Mathematics Mastery

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 analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. 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 u.

Logic, topology, calculus, and probability

Calculus, trigonometry, statistics, and arithmetic

Differential equations, abstract algebra, combinatorics, and set theory

Number theory, algebra, geometry, and analysis (correct)

Experimentation and observation of natural phenomena

Extrapolation of patterns from historical data

Discovery of properties of abstract objects and use of pure reason to prove them (correct)

Application of statistical analysis to real-world problems

<p>A succession of applications of deductive rules to already established results</p> Signup and view all the answers

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

<p>Abstractions from nature or entities stipulated to have certain properties</p> Signup and view all the answers