Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”)

1. Αα Alpha Νν Nu
Ββ Beta Ξξ Xi
Γγ Gamma Οο Omicron
Δδ Delta Ππ Pi
Εε Epsilon Ρρ Rho
Ζζ Zeta Σσς Sigma
Ηη Eta Ττ Tau
Θθ Theta Υυ Upsilon
Ιι Iota Φφ Phi
Κκ Kappa Χχ Chi
Λλ Lambda Ψψ Psi
Μμ Mu Ωω Omega
eta is often used to denote a variable in mathematics and physics, where it often has
specific meanings for certain applications, such as representing beta particles,
and beta radiation. In regression analysis, "B" symbolizes non-standardized partial
slope coefficients, whereas "β" represents standardized (standard deviation-score
form) coefficients; in both cases, the coefficients reflect the change in the criterion Y
per one-unit change in the value of the associated predictor X.
In the International Phonetic Alphabet, Greek minuscule beta denotes a voiced
bilabial fricative.
Gamma (uppercase Γ, lowercase γ; Greek: Γάμμα) is the third letter of the Greek
alphabet. In the system of Greek numerals it has a value of 3. It was derived from
the Phoenician letter Gimel . Letters that arose from Gamma include the
Roman C and G and the Cyrillic letters Ge Г and Ghe Ґ.
In Modern Greek, it represents either a voiced velar fricative / /ɣ or a voiced palatal
fricative / /ʝ . In Ancient Greek, it represented a voiced velar stop / /ɡ . Beforevelars, it
represents a velar nasal /ŋ/ in Modern as well as Ancient Greek, and a double
gamma represents the sequence /ŋ /ɡ (phonetically varying [ŋ ~ ]ɡ ɡ ) or /ŋ /ɣ .

2. Use as a symbol or a term
The lower-case letter γ is used as a symbol for:
 gamma radiation in nuclear physics
 surface energy in materials science
 the Lorentz factor in theory of relativity
 The heat capacity ratio Cp/Cv in thermodynamics
 The activity coefficient in thermodynamics
 The gyromagnetic ratio in electromagnetism
 gamma oscillation in neuroscience
 Gamma Motor Neurons in neuroscience
 antibiotic concentration (1 γ = 1 µg/ml) in microbiology
 the power by which the luminance of an image is increased in gamma
correction
 The Euler–Mascheroni constant
 Phonetics uses gamma as the symbol for the voiced velar fricative
 In mechanical engineering,
 specific weight
 The shear rate of a fluid is represented by a lower case gamma with a
dot above it:
 Austenite (also known as γ-iron), a metallic non-magnetic allotrope or
solid solution of iron.
The upper-case letter Γ is used as a symbol for:
 In mathematics, the gamma function (usually written as Γ-function) is an
extension of the factorial to complex numbers
 In probability theory and statistics, the gamma distribution is a two-parameter
family of continuous probability distributions.
 circulation in fluid mechanics
 As reflection coefficient in physics and electrical engineering
 The tape alphabet of a Turing machine
Delta (letter)
From Wikipedia, the free encyclopedia
Look
up Δ or δ in Wiktionary,

3. the free dictionary.
Greek alphabet
Αα Alpha Νν Nu
Ββ Beta Ξξ Xi
Γγ Gamma Οο Omicron
Δδ Delta Ππ Pi
Εε Epsilon Ρρ Rho
Ζζ Zeta Σσς Sigma
Ηη Eta Ττ Tau
Θθ Theta Υυ Upsilon
Ιι Iota Φφ Phi
Κκ Kappa Χχ Chi
Λλ Lambda Ψψ Psi
Μμ Mu Ωω Omega
Obsolete letters
Digamma Qoppa
San Sampi
Other characters
Stigma Sho

