A new breed of mathematical software brings computing power formerly reserved for mainframes to personal computers, allowing scientists with desktop machines to pose and answer problems of greater complexity than ever before. Those taking advantage of the increased availability of such sophisticated analytical support for their work include--perhaps expectedly--many physicists and engineers, but also biological researchers studying such phenomena as fish population cycles and the foraging habits of bees. Since the early days of room-sized digital machines, scientists have been putting computers to work crunching numbers for their research--the "grunt" work associated with long data columns. In the 1960s, several research groups began to extend the realm of computers from numerical calculations to symbolic manipulations--that is, the higher-level math that uses symbols to represent constants, variables, and mathematical operations.

The programs that resulted provided scientists with versatile new research tools, but they required mainframe computers to run, making them effectively...

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