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Mathematics

The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols.

The Special Theory of Relativity

The physical theory published in 1905 by Albert Einstein. It replaced Newtonian notions of space and time, and incorporated electromagnetism as represented by Maxwell's equations. The theory is called "special" because the theory does not include a description of gravity; ten years later, Einstein published the theory of general relativity, which is the extension of special relativity to incorporate gravitation.

General Relativity

The theory of gravitation published by Albert Einstein in 1915. According to general relativity the force of gravity is a manifestation of the local geometry of spacetime. Although the modern theory is due to Einstein, its origins go back to the axioms of Euclidean geometry and the many attempts over the centuries to prove Euclid's fifth postulate, that parallel lines remain always equidistant, culminating with the realization by Lobachevsky, Bolyai and Gauss that this axiom need not be true. The general mathematics of non-Euclidean geometries was developed by Gauss' student, Riemann, but these were thought to be wholly inapplicable to the real world until Einstein had developed his theory of relativity. 


Quantum Theory

A theory in physics based on the principle that matter and energy have the properties of both particles and waves, created to explain the radiation of energy from a blackbody, the photoelectric effect, and the Bohr theory, and now used to account for a wide range of physical phenomena, including the existence of discrete packets of energy and matter, the uncertainty principle, and the exclusion principle.

Uncertainty principle

A principle in quantum mechanics holding that increasing the accuracy of measurement of one observable quantity increases the uncertainty with which another conjugate quantity may be known.

Exclusion principle

The principle that two particles of a given type, such as electrons, protons, or neutrons, cannot simultaneously occupy a particular quantum state. Also called Pauli exclusion principle.

Photoelectric effect

Ejection of electrons from a substance by incident electromagnetic radiation, especially by visible light. Fermat's last theorem The theorem that the equation an + bn = cn has no solutions in positive integers a, b, c if n is an integer greater than 2. It was stated as a marginal note by Pierre de Fermat around 1630 and not proved until 1994 by the British mathematician Andrew Wiles (born 1953).

Euclidean geometry

geometry based on Euclid's axioms: e.g., only one line can be drawn through a point parallel to another line.

Hyperbolic geometry

a non-Euclidean geometry in which it is assumed that through any point there are two or more parallel lines that do not intersect a given line in the plane.

Abstract algebra

The field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. The term "abstract algebra" is used to distinguish the field from "elementary algebra" which teaches the correct rules for manipulating formulas and algebraic expressions involving real and complex numbers.

Butterfly effect

Used to describe many chaotic phenomena, was first described as such in reference to weather: that the beating of a butterfly's wings in Brazil might set off a tornado in Texas months later1.

Chaos theory

posits that complex systems such as the weather, or the stock market, are difficult to predict due to their sensitivity to small changes. The cumulative effect of these small changes, and their timing, makes it very difficult or impossible to predict future conditions with a high degree of certainty.

Lorentz transformation

Named after its discoverer, a Dutch physicist and mathematician Hendrik Antoon Lorentz (1853-1928), forms the basis for the special theory of relativity, that has been introduced to remove contradictions between the theories of electromagnetism and classical mechanics. Under these transformations, the speed of light is the same in all reference frames, as postulated by special relativity. Although the equations are associated with special relativity, they were developed before special relativity and were proposed by Lorentz in 1904 as a means of explaining the Michelson-Morley experiment through contraction of lengths. This is in contrast to the more intuitive Galilean transformation, which is sufficient at non-relativistic speeds.

Arithmetic

The mathematics of integers, rational numbers, real numbers, or complex numbers under addition, subtraction, multiplication, and division.

Algebra

1. A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.
2. A set together with a pair of binary operations defined on the set. Usually, the set and the operations include an identity element, and the operations are commutative or associative.

Astronomical fractions

Those fractions whose denominators are some power of sixty; as, 1/60, 1/3600, 1/216000, because formerly there were no others used in astronomical calculations.

Calculus

That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations.

Imaginary calculus

a method of investigating the relations of real or imaginary quantities by the use of the imaginary symbols and quantities of algebra.

Differential calculus

a method of investigating mathematical questions by using the ratio of certain indefinitely small quantities called differentials. The problems are primarily of this form: to find how the change in some variable quantity alters at each instant the value of a quantity dependent upon it.

