In recent years, artificial neural networks have attracted considerable attention as candidates for novel computational systems. Computer scientists and engineers are developing neural networks as representational and computational models for problem solving: neural networks are expected to produce new solutions or alternatives to existing models. This paper demonstrates the flexibility of neural networks for modeling and solving diverse mathematical problems including Taylor series expansion, Weierstrass's first approximation theorem, linear programming with single and multiple objectives, and fuzzy mathematical programming. Neural network representations of such mathematical problems may make it possible to overcome existing limitations, to find new solutions or alternatives to existing models, and to achieve synergistic effects through hybridization.

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