Today, computer hardware and Mathematics permeates our modern society. Computers are embedded in wristwatches, telephones, home appliances, buildings, automobiles, and aircraft. Science and technology demand high-performance hardware and high-quality Mathematics for making improvements and breakthroughs. We can look at virtually any industry - automotive, avionics, oil, telecommunications, banking, semi-conductors, pharmaceuticals - all these industries are highly dependent on computers for their basic functioning. When the requirements for and dependencies on computers increase, the possibility of cries from computer failures also increase. It is always desirable to remove a substantial number of faults from the Mathematics. In fact the reliability of the Mathematics is directly proportional to the number of faults removed. Hence the problem of maximization of Mathematics reliability is identical to that of maximization of fault removal. At the same time testing resource are not unlimited, and they need to be judiciously used.

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