending is a requirement for undergraduate students. Full time students (with 12 or more units) with freshman or sophomore standing must attend 36 of the 44 chapels offered in a given semester, and students with junior or senior standing are required to attend 28 chapels. Over time, many hypotheses have been generated regarding student chapel attendance, such as when during the semester students fulfill their chapel requirements or which types of chapels seem to have the highest attendance. It is the goal of this project to take a closer look at student chapel attendance to discover if any patterns or trends exist in student attendance. Chapel attendance data that has been collected since Fall 2006 is organized and analyzed for this purpose. Supplementary information about each individual student, including chapel requirement, gender, and pseudo-cohort, is used to analyze attendance within certain groups.
Interweaving Technology Education into University Curriculum
Mentor: Dr. Lori Carter
As Point Loma Nazarene University strives to equip students with skills needed in the workplace, the methods of how to teach technology are constantly being reconsidered. This project will look at the ways that discipline-specific computer applications can be included in existing classes rather than in generic separate modules as they are now. One way to do this is for the professor to demonstrate the use of the applications. For example, students could be taught in Problem Solving how to use Excel for calculating mortgage payments, or learn about PowerPoint as a tool for speech-making in Com 100. Research indicates however, that a more timely approach might be to help the students figure out on their own how to learn the necessary technology. This has the advantage of reducing the stress on the professor to constantly learn new things, and prepares the student for the possibility that what they are learning now may be obsolete when they actually enter the work force. Techniques employed in this project include professor interviews, online research into what other schools do to address this issue, and background research to understand how students learn best in this era of rapidly changing technology.
Studies on the Reaction Kinetics of Chlorosulfonyl Isocyanate with Monofluoro Substituted Alkenes and the History of the Relevant Differential Equations
Mentors: Dr. Maria Zack and Dr. Dale Shellhamer
Kinetic measurements with chlorosulfonyl isocyanate (CSI) and various monofluoroalkenes are compared to literature data with hydrocarbon alkenes to give insight into the pathway for reaction of monofluoroalkenes with CSI. Additionally, the history of the differential calculus involved will be analyzed to better understand the field of chemical kinetics.