Bruce W. Char

A tutorial introduction to Maple

The Maple computer algebra system is described. Brief sample sessions show the user syntax and the mathematical power of the system for performing arithmetic, factoring, simplification, differentiation, integration, summation, solving algebraic equations, solving differential equations, series expansions, and matrix manipulations. Time and space statistics for each sample session show that the Maple system is very efficient in memory space utilisation, as well as in time. The Maple programming language is presented by describing the most commonly used features, using some non-trivial computations to illustrate the language features.

The design of maple: A compact, portable and powerful computer algebra system

The Maple system has been under development at the University of Waterloo since December 1980. The kernel of the system is written in a BCPL-like language. A macroprocessor is used to generate code for several implementation languages in the BCPL family (in particular, C). Maple provides interactive usage through an interpreter for the user-oriented, higher-level, Maple programming language.

GCDHEU: Heuristic polynomial GCD algorithm based on integer GCD computation

A heuristic algorithm, GCDHEU, is described for polynomial GCD computation over the integers. The algorithm is based on evaluation at a single large integer value (for each variable), integer GCD computation, and a single-point interpolation scheme. Timing comparisons show that this algorithm is very efficient for most univariate problems and it is also the algorithm of choice for many problems in up to four variables.

Redesigning introductory computer programming using multi-level online modules for a mixed audience

We report here on an extensive redesign and unification of the Introductory Computer Programming sequences offered to computer science, computer engineering, information science and digital media majors. The redesign is intended to improve student learning while reducing costs. The approach makes use of substantial Web-based course material and course management tools, including multi-level online modules that individualize instruction and enable students to self-schedule learning each week. Each module covers a particular aspect of computer programming at different levels of knowledge. Students are assigned work and reading from the module at a level appropriate to the objectives of the long-term goals of their major. This allows students in different majors to acquire the appropriate skill level for each technique and concept. Peer mentors and teaching assistants provide assistance online or in person. In the future, we plan to expand the self-scheduling aspect of the course to allow students to enter the course at different modules, depending on their previous knowledge.

Symbolic computation in Java: an appraisement

Java, first developed as a programming interface for web browsers, is being pushed by a consortium of companies as a high level programming language for general programming. Sun Microsystems provides, in addition to a compiler into byte code for an interpreter (the Java virtual machine), a multitude of libraries, most notably an object hierarchy for building graphical user interfaces: the Abstract Windowing Toolkit and the Swing components from the Java Foundation Classes. Internet browsers contain Java virtual machines for interpreting byte code of Java programs that are embedded into Internet documents as applets. Java defines a standard framework for multi-threaded execution and for message passing via serialization and socket/datagram protocols. Java assists component composition in two ways. Java objects can discover how to invoke other Java objects at run-time through a process called reflection. Java also supports programming conventions (collectively referred to as “Java Beans”) for event-driven inter-component operation. The two together allow tools such as Java Studio [26] to provide convenient visual programming methods of connecting up Java software components. In short, Java is being vigorously developed and we ask the natural question whether Java is suited for symbolic computation and whether our discipline should take advantage of the plethora of freely available software. This article discusses Java as a symbolic computation development tool, expanding on the pioneering efforts of other researchers [39, 9]. We investigate if Java can compete with C++, or Maple/Mathematica/Axiom for efficient

Assessment of a course redesign: introductory computer programming using online modules

We assess the effectiveness of an extensive redesign of the first Computer Programming course offered to computer science and computer engineering majors. Our goals were to improve student learning while reducing costs by making use of substantial Web-based course material and course management tools, including multi-level online modules that individualize instruction and enable students to self-schedule learning each week. DFW rates and costs were significantly reduced by the redesign.

The maple symbolic computation system

The Maple system for algebraic computation is introduced. Samples of user/system interaction and of Maple programming are presented.

Academic dishonesty in a high-tech environment

Advances in computing and telecommunication technology provide abundant new opportunities for academic dishonesty. Anecdotal evidence suggests that students are far more aware than faculty of various mechanisms for cheating on exams, plagiarizing assignments, and soliciting work for pay. Fortunately, technological advances also provide the alert instructor with some tools for combating such academic dishonesty.In this session, we will present information on how calculators, cell phones, beepers, and other handheld technology may be used to cheat on exams; how the Internet is used to match students with sources for solutions to their assignments; and existing tools and services for the faculty member.The intention of this session is to inform faculty about various ways that students may commit academic fraud; and tools and approaches that are available to reduce their effectiveness. We also hope to gain further information from other faculty and/or students in attendance. We do not intend to debate whether these activities should be allowed due to the ease with which they are committed, as is often discussed.We will provide a bibliography of articles about high-tech academic dishonesty, software tools and services for detecting plagiarism (including shared code in programming assignments), and Internet resources.

Tools and techniques for large scale grading using Web-based commercial off-the-shelf software

Courseware/Course Management Systems (CMS) such as WebCT or Blackboard are an increasingly popular way to provide a web presence for a course. However, their current web-browser reliance makes it difficult for them to provide functionality that could be useful to computer science instructors. This paper describes our augmentation of a CMS in a large introductory computer science class. It further describes our enhancement of the CMS by clientside software (i.e. residing on the graders computer), written for use by the instructors and graders. Finally, it indicates how conventional CMS architecture can be extended to provide additional functionality that would be desirable for computer science instruction.

Automatic identification of time scales in enzyme kinetics models

Many chemical reaction systems studied in the pharmaceutical industry have phenomena that occur on two or more vastly different time scales. When modeling the chemical reaction system as ordinary differential equations, if a small parameter e can be identified then one can isolate the behavior of the system on long and short time scales using singular perturbation theory. In practice, the small parameter is discovered using knowledge about the chemical reaction system that is not necessarily contained in the mathematics of the model. If a small parameter cannot be easily identified, then the approach is typically abandoned. We present a procedure that derives algebraic expressions for dual time scales in mathematical models of chemical reaction systems. Unlike conventional practice, this derivation proceeds using only information cent ained in the model, without knowledge of a small parameter derived through external considerations. Our procedure Scales is based on rules that arise from the “art and practice” of applying the Quasi-Steady-State AssumpPermission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and Its date appear, and notice is given that copying is by permission of the Association of Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. ISAAC 94-7184 Oxford England UK @ 1994 ACM 0-89791 -838-7/84/0007..