4. Heta
Greek diacritics
Delta (uppercase Δ, lowercase δ; Greek: Δέλτα [ ðelta]ˈ , Dhelta) is the fourth letter of
the Greek alphabet. In the system of Greek numerals it has a value of 4. It was
derived from the Phoenician letter Dalet. In the Ancient Greek language, it
represented a voiced dental plosive /d/, while in Modern Greek it represents avoiced
dental fricative /ð/, hence it is pronounced as "th" in "that" or "this". It is romanised as
either "D" or "Dh."
A river delta (originally, the Nile River delta) is so named because its shape
approximates the upper-case letter delta (the shape is a triangle).
Contents
[hide]
1 The upper-case
letter Δ
2 The lower-case
letter δ
3 See also
4 References
The upper-case letter Δ
The upper-case letter Δ can be used to denote
 Change any type; (in science and engineering fields)
 Change; e.g. in
, the average change of y per unit x, i.e. the change of y over
the change of x
 More specifically, the difference operator.
 The Laplace operator:

5.  The discriminant of a polynomial equation, especially the quadratic
equation:
 A macroscopic change in the value of a variable in mathematics or
science
 Uncertainty in a physical variable as seen in for instance
the uncertainty principle
 An interval of possible values for a given quantity for instance
across a sample[citation needed]
 Any of the delta particles in particle physics
 The determinant of the matrix of coefficients of a set of linear
equations (see Cramer's Rule)
 That an associated locant number represents the location of
a covalent bond in an organic compound, the position of which is
variant between isomericforms
 In chemistry, it is often used to represent the addition of heat in a
reaction.
 In legal shorthand, it represents a defendant
 In the financial markets, it is one of the Greeks that describes the
rate of change of an option price for a given change in the
underlying benchmark
 It is the symbol of the Greek inventor and architect Daedalus
 In genetics, it can stand for a gene deletion, e.g. the CCR5-Δ32 a
deletion of the CCR5 at the 32nd base pair segment
 The American Dental Association cites it (together with omicron for
"odont") as the symbol of dentistry.[1]
The lower-case letter δ
The lower-case letter δ can be used to denote
 An infinitesimal change in the value of a variable in infinitesimal
calculus
 An auxiliary function in Calculus used to rigorously define
the limit or continuity of a given function.
 The Kronecker delta in mathematics

6.  The Dirac delta function in mathematics
 The transition function in automata
 Deflection in engineering mechanics
 The Force of Interest in actuarial science
 The chemical shift of Nuclear Magnetic Resonance in chemistry
 The relative electronegativity of different atoms in a molecule,
δ−
being more electronegative than δ+
 Text requiring deletion in proofreading. The usage is said to date
back to classical times
 In some of the manuscripts written by Dr. John Dee, the character
of delta is used to represent Dee
 The Computer Science chapter at the Royal Institute of
Technology[2]
 Is a subunit of the F1 sector of the F-ATPase
 The declination of an object in the equatorial coordinate
system of astronomy
 The dividend yield on the Black-Scholes option pricing formula
 Signifies a major seventh chord in jazz music notation.
 Ratios of environmental isotopes, such as 18
O/16
O and D/1
H from
waters are displayed using delta notation - δ18
O and δD,
respectively
 The rate of depreciation of the aggregate capital stock of an
economy in an exogenous growth model in macroeconomics.[3]
[edit]See also
 D, d
 Д, д
 Th
 Greek letters used in mathematics, science, and engineering
 Nabla symbol ( )
 ∂ - the partial derivative symbol, sometimes mistaken for a
lowercase Greek letter Delta.
Upper-case letter Λ
 Lambda can mean the empty set in mathematics, though other symbols are
more commonly used, such as .

