Mathematics Quiz

Number theory = Topics related to numbers and their properties Algebra = Manipulation and study of symbols and the rules for manipulating these symbols Geometry = Study of shapes and the spaces in which they are contained Analysis = Study of quantities and their changes

Mathematical activity = Involves the discovery of properties of abstract objects and the use of pure reason to prove them Proof = Consists of a succession of applications of deductive rules to already established results Theorems = Previously proved results used in proofs Axioms = Entities stipulated to have certain properties, used as starting points of the theory

Abstractions from nature = Objects consisting of properties considered true starting points of the theory Entities in modern mathematics = Stipulated to have certain properties, called axioms Axioms = Basic properties that are considered true starting points of the theory Proofs = Succession of applications of deductive rules to already established results

<p>Numbers and formulas = Represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis Abstract objects = Consist of either abstractions from nature or entities stipulated to have certain properties Mathematical theory = Involves the use of pure reason to prove properties of abstract objects Deductive rules = Used to prove properties of abstract objects</p> Signup and view all the answers

<p>Discovery of properties of abstract objects = Primary focus of mathematical activity Use of pure reason to prove properties = Primary focus of mathematical theory Application of deductive rules = Primary focus of proving properties of abstract objects Study of shapes and spaces = Primary focus of geometry</p> Signup and view all the answers