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Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers.
Mathematics has a remarkable ability to cross cultural boundaries and time periods. As a human activity, the practice of mathematics has a social side, which includes education, careers, recognition, popularization, and so on. In education, mathematics is a core part of the curriculum and forms an important element of the STEM academic disciplines.
Despite the close relationship between math and physics, they are not synonyms. In mathematics objects can be defined exactly and logically related, but the object need have no relationship to experimental measurements. In physics, definitions are abstractions or idealizations, approximations adequate when compared to the natural world.
Faculty of Mathematical Sciences at University of Khartoum, offers academic degrees in Mathematics, Computer Sciences and Statistics; Programs of the Mathematical Sciences Research Institute; Research topics studied at the Isaac Newton Institute for Mathematical Sciences; Mathematical Sciences in the U.S. FY 2016 Budget; a report from the AAAS
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge.
This involved philosophical questions about mathematical truth, the relationship of mathematics with reality, the reality of mathematical objects, and the nature of mathematics. For the problem of foundations, there was two main options for trying to avoid paradoxes.
inferential statistics – the part of statistics that draws conclusions from data (using some model for the data): For example, inferential statistics involves selecting a model for the data, checking whether the data fulfill the conditions of a particular model, and with quantifying the involved uncertainty (e.g. using confidence intervals).
In mathematics, an operation is a function from a set to itself. For example, an operation on real numbers will take in real numbers and return a real number. An operation can take zero or more input values (also called "operands" or "arguments") to a well-defined output value. The number of operands is the arity of the operation.