Mathematics: Fundamental Concepts
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Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and ______, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.

analysis

Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature or—in modern mathematics—entities that are stipulated to have certain properties, called ______.

axioms

A proof consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of the theory under consideration. Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science and the ______ sciences.

social

Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent from any scientific experimentation. Some areas of mathematics, such as ______ and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics.

<p>statistics</p> Signup and view all the answers

These topics are represented in modern mathematics with the major subdisciplines of ______ theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.

<p>number</p> Signup and view all the answers

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