The newest version of this versatile mathematics package for symbolic and numeric calculation features the usual technical sophistication combined with ever-more features and a learning curve that will leave the novice user breathless. The older features remain for the experienced user, but the developers have succeeded in applying so many user-friendly applications as to do the near impossible, i.e., make the learning of higher-level math much easier on the student. This is accomplished with access to palettes, student sub packages, an even-friendlier interface, plotting upgrades and continued innovations in the mathematics. A centerpiece of this innovation is the new Maplet application for the solution of ordinary differential equations (ODEs). The new Maplet tutors for calculus, pre-calculus and linear algebra are extraordinarily useful in providing complete solutions (all steps included) to a variety of standard problems encountered by college undergraduates. The software presently finds extensive use in science, mathematics, engineering and teaching and has amply built upon the companies 20+-year track record of innovation.

##### Installation

The new version is compatible with the following operating systems: Windows 98/NT and above, Linux and Unix (many versions — see the Maplesoft Web site), and MacOS X. For the Intel machines, at least a Pentium III with a 650 MHz clock and 256 MB of memory are recommended, as well as a CD-ROM for installation and a 16-bit color display at 800 x 600 resolution for the graphics. The standard version for a single user requires 200 MB of hard drive space. This review was based on the Windows version. Installation time was 85 seconds on a Pentium III with an 850 MHz clock, and proceeded without problems. The user is stepped thru the installation with a Wizard, but no special knowledge is required and the program is easily installed without the manuals.

##### Manuals

The package comes with three manuals and two very brief guides. The Getting Started Guide is a mere 31 pages long and orients the new user to installation and a few simple examples of math and graphics. The Resource Guide briefly summarizes the supplements and helps available as well as their URLs. The developers undoubtedly believe that this version is so easy to use that the only printed background material, aside from the above, is a 306-page Learning Guide and two programming manuals. The former will be useful to orient the new user to more examples and the programming guides only are consulted by the adventurous wishing to extend Maple’s already substantial capabilities. For any researcher already familiar with C code or SAS, the going should not be unduly challenging.

Figure 1: Simple 2-D Plot |

##### Mathematics

At the core of the program is a series of algorithms and applications that allow the scientist, engineer, mathematician or student to perform a bewildering array of analyses. Table 1 merely lists the main subject areas addressed, as a complete tabulation of all functions would take many pages.

The table gives the flavor of what is available and allows the reviewer to concentrate on several areas of interest and enthusiasm. For those in need of frequent help and advice, the new FunctionAdvisor will be most welcome. By merely invoking the name followed by the needed object in parentheses, Maple will return explanations and equations to clarify concepts and routines. For example, by typing in ‘FunctionAdvisor(csch);’ Maple returned the general class of function and the mathematical definition, as well as a number of useful properties. This type of instant help is appreciated and will replace valuable minutes spent rummaging through standard textbooks.

Another innovation is the Student Tools, a series of applets that allow the student (or those whose knowledge of the subject may be stale) to step through a problem with hints and any applicable mathematical rules, or to instantly visualize entire solutions. Some may consider this a double-edged sword, but features such as the interactive routines greatly simplify steps that are tedious by other means. For example, in the Student Linear Algebra Package, the Gauss-Jordan Elimination applet allows the user to easily operate on rows to reduce simultaneous linear equations for easy solution. The linear inequalities box will allow fast graphics relating to solutions of inequalities, and the ODE solver offers a variety of powerful features that not only assist symbolic and numerical solutions, but quickly graph the functions as well.

For statisticians, Maple offers a limited but useful package that can generate descriptive statistics, ANOVAs, linear regression and transformations. Although helpful, it is problematic to do so much work to generate simple statistics, and innovation is needed here to easily generate more complete analyses. Standard statistical programs easily import by filename or by cut and paste and instantly generate a variety of statistics, diagnostics and graphics so the developers do have further work here.

Figure 2: 3-D Plot |

The only drawbacks I found in many test runs were the slightly annoying tip-of-the-day (which can be disabled under the options menu), the SketchPad (which would be more useful if the text portions could be typed, as the manual drawing of letters is clumsy), and the noticeable decrement in performance speed under the new interface. The last is partially remedied by downloading the free upgrades. Also, for those interested in the latest modeling techniques, pre-programmed Wavelet functions or neural network capabilities will be sorely missed.

##### Graphics, programming and connectivity

Another excellent feature that greatly aids any analysis is the program’s visualization capabilities. 2-D and 3-D plots are easily generated (Figures 1 and 2) and modified, and the 3-D plots are now rotatable on two axes. There are animation features to further enhance the analysis, and a wide variety of coordinate systems are available. Color, intensity and shading features are quite good and code may be easily recycled for standard forms.

For the programmers, Maple algorithms are quickly accessed in compiled C form, and code may be generated for Visual Basic, MATLAB, JAVA, C and Fortran applications. For those knowledgeable in the finer points, debugging, profiling and library management tools also are available.

For those accustomed to an Excel environment and used to development with MATLAB, the built-in links and connectivity features are a very large plus. The cut and paste features are excellent, and those accustomed to this exercise will rapidly familiarize themselves with the formatting steps.

##### Summary

Most software firms are offering more and more help and support modes, and Maplesoft is no exception. Resources include MapleNet for online learning, MapleTA for automated testing and assessment, and Web-based helps such as The Maple Application Center offering many free downloads, MaplePrimes allowing access to many new features, The Maple Student Center with tutorials and extra course materials, and the Maple Power Tools suite of free courses and packages. This is above and beyond the help features built into the package. For the terminally confused, such as your reviewer, a technical help group is available by phone.

This new version is not a cosmetic upgrade but a very versatile and easy-to-use set of tools that is robust and quite cost effective.

##### Availability

•Commercial $1,795

•Academic $995

•Student ship/download $129/$99

*John A. Wass, Ph.D., is a statistician with GPRD Pharmacogenetics, Abbott Laboratories. He may be contacted at editor@scientificcomputing.com. *