In the paper ways in which computers are applied in mathematics are considered. An example of mathematical truth which possesses only computer-assisted proof is the fourcolor theorem. Based on the example of this theorem we discuss some... more
In the paper ways in which computers are applied in mathematics are considered. An example of mathematical truth which possesses only computer-assisted proof is the fourcolor theorem. Based on the example of this theorem we discuss some philosophy connected with admitting computer proofs in mathematics, in particular the status of mathematical knowledge as a pattern of science whose truths are known a priori. 1. The four-color theorem In 1976 the four color problem, formulated over a hundred years earlier by Francis Guthrie, was solved. This problem was whether every map on the plane or sphere can be colored by no more than four colors in such a way that neighboring regions are never colored alike. (By regions we mean connected domains and we treat as neighboring such regions whose borders have more than one common point.) The proof, published in 1976 by Kenneth Appel and Wolfgang Haken [1], takes a meaningful advantage of computers. The fact that the proof used computers, hence an ...
As defined by the National Institutes of Health: “Biomedical engineering integrates physical, chemical, mathematical, and computational sciences and engineering principles to study biology, medicine, behavior, and health”. Many issues in... more
As defined by the National Institutes of Health: “Biomedical engineering integrates physical, chemical, mathematical, and computational sciences and engineering principles to study biology, medicine, behavior, and health”. Many issues in this area are closely related to fluid dynamics. This paper provides an overview of the basic concepts concerning Computational Fluid Dynamics and its applications in medicine.
