Mathematics Mastery

Number theory = Topics of numbers and related structures Algebra = Formulas and quantities and their changes Geometry = Shapes and the spaces in which they are contained Analysis = Quantities and their changes

Discovery of properties of abstract objects = Most mathematical activity Use of pure reason to prove properties = Proving properties with deductive rules Proof = Succession of applications of deductive rules Axioms = Entities stipulated to have certain properties

Independent from any scientific experimentation = Fundamental truths of mathematics Developed in close correlation with their applications = Some areas of mathematics like statistics and game theory Grouped under applied mathematics = Areas developed in close correlation with their applications Modeling phenomena extensively = Extensive use for modeling phenomena

<p>Natural sciences = Mathematics is essential Engineering = Mathematics is essential Medicine = Mathematics is essential Statistics and game theory = Developed in close correlation with their applications</p> Signup and view all the answers

<p>Succession of applications of deductive rules = Description of a proof Applications of deductive rules to already established results = Description of a proof Previously proved theorems, axioms, and basic properties = Results included in a proof Abstract objects and stipulated entities = Objects involved in a proof</p> Signup and view all the answers