|
|
Overview of Mathematics
Kosmoi.com 
Science
Mathematics
: About, Algebra, Analysis, Applied, Calculus, Chaos, Crossword, Fractals, Game_Theory, Games, Geometry, Graphs, History, Infinity, Logic, Measurement, Number • Books
Mathematics (from Greek mathema: science, knowledge, learning;
mathematikos: fond of learning) is the study of patterns of quantity,
structure, change and space. In the modern view, it is the investigation
of axiomatically defined abstract structures using formal logic as the
common framework. The specific structures investigated often have their
origin in the natural sciences, most commonly in physics, but
mathematicians also define and investigate structures for reasons purely
internal to mathematics, for instance because they realize that the
structure provides a unifying generalization for several subfields or a
helpful tool in common calculations. Finally, many mathematicians study
in the areas that they do for aesthetic reasons - simply because they
find the structures they investigate beautiful in and of themselves.
Arithmetic
refers generally to the study of the nature and properties of
numbers, measurement, and numerical computation (that is, the study of
the algorithms of calculation with numbers, the fundamental operations
of addition, subtraction, multiplication, and division, as well as
raising to powers, and extraction of roots.
Algebra is "arithmetic with symbols."
Unlike arithmetic, which deals with specific numbers, algebra introduces
'variables' that greatly extend the generality and scope of arithmetic.
Algebra may be described as a generalization and extension of arithmetic.
|
Analysis deals with the real and complex numbers and their functions.
Analysis is concerned with abstract objects such as sets of numbers,
sets of geometric points, or sets of functions that map numbers into
numbers or points into points and with the processes, called
limit processes, that depend on a measure of closeness between
numbers, points, or functions.
Analysis uses the concept of a limit.
It has its beginnings in the rigorous formulation of calculus and
studies concepts such as continuity, integration and differentiability
in general settings.
|
Calculus is concerned with concepts such as the rate of change of one
variable quantity with respect to another,
the slope of a curve at a prescribed point,
the computation of the maximum and minimum values of functions,
and the calculation of the area bounded by curves.
Evolved from algebra, arithmetic, and geometry,
it is the basis of that part of mathematics called analysis.
|
Established in the 1960s, chaos theory deals with dynamical systems
that, while in principle deterministic, have a high sensitivity to
initial conditions, because their governing equations are nonlinear.
Examples for such systems are the atmosphere, plate tectonics,
economics, and population growth.
|
Fractals are a class of complex geometric shapes that commonly exhibit
the property of self-similarity. such that a small portion of it can be
viewed as a reduced scale replica of the whole. The term fractal is
derived from the Latin word fractus ("fragmented," or "broken").
|
Game Theory -- the abstract study of games, or the mathematics of competition and cooperation -- analyzes situations in terms of gains and losses of opposing players. Two major theories about modern life have come out of games. The first is probability theory, which was first developed out of games of chance in the 17th century by Blaise Pascal. The strategies used to achieve success on the game board can also be applied in many real-life situations.
|
Geometry is concerned with the properties of space and of objects in
space; e.g. points, lines, surfaces, and solids.
In its most elementary form geometry is concerned with such metrical
problems as determining the areas and diameters of two-dimensional
figures and the surface areas and volumes of solids.
The study of plane curves, angles, polygons, and lines is called
plane geometry.
The study of curves in three-dimensional space such as
spheres, cones, cylinders, and polyhedra is called solid geometry.
|
A graph is a two-dimensional representation of data. A typical example would be a graph of some quantity varying with time, e.g. daily temperature. In science, we often use graphs to give us a picture of the relationships between variables.
|
Infinity refers to the concept of limitlessness and unboundedness in size, number or extent. One distinguishes between potential infinity and actual infinity.
|
Measurement is the determination of the size or magnitude of something. Measurement is not limited to physical quantities, but can extend to quantifying almost any imaginable thing such as degree of uncertainty, consumer confidence, or the rate of increase in the fall in the price of beanie babies.
|
Logic is regarded as a branch both of philosophy and of mathematics. A system of logic (or simply "a logic") is a set of rules for reasoning about a given domain. Many different systems of logic have been devised. Such artificial systems of reasoning now find many practical applications in computing.
|
A number system is any of various sets of symbols and the rules for using them to express quantities as the basis for counting, comparing amounts, performing calculations, determining order, making measurements, representing value, setting limits, abstracting quantities, coding information, and transmitting data.
|
About Overview of Mathematics
|
|
