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the branch of mathematics that deals with the mathematical aspects of problems from science and engineering: applied analysis, numerical mathematics, applied statistics etc. (For applications of mathematics in general, cf. also the [applications] tag.)
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Mathematics and cancer research
The Center for Mathematical Medicine at the Fields Institute at the University of Toronto does much mathematical research related to cancer. For example, see http://www.fields.utoronto.ca/programs/sc …
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Examples of research on how people perceive mathematical objects
The golden ratio is often cited in research on pleasing shapes to the human eye in art and architecture. For example, see http://plus.maths.org/content/os/issue22/features/golden/index