7.  The lambda particle is a type of subatomic particle in subatomic particle
physics.
 Lambda is the set of logical axioms in the axiomatic method of logical
deduction in first-order logic.
 Lambda was used as a shield pattern by the Spartan Army. This stood
for Lakedaimon, the name of the region of Sparta.
 Lambda is the von Mangoldt function in mathematical number theory.
 In statistics, Wilks's lambda is used in multivariate analysis of variance
(MANOVA analysis) to compare group means on a combination of dependent
variables.
 In the spectral decomposition of matrices, lambda indicates the diagonal
matrix of the eigenvalues of the matrix (mathematics).
 In computer science, lambda is the time window over which a process is
observed for determining the working memory set for a digital computer's virtual
memory management.
 In astrophysics, lambda represents the likelihood that a small body will
encounter a planet or a dwarf planet leading to a deflection of a significant
magnitude. An object with a large value of lambda is expected to have cleared its
neighborhood, satisfying the current definition of a planet.
 In crystal optics, lambda is used to represent the period of a lattice.
 In NATO military operations, a chevron (a capital lambda symbol) is painted
on the vehicles of this military alliance for identification. (The Spartan armyused a
capital lambda on its shields.)
 In electrochemistry, lambda denotes the "equivalent conductance" of
an electrolyte solution.
 In cosmology, lambda is the symbol for the cosmological constant.
 In optics, lambda denotes the grating pitch of a Bragg reflector.
[edit]Lower-case letter λ
Lower-case lambda

8.  Lambda indicates the wavelength of any wave, especially
in physics, electronics engineering, and mathematics.
 Lambda indicates the radioactivity decay constant in nuclear
physics and radioactivity. This constant is very simply related (by a multiplicative
constant) to the half-life of any radioactive material.
 In mathematical logic and computer science, lambda is used to introduce
an anonymous function expressed with the concepts of lambda calculus.
 Lambda is a non-SI metric unit of measure of volume (symbol λ) equal to
one microliter (1 μL) or one cubic millimeter (1 mm3
). This always rare use is
currently deprecated.
 Lambda indictes an eigenvalue in the mathematics of linear algebra.
 In the physics of electric fields, lambda sometimes indicates the linear charge
density of a uniform line of electric charge (measured in coulombs per meter).
 Lambda denotes a Lagrange multiplier in multi-dimensional calculus.
 In solid-state electronics, lambda indicates the channel length
modulation parameter of a MOSFET.
 There is a lambda phage virus in biology.
 In ecology, lambda denotes the long-term intrinsic growth rate of a population.
This value is often calculated as the dominant eigenvalue of the age/size
class matrix (mathematics).
 In formal language theory and in computer science, lambda denotes
the empty string.
 In telecommunications, lambda indicates the wavelength in a wavelength-
division multiplexing optical communications system. This is actually a form of the
long-established concept of frequency-division multiplexing.
 Lambda denotes the Lebesgue measure in mathematical set theory.
 The Goodman and Kruskal's lambda in statistics indicates the proportional
reduction in error when one variable's values are used to predict the values of
another variable.
 Lambda denotes the oxygen sensor in a vehicle that measures
the stoichiometric air-to-fuel ratio in the exhaust gases of an internal-combustion
engine.
 The Lambda (rocket) is a version of a large booster rocket in Japanese outer-
space technology.
 Lambda denotes the failure rate of devices and systems in reliability theory,
and it is measured in failure events per hour. Numerically, this lamba is also the
reciprocal of the Mean time between failures.
 In criminology, lambda denotes an individual's frequency of offenses

9.  In cartography and navigation, lambda denotes the longitude or a location.
 Lambda is the symbol of the musician Richard D. James or Aphex Twin.
 Lambda denotes Christopher Langton's parameter for the classification
of Stephen Wolfram's classes of cellular automata.
 In electrochemistry, lambda also denotes the ionic conductance of a given ion
(The composition of the ion is generally shown as a subscript to the lambda
character).
 In neurobiology, lambda denotes the length constant (or exponential rate of
decay) of the electric potential across the cell membrane along a length of a
nerve cell's axon.
 In the science and technology of heat transfer, lambda denotes the heat of
vaporization per mole of material (a.k.a. its "latent heat").[3]
.
 In the technology and science of celestial navigation, lambda denotes
the longitude as opposed to the Roman letter "L" which denotes the latitude.
 King Louis XIII of France used the letter lambda as his personal symbol rather
than monogram.
 In Volvo automobiles, lambda denotes an engine, fuel, or ignition system
failure.
 Lambda is used as a recurring symbol for the human resistance in
the Valve computer game series Half-L
Lambda, the word
 In anatomy, the lambda is the point on the skull where the two parietal
bones and the occipital bone come together. The configuration of the sutures of
the skull resembles an upper case lambda, and the suture between each parietal
bone and the occipital bone is called the lambdoid suture.
 In programming languages such as Lisp and Python, lambda is an operator
used to denote anonymous functions or closures, following the usage of lambda
calculus. An example of this use of lambda in the Python language is this section
of computer code that sorts a list alphabetically by the last character of each
entry:
>>> list = ['woman', 'man', 'horse', 'boat', 'plane', 'dog']
>>> sorted(list, key=lambda word: word[-1])
['horse', 'plane', 'dog', 'woman', 'man', 'boat']

