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Mathematical topics that used to be considered higher math are increasingly in the mainstream of an enterprise IT administrators concerns. Near the top of any modern-day IT pros to-do list might be information security, network capacity planning and supply chain optimization projects.
Taking a broader view, the list might expand to include financial asset allocation and the increasing shift of manufacturing operations from traditional to computer-based methods—for example, the replacement of physical models with CAD visualization and the replacement of traditional pharmaceutical development techniques with disciplines based on molecular design.
All these tasks are profoundly mathematical—not in the limited sense of floating-point computation but in the general sense of the term. Math subdisciplines bearing on todays real-world demands include the number theory of modern cryptography, the formal systems theory of security and verification, and the optimization algorithms of operations research.
Turning the promise of new hardware into bottom-line benefit requires the geometry of CAD and numerically controlled manufacturing, as well as the algorithm theory required to make effective use of distributed and parallel computing platforms.
In the face of these needs, the widespread availability of spreadsheets in personal productivity suites can be a seductive trap. The speed and power of the modern spreadsheet, combined with its familiarity, make the spreadsheet a hammer thats already in the users hand—ready to make every problem look deceptively like a nail.
Beginning with the parts of the problem that are obvious and that a spreadsheet can easily handle, a user can wind up constructing a massive apparatus that does indeed solve the problem but that has to be rebuilt and even rethought from scratch when the problem evolves. The generality of higher-level math, not to mention literally centuries of progress in formulating and presenting those mathematical statements, is buried beneath the grids of spreadsheet cells.
Tools such as Maple 10, from the Maplesoft division of Waterloo Maple Inc.; Wolfram Research Inc.s Mathematica 5.1; and The MathWorks Inc.s Matlab 7.0, therefore, should be considered for adoption in a wider range of environments than the research and engineering departments where theyre most commonly found. Their value in focusing the statement of a problem, in generalizing the solution to meet new needs and in presenting that solution to stakeholders adds up to high returns on the costs of acquisition and training.
Those adoption barriers, moreover, get lower with every release as these products improve in usability, as they offer additional tools for custom application development and enterprise platform integration, and as they make their power available through Web interfaces that lower their per-user cost.