Mathematics - Learning with Fun

Mathematics is the study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. It is the science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation.

Math also deals with concepts such as quantity, structure, space and change. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement and the study of the shapes and motions of physical objects. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.

Mathematics is very broadly divided into foundations, algebra, analysis, geometry, and applied mathematics, which includes theoretical computer science.
Foundations
The term foundation is used to refer to the formulation and analysis of the language, axioms, and logical methods on which all of mathematics rests.
Algebra
Algebra is the study of solutions of one or several algebraic equations, involving the polynomial functions of one or several variables. The case where all the polynomials have degree one (systems of linear equations) is called linear algebra. The case of a single equation, in which one studies the roots of one polynomial, is called field theory.
Analysis
The essential ingredient of analysis is the use of infinite processes, involving passage to a limit. Its basic branch is calculus.
Geometry
The shape, size, and other properties of figures and the nature of space are in the province of geometry.
Applied Mathematics
The term applied mathematics loosely designates a wide range of studies with significant current use in the empirical sciences.
Quantity
The study of quantity starts with numbers, first the familiar natural numbers and integers ("whole numbers") and arithmetical operations on them, which are characterized in arithmetic and later called number theory.
Space
It involves geometry, trigonometry, Topology, differential geometry.
Change
It involves Calculus, Vector calculus, differential equation, Dynamic system & chaos theory.
Structure
It includes number theory, abstract algebra, Group theory and Order theory.
Discrete mathematics
Discrete mathematics is the common name for the fields of mathematics most generally useful in theoretical computer science. This includes computability theory, computational complexity theory, and information theory.
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