10.  The language Unlambda is a functional programming language based
upon combinatory logic, a simplification of the lambda calculus that does not
involve the lambda at all, hence the un- prefix.
 An automotive oxygen sensor (O2 sensor) is also known as a lambda probe,
sensor, sond, or sonde.
 Lambda is used in art and photography to refer to a digital Type C print, or to
the equipment that is used to produce it.
 Lambda was used by Pythagoras to denote the "Lambda number sequence" {
1, 2, 3, 4, 8, 9, 27, ... }
[edit]Lambda as a name
 The popular science fiction universe of Star Wars uses a transport vehicle
known as the Lambda-class shuttle that when viewed forward has the shape of
the lowercase lambda.
 Lambda is occasionally used in graphic design to represent a stylised 'A'.
Examples include the Disney movie Atlantis: The Lost Empire, the logo of the
band Angels & Airwaves, the logo of the bandDream Theater, and the logo of
electronics company Samsung. Conversely, the name of the
band Λucifer (pronounced lucifer) is sometimes spelt Aucifer.
A capital Lambda
 Stargate SG-1 uses a modified upper-case lambda, with a small circle above
the apex, to indicate Earth. This symbol has since become associated with the
entire franchise.[citation needed]
 GM Lambda platform, a crossover SUV automobile platform from General
Motors
 Lancia Lambda, a historic Italian automobile.
 In the Sailor Moon manga, the character Sailor Cosmos claimed to have the
ultimate "Lambda Power", which was stated to be the power of rebirth.
 Lambda Legal is a gay & lesbian legal advocacy group in the United States.

11.  Lambda Literary Awards is the name of a group of U.S. book awards
presented annually for gay and lesbian literature.
 Lambda Particles is the name for the LGBT group at the Stanford Linear
Accelerator Center.[4]
 Lambda Rising is a gay & lesbian bookstore in the Dupont
Circle neighborhood of Washington, D.C. which created the Lambda Literary
Award in 1989.
 National LambdaRail is a research high-speed computer network.
 Lambda-Delta (or Lambdadelta) is the name of a witch in the Umineko no
Naku Koro ni doujin game.
 In the popular anime Full Metal Panic, a Lambda Driver is a device which is
used to generate tremendous forces from the impulses of the pilot of an Arm
Slave in order to defend as well as attack.
 Lambda-11 is the name of a character in the BlazBlue series, appearing
in BlazBlue: Continuum Shift as a
Psi (uppercase Ψ, lowercase ψ; pronounced in English as / sa /ˈ ɪ , sigh) is the 23rd
letter of the Greek alphabet and has a numeric value of 700. In
both Classicaland Modern Greek, the letter indicates the combination /ps/ (like in
English "lapse"). The letter was adopted into the Old Italic alphabet, and its shape is
continued into the Algiz rune of the Elder Futhark. Psi was also adopted into
the early Cyrillic alphabet as Ѱ. In Greek loanwords in Latin and modern languages
with Latin alphabets, Psi is usually transliterated as "ps". In English, due
to phonotactic constraints, its pronunciation is usually simplified to /s/.
The letter psi is commonly used in physics for representing
a wavefunction in quantum mechanics, particularly with the Schrödinger
equation and bra-ket notation: . It is also used to represent the (generalized)
positional states of a qubit in a quantum computer.
Psi is also used as the symbol for the polygamma function, defined by
where Γ(x) is the gamma function.
The letters Ψ or ψ can also be a symbol for:
 psychology, psychiatry, and
sometimes parapsychology (involving paranormal or relating with
the supernatural subjects).

