"The topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes."
It is a study of numbers, quantity, and mathematical structures, including the development of mathematical algorithms used in cryptography.
Number Theory: The study of properties of numbers, including prime numbers, divisibility, and modular arithmetic.
Algebra: The study of mathematical symbols and operations that represent numbers and their relationships.
Geometry: The study of spatial relationships between points, lines, and surfaces.
Calculus: The study of mathematical operations that deal with changes and rates of change, including derivatives and integrals.
Probability theory: The study of chance and randomness, including calculating and describing the likelihood of events.
Statistics: The study of the collection, analysis, and interpretation of data.
Linear algebra: The study of mathematical structures and methods for solving systems of linear equations.
Differential equations: The study of equations that describe relationships and rates of change between variables.
Discrete mathematics: The study of mathematical structures and relationships that are not continuous, such as networks and graphs.
Number systems: The study of different ways of representing numbers, including real numbers, complex numbers, and imaginary numbers.
Logic: The study of reasoning and argumentation, including deductive and inductive reasoning.
Topology: The study of spatial relationships that are preserved by continuous transformations.
Mathematical modeling: The process of creating mathematical representations of real-world phenomena to make predictions and solve problems.
Combinatorics: The study of counting and arrangements, including permutations and combinations.
Cryptography: The study of creating and analyzing systems for secure communication.
Game theory: The study of decisions made in competitive situations, including analyzing strategies and outcomes.
Set theory: The study of sets, including set operations and infinite sets.
Nonlinear dynamics: The study of complex systems that exhibit nonlinear behavior and chaotic behavior.
Abstract algebra: The study of mathematical structures and systems, including groups, rings, and fields.
Computer science: The study of algorithms and programming, including applications in mathematics and other fields.
Algebra: :.
Geometry: :.
Trigonometry: :.
Calculus: :.
Number Theory: :.
Topology: :.
Analysis: :.
"Number theory, algebra, geometry, and analysis."
"No general consensus among mathematicians about a common definition."
"The discovery of properties of abstract objects and the use of pure reason to prove them."
"A proof consists of a succession of applications of deductive rules to already established results."
"Independent from any scientific experimentation."
"The natural sciences, engineering, medicine, finance, computer science, and the social sciences."
"Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications."
"Other areas are developed independently from any application (and are therefore called pure mathematics), but often later find practical applications."
"The problem of integer factorization, for example, which goes back to Euclid in 300 BC, had no practical application before its use in the RSA cryptosystem, now widely used for the security of computer networks."
"Historically, the concept of a proof and its associated mathematical rigor first appeared in Greek mathematics, most notably in Euclid's Elements."
"Mathematics was essentially divided into geometry and arithmetic (the manipulation of natural numbers and fractions)."
"The 16th and 17th centuries."
"The interaction between mathematical innovations and scientific discoveries has led to a rapid lockstep increase in the development of both."
"The foundational crisis of mathematics at the end of the 19th century."
"It heralded a dramatic increase in the number of mathematical areas and their fields of application."
"More than 60 first-level areas of mathematics."
"Mathematics is extensively used for modeling phenomena."
"Certain properties called axioms."
"Some basic properties that are considered true starting points of the theory under consideration."