Mathematics: The Study of Numbers and Structures

The major subdisciplines of modern mathematics mentioned in the text are number theory, algebra, geometry, and analysis.

A proof in mathematics 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 social sciences.

<p>The fundamental truths of mathematics are independent from any scientific experimentation.</p> Signup and view all the answers

<p>Some areas of mathematics mentioned in the text that are often grouped under applied mathematics are statistics and game theory.</p> Signup and view all the answers

<p>The major subdisciplines of modern mathematics mentioned in the text are number theory, algebra, geometry, and analysis.</p> Signup and view all the answers

<p>Mathematical activity is described in the text as involving 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 entities that are stipulated to have certain properties, called axioms.</p> Signup and view all the answers

<p>Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences.</p> Signup and view all the answers

<p>A proof in mathematics consists of a succession of applications of deductive rules to already established results, including previously proved theorems, axioms, and some basic properties that are considered true starting points of the theory under consideration.</p> Signup and view all the answers

<p>Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics.</p> Signup and view all the answers