Symbolic-numeric interface: A review

A survey of the use of a combination of symbolic and numerical calculations is presented. Symbolic calculations primarily refer to the computer processing of procedures from classical algebra, analysis, and calculus. Numerical calculations refer to both numerical mathematics research and scientific computation. This survey is intended to point out a large number of problem areas where a cooperation of symbolic and numerical methods is likely to bear many fruits. These areas include such classical operations as differentiation and integration, such diverse activities as function approximations and qualitative analysis, and such contemporary topics as finite element calculations and computation complexity. It is contended that other less obvious topics such as the fast Fourier transform, linear algebra, nonlinear analysis and error analysis would also benefit from a synergistic approach

The police in different voices: Isaac Newton and his programme of purification.

This work positions Isaac Newton's three areas of inquiry---Natural Philosophy, alchemy, and theology---as three inter-locked "literacies, " each with its own corrupt text and purifying method of reading. Newton's natural philosophical literacy, a method of purifying reading the book of nature, is driven by coded concepts, including crypticity, Oneness, and purification, drawn from Newton's heretical Christianity. Those concepts also drive his interactions with the Royal Society and his contemporary Enlightenment scientists. Newton's alchemical literacy, a transmutative method of reading the book of self, is expressive of both Newton's will to superiority and his ambivalent and complex placement of the female in his system of representation. Newton's theological literacy, a purifying method of reading scriptures, employs a hermeneutics using criteria of Enlightenment science to purge scripture of idolatrous complexity. That theological literacy Newton extends to the world of politics in his work at the London mint, where he purifies the mint of inefficiency and the underworld of counterfeiters. Newton's overall method of working in seemingly opposed systems of representation is juxtaposed to Niels Bohr's "Unity of Knowledge, " with both demonstrating a Kierkegaardian "dance of the absurd" in their productive use of contradiction. However, Bohr's complementarity accounts for and goes beyond the limits of Newton's approach. Employing Bohr's complementarity as meta-epistemological frame, Walter Benjamin's method of constellation, Werner Heisenberg's uncertainty principle, and Kurt Godel's incompleteness theorem are positioned as three post Enlightenment responses to Newton's characteristics of science outlined in his "Rules of Reasoning." Mutually exclusive yet interdependent, these epistemological complementarities are framed as possibilities for construction of a human(e) science

Developing Mathematics Enrichment Workshops for Middle School Students: Philosophy and Sample Workshops

This paper describes our approach to organizing enrichment activities using advanced mathematics topics for diverse audiences of middle school students. We discuss our philosophy and approaches for the structure of these workshops, and then provide sample schedules and resource materials. The workshops cover activities on the following topics: Graphing Calculators; The Chaos Game; Statistical Sampling; CT Scans–the reconstruction problem; The Platonic and Archimedean solids; The Shape of Space; Symmetry; The Binary Number System and the game of NIM; Graph Theory: Proof by Counterexample

Impact of Two Interventions on ISAT Scores in a Small, Rural School District

This case study sought to determine the impact that an after school program and summer school program may have had on the ISAT reading scores of elementary students in a small, rural school in the Midwest. A secondary purpose was to determine if other factors may have impacted the effectiveness of the two interventions. Quantitative data indicated that the after school program had a positive effect on ISAT reading scores for those students who participated, raising the median raw score of the ISAT reading test by 2.23 points. On the other hand, there was no evidence that the summer school program had any positive effect on ISAT reading scores. The median raw score of the ISAT reading test of students who participated in the summer school program was not statistically significant when compared to the scores of the control group. Furthermore, the qualitative data indicated areas of concern that may have impacted the effectiveness of the interventions including curriculum used, professional development, student motivation, and communication among stakeholders

Impact of Two Interventions on ISAT Scores in a Small, Rural School District

This case study sought to determine the impact that an after school program and summer school program may have had on the ISAT reading scores of elementary students in a small, rural school in the Midwest. A secondary purpose was to determine if other factors may have impacted the effectiveness of the two interventions. Quantitative data indicated that the after school program had a positive effect on ISAT reading scores for those students who participated, raising the median raw score of the ISAT reading test by 2.23 points. On the other hand, there was no evidence that the summer school program had any positive effect on ISAT reading scores. The median raw score of the ISAT reading test of students who participated in the summer school program was not statistically significant when compared to the scores of the control group. Furthermore, the qualitative data indicated areas of concern that may have impacted the effectiveness of the interventions including curriculum used, professional development, student motivation, and communication among stakeholders

