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<P>Motivations: What is Constraint Theory and why is it important?- The Four-fold way: How to Perceive Complex Mathematical Models and Well-Posed Problems.- General Results: From Protomath to Math to Metamath.- Regular Relations: Searching for the Kernels of Constraint.- Discrete and Interval Relations: The Diminished Utility of Metamodels.- The Logical Structure of Constraint: Theory A Compact Summary.- Examples of Constraint Theory Applied to Real-World Problems.- Manager and Analyst Meet Again: Gists and Schizophrenia.</P>

<P>The enormous potential of digital computation to manage new complex systems is impeded by exponential increases in complexity. As the model's dimensionality increases from hundreds to thousands of variables, and as submodels constructed by diverse technical teams are integrated into the total model, the model is likely to become inconsistent and even more likely, the computational requests on the model become unallowable. This text analyzes the way constraint theory employs bipartite graphs and constraint matrices to detect and correct these well-posed problems. It also presents the process of locating the "kernel of constraint", literally trillions of times faster than a random search, determining consistency and compatibility within seconds. This text is an invaluable reference for all engineers, mathematicians and managers concerned with modeling.</P>
<P>"Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory." --Cornelius T. Leondes, UCLA</P>
<P>"Groundbreaking work.&nbsp;... Friedman's accomplishment represents engineering at its finest.&nbsp;... The credibility of the theory rests upon the formal proofs which are interspersed among the illuminating hypothetical dialog sequences between manager and analyst, which bring out distinctions that the organization must face, en route to accepting Friedman's work as essential to achieve quality control in developing and applying large models." --John N. Warfield</P>

Provides a practical and rigorous set of processes to manage problems of model consistency and computational allowability in the construction and use of multidimensional math models

This text analyses the defectiveness of large mathematical models of physical systems. It demonstrates how to use the bipartite graph of the defective model to pinpoint and overcome that inconsistency. Enriched "with formal proofs interspersed among the illuminating hypothetical dialog sequences between manager and analyst, this work is an essential tool in achieving quality control in developing and applying large models." - John Warfield. It is an indispensable reference for mathematician, engineer and manager alike.&nbsp;