Integral calculus

a method which in the reverse of the differential, the primary object of which is to learn from the known ratio of the indefinitely small changes of two or more magnitudes, the relation of the magnitudes themselves, or, in other words, from having the differential of an algebraic expression to find the expression itself.

Barycentric calculus

a method of treating geometry by defining a point as the center of gravity of certain other points to which coefficients or weights are ascribed.

Geometry

The mathematics of the properties, measurement, and relationships of points, lines, angles, surfaces, and solids.

Descriptive geometry

that part of geometry which treats of the graphic solution of all problems involving three dimensions.

Higher geometry

that pert of geometry which treats of those properties of straight lines, circles, etc., which are less simple in their relations, and of curves and surfaces of the second and higher degrees.

Trigonometry

That branch of mathematics which treats of the relations of the sides and angles of triangles, which the methods of deducing from certain given parts other required parts, and also of the general relations which exist between the trigonometrical functions of arcs or angles.

Analytical trigonometry

that branch of trigonometry which treats of the relations and properties of the trigonometrical functions.

Plane trigonometry

Without elevations or depressions; even; level; flat; lying in, or constituting, a plane; as, a plane surface.

Spherical trigonometry

Without elevations or depressions; even; level; flat; lying in, or constituting, a plane; as, a plane surface.

Differential equation

An equation that expresses a relationship between functions and their derivatives.

Physics

The science of matter and energy and of interactions between the two, grouped in traditional fields such as acoustics, optics, mechanics, thermodynamics, and electromagnetism, as well as in modern extensions including atomic and nuclear physics, cryogenics, solid-state physics, particle physics, and plasma physics.

Acoustics

The scientific study of sound, especially of its generation, transmission, and reception. Note: The science is, by some writers, divided, into diacoustics, which explains the properties of sounds coming directly from the ear; and catacoustica, which treats of reflected sounds or echoes.

Optics

The branch of physics that deals with light and vision, chiefly the generation, propagation, and detection of electromagnetic radiation having wavelengths greater than x-rays and shorter than microwaves.

Mechanics

That science, or branch of applied mathematics, which treats of the action of forces on bodies.

Statics

That branch of mechanics which treats of the equilibrium of forces, or relates to bodies as held at rest by the forces acting on them.

Dynamics

The branch of mechanics that is concerned with the effects of forces on the motion of a body or system of bodies, especially of forces that do not originate within the system itself. Also called kinetics.

Kinetics

a branch of science that deals with the effects of forces upon the motions of material bodies or with changes in a physical or chemical system. Hydraulics The physical science and technology of the static and dynamic behavior of fluids.

Pneumatics

The study of the mechanical properties of air and other gases. Thermodynamics Physics that deals with the relationships and conversions between heat and other forms of energy.

Electromagnetism

The magnetism developed by a current of electricity; the science which treats of the development of magnetism by means of voltaic electricity, and of the properties or actions of the currents evolved.

Nuclear physics

The scientific study of the forces, reactions, and internal structures of atomic nuclei.

Cryogenics

The branch of physics that studies the phenomena that occur at very low temperatures.

Solid-state physics

The branch of physics that deals with the physical properties of solid materials, especially the electromagnetic, thermodynamic, and structural properties of crystalline solids. Also called condensed matter physics.

Particle physics

the branch of physics that studies subatomic particles and their interactions.

Plasma physics

the branch of physics concerned with matter in its plasma phase.

Plasma

An electrically neutral, highly ionized gas composed of ions, electrons, and neutral particles. It is a phase of matter distinct from solids, liquids, and normal gases.

Chemistry

The science of the composition, structure, properties, and reactions of matter, especially of atomic and molecular systems.

Discrete Mathematics

Discrete mathematics is mathematics that deals with discrete objects. Discrete objects are those which are separated from (not connected to/distinct from) each other. Integers (aka whole numbers), rational numbers (ones that can be expressed as the quotient of two integers), automobiles, houses, people etc. are all discrete objects. On the other hand real numbers which include irrational as well as rational numbers are not discrete. As you know between any two different real numbers there is another real number different from either of them. So they are packed without any gaps and can not be separated from their immediate neighbors. In that sense they are not discrete