How good are Global Newton methods? Part 2

Newton's method applied to certain problems with a discontinuous derivative operator is shown to be effective. A global Newton method in this setting is exhibited and its computational complexity is estimated. As an application a method is proposed to solve problems of linear inequalities (linear programming, phase 1). Using an example of the Klee-Minty type due to Blair, it was found that the simplex method (used in super-lindo) required over 2,000 iterations, while the method above required an average of 8 iterations (Newton steps) over 15 random starting values.Naval Surface Weapons Center, Dahlgren, VAhttp://archive.org/details/howgoodareglobal00goldO&MN Direct FundingApproved for public release; distribution is unlimited

Status report, June 1988 - April 1992

The Mars Mission Research Center (MMRC) is one of nine University Space Engineering Research Centers established in June 1988 by NASA's Office of Aeronautics and Space Technology to broaden the nation's engineering capability to meet the critical needs fo the civilian space program. It includes North Carolina State University (NCSU) at Raleigh and on North Carolina A&T State University at Greensboro. The goal of the Center is to focus on research and educational technologies necessary for planetary exploration, especially transportation to and from our moon and Mars. The research combines mission analysis and design, hypersonic aerodynamics, structures and controls, composite materials, and fabrications. Covered here are activities of the Center from June to April 1992. The Center supports 26 graduate students, 29 undergraduates, 27 faculty and 6 staff. An additional 88 undergraduates worked on four special projects. Three facilities at A&T were renovated and a new 7,000 square foot facility was occupied at NCSU in October 1991. Five laboratories have been developed for composite processing and fabrication facility (A&T), materials testing (A&T), weaving (NCSU), braiding (NCSU), and structures (NCSU). During the past two years, the Center added a new dimension to its program - special projects which involve analysis, design, construction, and testing. The first two projects were full-scale research models of a Mars aerobrake and the HL-20 Personnel Launch System. Both projects received considerable new coverage and appeared in national publications. Additional projects include a model of a Mars Exclusion Vehicle, an Orbiter Ejector, and a Remotely Operated Vehicle. The Orbiter Ejector is scheduled to fly on Shuttle Flight STS-47 in October 1992. Special projects have increased undergraduate student participation and provided a mechanism for more interaction between the universities, NASA centers, and industries. The faculty developed 26 new courses related to the activities of the Center. They conducted four workshops on interplanetary spacecraft, lunar/Mars aerobrakes, spacecraft controls, and aerodynamic heating. The Outreach Program developed into a significant component of the Center. Faculty and students have conducted 12 tours of facilities and given 67 lectures to schools (grade k-12) and civic organizations

Director's discretionary fund report for FY 1991

The Director's Discretionary Fund (DDF) at the Ames Research Center was established to fund innovative, high-risk projects in basic research which would otherwise be difficult to initiate, but which are essential to our future programs. Here, summaries are given of individual projects within this program. Topics covered include scheduling electric power for the Ames Research Center, the feasibility of light emitting diode arrays as a lighting source for plant growth chambers in space, plasma spraying of nonoxide coatings using a constricted arcjet, and the characterization of vortex impingement footprint using non-intrusive measurement techniques

