Uncovering the World of Mathematics

Number theory = Topics of numbers and related structures Algebra = Formulas and quantities Geometry = Shapes and spaces 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 Abstractions from nature or stipulated entities = Objects in modern mathematics

Natural sciences, engineering, medicine, finance, computer science, social sciences = Essential in various fields Modeling phenomena = Extensively used for modeling phenomena Fundamental truths independent from scientific experimentation = Fundamental truths of mathematics Statistics and game theory = Developed in close correlation with their applications

<p>Axioms = Entities stipulated to have certain properties Proofs = Successions of applications of deductive rules Theorems, axioms, and basic properties = Already established results in a proof Abstract objects from nature or stipulated entities = Objects consisting of abstractions from nature or stipulated entities</p> Signup and view all the answers

<p>Statistics and game theory = Developed in close correlation with applications Number theory, algebra, geometry, analysis = Major subdisciplines in modern mathematics Discovery of properties of abstract objects and use of pure reason to prove them = Most mathematical activity involves these Fundamental truths independent from scientific experimentation = Fundamental truths of mathematics</p> Signup and view all the answers