This paper presents a new mathematics elective for an undergraduate Computationa . . .
l Science program. Algebraic Geometry is a theoretical area of mathematics with a long
history, often highlighted by extreme abstraction and difficulty.
This changed in the 1960s when Bruno Buchberger created an algorithm that allowed Algebraic Geometers to compute examples for many of their theoretical results and gave birth to a subfield called Computational Algebraic Geometry (CAG). Moreover, it introduced many rich applications to biology, chemistry, economics, robotics, recreational mathematics, etc. Computational Algebraic Geometry is usually taught at the graduate or advanced undergraduate level. However, with a bit of work, it can be an extremely valuable course to anyone with decent algebra skills. This manuscript describes Math 380: Computational Algebraic Geometry and shows the usefulness of the class as an elective to a Computational Science program. In addition, a module that gives students a high-level introduction to this valuable computational method was constructed for our Introductory Computational Science course.
The Use of Spreadsheets and Service-Learning Projects in Mathematics Courses
In the Indiana University system, as well as many other schools, finite mathemat . . .
ics is a prerequisite for most majors, especially business, public administration, social sciences, and some life science areas. Statisticians Moore, Peck, and Rossman (2002) articulate a set of goals for mathematics prerequisites: including instilling an appreciation of the power of technology and developing skills necessary to use appropriate technology to solve problems, developing understanding, and exploring concepts. The paper describes the use of Excel spreadsheets in the teaching and learning of finite mathematics concepts in the linked courses Mathematics in Action: Social and Industrial Problems and Introduction to Computing taught for business, liberal arts, science, nursing, education, and public administration students. The goal of the linked courses is to encourage an appreciation of mathematics and promote writing as students see an immediate use for it in completing actual real-world projects. The courses emphasize learning and writing about mathematics and the practice of computer technology applications through completion of actual industrial group projects. Through demonstration of mathematical concepts using Excel spreadsheet, we stress synergies between mathematics, technology, and real-world applications. These synergies emphasize the learning goals such as quantitative skill development, analytical and critical thinking, information technology and technological issues, innovative and creative reasoning, and writing across the curriculum.
An Automated Approach to Multidimensional Benchmarking on Large-Scale Systems
High performance computing raises the bar for benchmarking. Existing benchmarkin . . .
g applications such as Linpack measure raw power of a computer in one dimension, but in the myriad architectures of high performance cluster computing an algorithm may show excellent performance on one cluster while on another cluster of the same benchmark it performs poorly.
For a year a group of Earlham student researchers worked through the Undergraduate Petascale Education Program (UPEP) on an improved, multidimensional benchmarking technique that would more precisely capture the appropriateness of a cluster resource to a given algorithm. We planned to measure cluster effectiveness according to the thirteen dwarfs of computing as published in Berkeley's parallel computing research paper. To accomplish this we created PetaKit, a software stack for building and running programs on cluster computers.
Using WebMO to Investigate Fluorescence in the Ingredients of Energy Drinks
With computers gaining more powerful processors, computational modeling can be i . . .
ntroduced gradually to secondary students allowing them to visualize complex topics and gather data in the different scientific fields. In this study, students from four rural high schools used computational tools to investigate attributes of the ingredients that might cause fluorescence in energy drinks. In the activity, students used the computational tools of WebMO to model several ingredients in energy drinks and gather data on them, such as molecular geometry and ultraviolet-visible absorption spectra (UV-Vis spectra). Using the data they collected, students analyzed and compared their ingredient molecules and then compared them to molecules that are known to fluoresce to determine any patterns. After students participated in this activity, data from testing suggest they were more aware of fluorescence, but not more aware of how to read an UV-Vis spectrum.
In this paper we describe an ongoing project where the goal is to develop compet . . .
ence and confidence among chemistry faculty so they are able to utilize computational chemistry as an effective teaching tool. Advances in hardware and software have made research-grade tools readily available to the academic community. Training is required so that faculty can take full advantage of this technology, begin to transform the educational landscape, and attract more students to the study of science.
Parallelization of Particle-Particle, Particle-Mesh Method within N-Body Simulation
The N-Body problem has become an intricate part of the computational sciences, a . . .
nd there has been rise to many methods to solve and approximate the problem. The solution potentially requires on the order of calculations each time step, therefore efficient performance of these N-Body algorithms is very significant . This work describes the parallelization and optimization of the Particle-Particle, Particle-Mesh (P3M) algorithm within GalaxSeeHPC, an open-source N-Body Simulation code. Upon successful profiling, MPI (Message Passing Interface) routines were implemented into the population of the density grid in the P3M method in GalaxSeeHPC. Each problem size recorded different results, and for a problem set dealing with 10,000 celestial bodies, speedups up to 10x were achieved. However, in accordance to Amdahl's Law, maximum speedups for the code should have been closer to 16x. In order to achieve maximum optimization, additional research is needed and parallelization of the Fourier Transform routines could prove to be rewarding. In conclusion, the GalaxSeeHPC Simulation was successfully parallelized and obtained very respectable results, while further optimization remains possible.
Testing the Waters with Undergraduates (If you lead students to HPC, they will drink)
For the Blue Waters Undergraduate Petascale Education Program
(NSF), we develope . . .
d two computational science modules,
"Biofilms: United They Stand, Divided They Colonize" and
"Getting the 'Edge' on the Next Flu Pandemic: We Should'a 'Node'
Better." This paper describes the modules and details our
experiences using them in three courses during the 2009-2010
academic year at Wofford College. These courses, from three
programs, included students from several majors: biology,
chemistry, computer science, mathematics, physics, and
undecided. Each course was evaluated by the students and
instructors, and many of their suggestions have already been
incorporated into the modules.
It is with great pleasure that we release the first issue of the Journal of Comp . . .
utational Science Education. The journal is intended as an outlet for those teaching or learning computational science to share their best practices and experiences with the community. Included are examples of programs and exercises that have been used effectively in the classroom to teach computational science concepts and practices, assessments of the impact of computational science education on learning outcomes in science and engineering fields, and the experiences of students who have completed significant computational science projects. With a peer-reviewed journal, we hope to provide a compendium of the best practices in computational science education along with links to shareable educational materials and assessments.
The Journal of Computational Science Education Volume 1 Issue 1
The Journal of Computational Science Education (JOCSE) promotes the use of compu . . .
tation in education through disseminating unique uses of computation in the classroom as well as research findings in computational science education, with submissions from both professionals and students. JOCSE utilizes internet technology and a web-based format to allow for enhanced interactivity in all publications.
Introducing Matrix Operations through Biological Applications
For the Blue Waters Undergraduate Petascale Education Program
(NSF), we develope . . .
d a computational science module, "Living
Links: Applications of Matrix Operations to Population Studies,"
which introduces matrix operations using applications to
population studies and provides accompanying programs in a
variety of systems (C/MPI, MATLAB, Mathematica). The
module provides a foundation for the use of matrix operations that
are essential to modeling numerous computational science
applications from population studies to social networks. This
paper describes the module; details experiences using the material
in two undergraduate courses (High Performance Computing and
Linear Algebra) in 2010 and 2011 at Wofford College and two
workshops for Ph.D. students at Monash University in Melbourne,
Australia, in 2011; and describes refinements to the module based
on suggestions in student and instructor evaluations.