*CiSE*, we'll explore the three preeminent productivity tools for scientific and engineering computation. Although hardly identical, the packages have extensive similarities in the computational work they're intended to support. In areas in which they overlap, we'll look at how they compare, even as we contrast their scopes where they extend beyond one another. Given that you probably already use one of these tools sets, our goal is to help you decide whether one of them as now packaged is better suited to your temperament or your current technological practice than when you made your original choice. In each article, we'll examine how these packages support one of three different categories of professional work: undergraduate education, scientific and engineering computation, and technical communication and publication.

*The Mathematica Book*(5th edition, Wolfram Media, 2003), itself a monument to the self-confidence of its author, Steven Wolfram:

Having started to use computers in 1973, Wolfram ... in 1979 began the construction of SMP—the first modern computer algebra system, which he released commercially in 1981 ... It is often said that the release of Mathematica marked the beginning of modern technical computing. Ever since the 1960s individual packages had existed for specific numerical, algebraic, graphical and other tasks ... The concept of Mathematica was a single system that could handle all [these tasks] ... Wolfram began the development of Mathematica in late 1986. The first version ... was released on June 23, 1988 ... [as] the world's only fully integrated environment for technical computing.

Wolfram's papers on cellular automata led to a major shift in scientific thinking and laid the groundwork for a new field of science that Wolfram named "complex systems research." … Following the release of Mathematica Version 2 in 1991, Wolfram began to divide his time between Mathematica development and scientific research. Building on his work from the mid-1980s (on complexity and cellular automata), and now with Mathematica as a tool, ... Wolfram finally described ... inA New Kind of Science, released on May 14, 2002, a paradigm shift of historic importance in science.

*The Maple Reporter*, the Waterloo Maple newsletter:

From its humble beginnings as a research project at a university to the position of an influential technology in education, research, and industry, Maple has fundamentally changed the way we do math … [reflecting] how the mathematical community itself has evolved. … In the '80s, Maple was a pure programming language optimized for mathematical applications. In the early '90s Maple V Releases 1 through 4 saw … development of the Maple user interface ... to display mathematics in high resolution ... [and] dynamically interact with 3D plots … [facilitating] student use. In the late '90s, Release 5 introduced Web publishing ... enabling Maple documents [to be] translated to professional HTML pages for rapid publication on the Web…Maple 6 and 7 establish a new standard … [of] connectivity with other software. The Maple Application and Student Centers ... [help] users take advantage of … a living concept continually enriched and expanded by the energy and creativity of its user base.

*The Maple Reporter*:

In the autumn of 1980, I called a meeting of various Computer Science faculty of the University of Waterloo to discuss the idea of how we could get … a system like MACSYMA ... It was at this meeting, in November 1980, that the Maple system was conceived. ... By the first week in December we had an operational Maple system, and it evolved from there. … By January of 1981, we started using Maple in a course, "Introduction to Symbolic Computation" ... Mathematicians started to use the system for research in 1982. By 1983, researchers at various institutions were using [it] in various other disciplines, including computer science, engineering, physics, and economics … and there were about 50 installations … By 1987 there were 300 installations worldwide ... In April of 1988, we incorporated Waterloo Maple Software ... to market, distribute, and support Maple … and by 1990 the installed base grew to 2000.

Until 1990 or so, it was never about making a commercially successful product. Our vision was about creating a powerful system for symbolic mathematics.

Matlab began life in 1984 as a response [to a] recognized need among engineers and scientists for more … productive computation environments [than] those provided by languages such as Fortran and C. [It is] a high-performance technical computing environment … combining comprehensive math and graphics functions with a powerful high-level language … Our goal [was and] is to change the world by accelerating the pace of discovery, innovation, development, and learning in engineering and science … [with a] computing environment for technical computation, visualization, simulation, design, and implementation.

At the MathWorks, we express who we are as an organization through our guiding principle, our mission, and our core values. Developed over time, each represents a philosophy or goal that is intrinsically important to the organization ... Our guiding principle is "Do the Right Thing," … meaning doing what is best for our staff members, customers, business partners, and communities for the long term… It also means measuring our success … by how consistently we act according to this principle. Our mission and core values express what "doing the right thing" means in our day-to-day work … Our [technological mission] is to change the world by accelerating the pace of discovery, innovation, development, and learning in engineering and science … [We want our] core values, … essential and enduring principles …. unaffected by the trends of the day or changing market conditions, … [to be] understood and practiced throughout the organization.

The visionary concept of Mathematica was to create … a single system that could handle all the various aspects of technical computing in a coherent and unified way. A key ... [was] a new kind of symbolic computer language that could … manipulate the very wide range of objects involved in technical computing using only a fairly small number of basic primitives.At a technical level, Mathematica ... is one of the largest single-application programs ever developed ... Among its core innovations are its interconnected algorithm knowledge base and its concepts of symbolic programming and document-centered interfaces.

