Generalizing Binary Operations

Most day to day calculations take place within the field of real numbers with the two binary operations of addition and multiplication. In this field, these two operations are definitionally independent of one another. However, if we approach binary operations from a different point of view, e.g. that of recursive formulae, we can develop multipli cation from addition by use of the concept of repeated addition. Along similar lines, we can develop exponentiation from multiplication by re peated multiplication. The next logical step would be to try to develop another binary operation based on repeated exponentiation

Teaching Mathematics in the Seventeenth and Twenty-First Centuries

In the late 1960s, many people saw a fictional vision of the beginning of the twenty-first century via the movie, 2001: A Space Odyssey. Early in the movie, a lunar expedition uncovers a large, black monolith in the crater Clavius. Although the movie was fictional, and computers have not yet reached HAL\u27s ability to speak and read lips, the lunar crater Clavius does exist and is named after a sixteenth century scholar who was instrumental in introducing mathematics into the university curriculum. Christopher Clavius (1538-1612) is often associated with the astronomical and mathematical justification for shifting from the Julian to the Gregorian calendar. He was also a university professor who was convinced that mathematics should be a stan- dard part of a university curriculum and who saw the need to train instructors of math- ematics. He exerted his influence on the Ratio Studiorum (The Plan of Studies), a 1599 document that included administrative norms and curricular guidelines for Jesuit schools as well as offering pedagogical suggestions in the form of Rules for teachers of various subjects (the Latin text [15] and English translations [6, 7] are available

A first course in computer science: Languages and goals

The College Board Advanced Placement exam in computer science will use the language Java starting in fall 2003. The language chosen for this exam is based on the language commonly taught in introductory computer science courses at the university level. This article reviews the purpose of an introductory course and the various suggestions for the curriculum of introductory courses published by the Association for Computing Machinery. It then proposes that such a course stress foundational concepts over specific language syntax, and then provides a list of such foundational concepts and related topics. Based on this fundamental curriculum, the article recommends C++ as the most appropriate language. An appendix provides a sample syllabus

Shedding New Light on Exploding Stars: Terascale Simulations of Nuetrino-Dreiven Supernovas and Their Nucleosynthesis

Project Abstract This project was a continuation of work begun under a subcontract issued off of TSI-DOE Grant 1528746, awarded to the University of Illinois Urbana-Champaign. Dr. Anthony Mezzacappa is the Principal Investigator on the Illinois award. A separate award was issued to Santa Clara University to continue the collaboration during the time period May 2003 ? 2004. Smolarski continued to work on preconditioner technology and its interface with various iterative methods. He worked primarily with F. Dough Swesty (SUNY-Stony Brook) in continuing software development started in the 2002-03 academic year. Special attention was paid to the development and testing of difference sparse approximate inverse preconditioners and their use in the solution of linear systems arising from radiation transport equations. The target was a high performance platform on which efficient implementation is a critical component of the overall effort. Smolarski also focused on the integration of the adaptive iterative algorithm, Chebycode, developed by Tom Manteuffel and Steve Ashby and adapted by Ryan Szypowski for parallel platforms, into the radiation transport code being developed at SUNY-Stony Brook

The Jesuit Ratio Studiorum, Christopher Clavius, and the Study of Mathematical Sciences in Universities

In this paper, I examine the treatment of mathematics in the definitive 1599 Ratio Studiorum of the Jesuit Order and in the preliminary drafts of the Ratio that were done in 1586 and 1591. Drawing on some additional writings of the Jesuit mathematician Christopher Clavius and his view of the importance of mathematics in a university curriculum, I suggest that the inclusion of mathematics as a standard part of the curriculum in Jesuit schools at the beginning of the “scientific revolution” was of significant importance in a climate that often demeaned the work of mathematicians. Jesuit schools were being founded around the time of Galileo and other key figures who influenced the scientific revolution. The introduction of mathematical sciences into universities and the textbooks of Clavius laid the groundwork for generations of students to become better acquainted with mathematics and the sciences that were being developed during that period of history

Diagonally-striped matrices and approximate inverse preconditioners

The inverse of a banded matrix is, in general, dense. If the structure of the original banded matrix is “striped”, that is, the non-zero diagonals are separated by one or more zero diagonals, the inverse may exhibit a similar striped structure. The motivation for studying inverses of striped matrices is to obtain efficient preconditioners for systems arising from radiation transport equations, whose matrices include dominant values along diagonal stripes. Linear systems whose system matrix has a striped inverse lend themselves to the use of a sparse approximate inverse (SPAI) preconditioner whose structure is derived from that of the actual inverse

A first course in computer science: languages and goals

The College Board Advanced Placement exam in computer science will use the language Java starting in fall 2003. The language chosen for this exam is based on the language commonly taught in introductory computer science courses at the univer-sity level. This article reviews the purpose of an introductory course and the various suggestions for the curriculum of introductory courses published by the Association for Computing Machinery. It then proposes that such a course stress foundational concepts over specic language syntax, and then provides a list of such foundational concepts and related topics. Based on this fundamental curriculum, the article recommends C++ as the most appropriate language. An appendix provides a sample syllabus

Ethics in the classroom: a reflection on integrating ethical discussions in an introductory course in computer programming

In this paper, we describe our recent approaches to introducing students in a beginning computer science class to the study of ethical issues related to computer science and technology. This consists of three components: lectures on ethics and technology, in-class discussion of ethical scenarios, and a reflective paper on a topic related to ethics or the impact of technology on society. We give both student reactions to these aspects, and instructor perspective on the difficulties and benefits in exposing students to these ideas