Mathematics is essential to many sciences. One important function of mathematics in science is the role it plays in the expression of scientific models. Observing and collecting measurements, as well as hypothesizing and predicting, often require mathematical models and extensive use of mathematics. Mathematical branches most often used in science include calculus and statistics, although virtually every branch of mathematics has applications, even "pure" areas such as number theory and topology. Mathematics is fundamental to the understanding of the natural sciences and the social sciences, all of which rely heavily on statistics. Statistical methods, comprised of accepted mathematical formulas for summarizing data, allow scientists to assess the level of reliability and the range of variation in experimental results.
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