2003 AAPP Monograph Series

It is significant that the African American Professors Program (AAPP) at the University of South Carolina is producing the third edition of its annual monograph series at this time-the fifth anniversary of AAPP. The program graciously accepts the challenge of putting into place a requirement for the scholars to produce quality research papers worthy of publication. This provides widespread visibility for them and enhances their curriculum vitae concurrently. Scholars who have contributed manuscripts for this monograph are to be commended for adding this additional responsibility to their academic workload. Writing across disciplines adds to the intellectual diversity of these papers. From neophytes, relatively speaking, to an array of very experienced individuals, the chapters have been researched and comprehensively written. Founded in 1997 through the Department of Educational Leadership and Policies in the College of Education, AAPP was designed to address the underrepresentation of African American professors on college and university campuses. Its mission is to expand the pool of these professors in critical academic and research areas. Sponsored by the University of South Carolina, the W. K. Kellogg Foundation, and the South Carolina General Assembly, the program recruits students with bachelor\u27s, master\u27s, and doctoral degrees for disciplines in which African Americans currently are underrepresented. An important component of the program is the mentoring experience that is provided. Each student is assigned to a mentor/professor who guides the student through a selected academic program and provides various learning experiences. When possible, the mentor serves as chair of the student\u27s doctoral committee. The mentor also provides opportunities for the student to team teach, conduct research, and co-author publications. Students have the advantage of attending committee, faculty, and professional meetings, as well as engaging in a range of activities that characterize professional life in academia. Scholars enrolled in the program also are involved in programmatic and institutional workshops, independent research, and program development. The continuation of this monograph series is seen as responding to a window of opportunity to be sensitive to an academic expectation of graduates as they pursue career placement and, at the same time, one that allows for the dissemination of AAPP products to a broader community. The importance of this monograph series has been voiced by one of our 2002 AAPP graduates, Dr. Shundelle LaTjuan Dogan, a recent Harvard Administrative Fellow at Harvard University and now Program Officer for the Southern Education Foundation, Atlanta, Georgia. Dr. Dogan wrote: One thing in particular that I want to thank you for is having the African American Professors Program scholars publish articles for the monograph. I have to admit that writing the articles seemed like extra work at the time. However, in my recent interview process, organizations have asked me for samples of my writing. Including an article from a published monograph helped to make my portfolio much more impressive. You were right on target in having us do the monograph series. We hope that you will read this monograph of the African American Professors Program with enthusiasm or enlightenment. John McFadden, Ph.D. The Benjamin Elijah Mays Professor Director, African American Professors Program University of South Carolinahttps://scholarcommons.sc.edu/mcfadden_monographs/1006/thumbnail.jp

Pierre Duhem’s philosophy and history of science

LEITE (Fábio Rodrigo) – STOFFEL (Jean-François), Introduction (pp. 3-6). BARRA (Eduardo Salles de O.) – SANTOS (Ricardo Batista dos), Duhem’s analysis of Newtonian method and the logical priority of physics over metaphysics (pp. 7-19). BORDONI (Stefano), The French roots of Duhem’s early historiography and epistemology (pp. 20-35). CHIAPPIN (José R. N.) – LARANJEIRAS (Cássio Costa), Duhem’s critical analysis of mecha­ni­cism and his defense of a formal conception of theoretical phy­sics (pp. 36-53). GUEGUEN (Marie) – PSILLOS (Stathis), Anti-­scepticism and epistemic humility in Pierre Duhem’s philosophy of science (pp. 54-72). LISTON (Michael), Duhem : images of science, historical continuity, and the first crisis in physics (pp. 73-84). MAIOCCHI (Roberto), Duhem in pre-war Italian philos­ophy : the reasons of an absence (pp. 85-92). HERNÁNDEZ MÁRQUEZ (Víctor Manuel), Was Pierre Duhem an «esprit de finesse» ? (pp. 93-107). NEEDHAM (Paul), Was Duhem justified in not distinguishing between physical and chemical atomism ? (pp. 108-111). OLGUIN (Roberto Estrada), «Bon sens» and «noûs» (pp. 112-126). OLIVEIRA (Amelia J.), Duhem’s legacy for the change in the historiography of science : An analysis based on Kuhn’s writings (pp. 127-139). PRÍNCIPE (João), Poincaré and Duhem : Resonances in their first epistemological reflec­tions (pp. 140-156). MONDRAGON (Damián Islas), Book review of «Pierre Duhem : entre física y metafísica» (pp. 157-159). STOFFEL (Jean-François), Book review of P. Duhem : «La théorie physique : son objet, sa structure» / edit. by S. Roux (pp. 160-162). STOFFEL (Jean-François), Book review of St. Bordoni : «When historiography met epistemology» (pp. 163-165)