Wolfram Research's leadership … stems from its ability to set the direction for new technology. The Wolfram Group is characterized by an individualist approach, a "no compromises" attitude to design, welcoming of innovation, a deep respect for the … user base and users' suggestions, and constant search for good general approaches rather than quick fixes.

*The Maple Reporter*:

The primary goal [was] to design a computer algebra system that would be accessible to large numbers of researchers in mathematics, engineering, and science, and to large numbers of students for educational purposes ... transforming the way engineers and scientists use technology.

• a context-intelligent right-click operation menu and an extensive selection of user-interface features obviating the need to memorize commands;

• interactive visualization to let users explore data efficiently and intuitively;

• extensive connectivity features, including Microsoft Excel, Matlab, TCP/IP, and OpenMaple;

• programming language features, intuitive syntax, easy debugging, and a rich feature set to support complex applications; and

• free resources, as embodied by the Maple Application Center.

*Mathematica Book*'s preface, we get the following:

At first, Mathematica's impact was felt mainly in the physical sciences, engineering and mathematics. But over the years, [it] has become important in a remarkably wide range of fields … physical, biological, and social sciences, and other fields outside the sciences, ... all of the Fortune 50 companies, all 15 major departments of the US government, and all the [world's] 50 largest universities.

In engineering, Mathematica … [is a] tool for development and production. In commerce, [it] has played a significant role in ... financial modeling, as well as ... general planning and analysis. [It] has also emerged as an important tool in computer science and software development: its language component is widely used as a research, prototyping, and interface environment.

*,*rather than applications of mathematics to other disciplines. This suggests that a substantial number of the users are academics, and their applications are pedagogical. On the other hand, titles wouldn't reveal commercial users, who are unlikely to publish the results of their proprietary application-development work as books.

Maple 9.5 is the environment of choice for scientific and engineering problem-solving, mathematical exploration, data visualization, and technical authoring. [It] transforms the way technical professionals and students use technology, ... integrating the power of … numerics with … symbolics [with] full computing support for any activity involving mathematics ... it allows [the user] to encapsulate and manage technical knowledge. In industry, [it] facilitates true collaborative knowledge management. In the classroom, [it] frees the student and teacher to focus on concepts ... A rich user environment ... shortens the learning curve and maximizes productivity gains.

Highly integrated product suite delivers a flexible platform to compute, deploy, and share technical information.

Highly integrated product suite and an extensive set of free resources increase the effectiveness and efficiency of any academic activity that depends on mathematical information.

MapleNet enables enterprise-wide collaboration through sharing results data and analytical knowledge over the Web. Professional toolboxes offer domain-specific tools to transform the core [Maple] ... to discipline-specific applications. Resources/services [afford] ... Web resources.

MapleNet is a full environment for online, e-learning, providing an … interactive Web-based environment … for [educational] content creation [and] deployment. Maple T.A. ... for Web-based testing and assessment includes access control, interactive grade book, algorithmic question generation, and intelligent assessment of mathematical responses. The Maple Application Center offers … free downloadable resources ... simple classroom demos, curricula for entire courses ... in calculus, differential equations, classical mechanics, linear algebra, statistics, etc.

*use context*. Accordingly, we'll try to explicitly define the uses we have in mind when formulating each critique.

*in situ*or otherwise publish science and engineering material.

• What is the price of going with a single integrated package rather than adopting a piecemeal approach?

• What differences in the packages' historical genesis and development might indicate future evolution patterns?

• To what extent are the packages equivalent?

• Are there significant differences between versions of Mathematica, Maple, and Matlab for the Macintosh, Windows, and Linux platforms?

• Are their differences in the distribution of uses according to discipline or workplace?

**Norman Chonacky**is a research fellow in the Center for United Nations Studies in the Political Science Department at Yale University. His research interests include cognitive processes in research and education, environmental sensors and the management of data derived from sensor arrays, the physico-chemical behavior of material in environmental systems, and applied optics. Chonacky received a PhD in physics from the University of Wisconsin, Madison. He is a member of the IEEE Computer Society, the American Association of Physics Teachers (AAPT), American Physical Society (APS), and American Association for the Advancement of Science (AAAS). Contact him at norman.chonaky@yale.edu.

**David Winch**is emeritus professor of physics at Kalamazoo College. His research interests are focused on educational technologies. Winch received a PhD in physics from Clarkson University. He is coauthor of

*Physics: Cinema Classics*(ZTEK, videodisc/CD 1993, DVD/CD 2004). Contact him at dmwinch@kitcarson.net.

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