*This newest version contains 270 new mathematical functions and over 1000 enhancements to existing algorithms*

For those new to this software, perhaps a little background is in order. Maple is mathematical software that is constantly being improved as to breadth of the calculation routines, optimality of the algorithms, speed of computation, and ease-of-use. The last is one of the most useful features, as the new user can quickly come up to speed by testing the menu items, going through the tutorials and reading the pertinent sections of the manuals (there are just two; a User’s Manual and a Programming Manual). If this doesn’t do it, there is an excellent support desk, and the user community called Maple Primes.

Figure 2 | Figure 1 |

As a help to getting to the help, the developers offer a Maple Portal that contains tutorials, a number of ‘How Do I…’ questions, and a tools and features summary. I would strongly recommend novices start with the tutorials. There are separate portals for engineers, students and teachers. While directed at mathematicians, physicists and engineers, the software may be profitably used by other scientists and in economic/business applications.

This newest version contains a number of upgrades, including 270 new mathematical functions and over a thousand enhancements to existing algorithms. Most of these employ a high degree of leveraging with the newer, multicore computers. For a nice (and colorful) overview of the new features, go to: www.maplesoft.com/products/maple/new_features/index.aspx

These improvements will noticeably speed calculations now routinely done on the huge databases encountered in many areas of science and business.

Now, let’s take a closer look and work through a simple example. Upon startup, the main screen (with palettes selected) appears in Figure 1.Other than the top menu bars, the analyst has immediate access to the Quick Help area (a mini help-desk); the Startup Navigator, which offers a ‘tip of the day’ feature; and the Maple Portal, which contains the tutorials and startup instructions, as well as many other help items. Basically, the developers have attempted to maximally flatten the learning curve. By following the tutorials and just typing, the novice can start immediately to solve simple problems and learn the ins and outs of entering equations, data and formatting output. The palettes aligned on the left expand by clicking the arrows and offer one-click access to a variety of symbols and operations (Figure 2).

Notice that we are now in the worksheet mode, which is a large writing area with a “>” at top left indicating that Maple will receive input. Also note that Maple has over 1000 palette symbols contained in over 20 palettes. As with most mathematical software these days, Maple has its own requirements for properly typing in an equation, function, or string:

- Maple is case-sensitive.
- To suppress the result of any Maple operation, end your statement with a colon (:).
- If the input is not correctly typed, it may return the statement exactly as it was typed.

Figure 3 |

With all that basic Maple does, it has its own programming language (with both paper and electronic versions of the manual) to further expand its already considerable capabilities. Now, to tackle a common statistical problem: the computation of a maximal likelihood estimate from a data sample. This is accomplished in Maple 15 by using just a few simple commands on a randomly generated data set (Figure 3).

Figures 4 & 5 |

By merely using the commands after the red carat, the complex calculation is easily computed. Defining and graphing complex surfaces is just as easy. The example in Figures 4 and 5 defines the two surfaces, combines them on a single plot and assigns the colors.

If this all seems too easy, it’s because entry-level examples were used. To get a better appreciation of its true capabilities, the following blurb from the ‘What’s New’ pamphlet is instructive: “Seventeen new commands in the Differential Geometry package support advanced computations in the area of general relativity.” As I rarely do differential geometry or calculations in the area of relativity, this was rather impressive!

Targeted at scientists, engineers and students, Maple 15 is an excellent tool for the mathematician. Although there are many packages that can do math well, this one distinguishes itself by the power of its support functions so as not to overwhelm the new user while fully supporting the experienced mathematician. For those wishing to take a test drive, a 30-day trial download is available.

**Availability**$2,275 Single user commercial

$1,245 Single user academic

$2,155 Single user government

Multi-user — call for pricing

**Maplesoft**

615 Kumpf Drive, Waterloo, ON

Canada, N2V 1K8

519-747-2373; Fax: 519-747-5284

www.maplesoft.com i[email protected]

*John Wass is a statistician based in Chicago, IL. He may be reached at* *[email protected]**.*