12.  In mathematics, the reciprocal Fibonacci constant.
 Water potential in movement of water between plant cells.
 In biochemistry, it denotes the rare nucleotide pseudouridilic acid.
 Stream function in fluid mechanics defining the curve to which the flow
velocity is always tangent.
 One of the dihedral angles in the backbones of proteins
 The planet Neptune
 The Schrödinger equation and throughout quantum mechanics, ψ(x) stands
for the wave function
 Indiana University (as a superimposed I and U)
 Gangster Disciples
 A Sai, the name of which is pronounced the same way.
 Pharmacology, general pharmacy
 In virology the ψ site is a viral packaging signal.
 The J/ψ meson, in particle physics.
 In the Computability Theory, represents the return value of a
program .
 In the comic Monochrome, Psi is a mentally disturbed character, though her
name is usually spelled out.
 In the television show Babylon 5, Ψ is the symbol of the Psi Corps.
 On Wikipedia, it stands for the currency WikiMoney, an inactive mutual funds
system.
The lower-case letter (or often its variant, ) is often used to represent the
following:
 The golden ratio in mathematics, art, and architecture.
 Euler's totient function φ(n) in number theory; also called Euler's phi function.
 In algebra, group or ring homomorphisms
 In probability theory, ϕ(x) = (2π)−½
e−x2/2
is the probability density function of
the normal distribution.
 In probability theory, φX(t) = E[ eitX
] is the characteristic function of a random
variable X.
 An angle, typically the second angle mentioned, after θ (theta). Especially:
 The argument of a complex number.
 The phase of a wave in signal processing.

13.  In spherical coordinates, mathematicians usually refer to phi as the
polar angle (from the z-axis). The convention in physics is to use phi as the
azimuthal angle (from the x-axis).
 One of the dihedral angles in the backbones of proteins.
 Internal or effective angle of friction.
 Electric potential in physics.
 The work function in electronics.
 A shorthand representation for an aromatic functional group in organic
chemistry.
 The fugacity coefficient in thermodynamics.
 The ratio of free energy destabilizations of protein mutants in phi value
analysis.
 In cartography and navigation, latitude.
 In combustion engineering, equivelance ratio. The ratio between the actual
fuel air ratio to the stoichiometric fuel air ratio.
 A sentence in first-order logic.
 Porosity in geology and hydrology.
 Strength (or resistance) reduction factor in structural engineering, used to
account for statistical variabilities in materials and construction methods.
 The symbol for a voiceless bilabial fricative in the International Phonetic
Alphabet (using the straight line variant character)
 In economics, this is usually an additive term.[clarification needed]
The upper-case letter Φ is used as a symbol for:
 The golden ratio conjugate −0.618... in mathematics.
 The magnetic flux and electric flux in physics, with subscripts distinguishing
the two.
 The cumulative distribution function of the normal
distribution in mathematics and statistics.
 Philosophy.
 The number of phases in a power system in electrical engineering, for
example 1Φ for single phase, 3Φ for three phase.
 A common symbol for the parametrization of a surface in vector calculus.
 In Lacanian algebra, Φ stands for the imaginary phallus and also represents
phallic signification. -Φ stands in for castration.[2]

14. The diameter symbol in engineering, ⌀, is often incorrectly referred to as "phi". This
symbol is used to indicate the diameter of a circular section, for example "⌀14",
means the diameter of the circle is 14units.
[edit]Computing
In Unicode, there are multiple forms of the phi letter:
Characte
r
Name
Correct
appearance
Your
browser
Usage
U+03A6
GREEK
CAPITAL
LETTER PHI
Φ used in Greek texts
U+03C6
GREEK SMALL
LETTER PHI or φ
used in Greek texts (contrary to
what is shown here, it is
normally not italicized)
U+03D5
GREEK PHI
SYMBOL
ϕ
used in mathematical and
technical contexts[3]
U+0278
LATIN SMALL
LETTER PHI
ɸ
used in IPA to symbolise
a voiceless bilabial fricative
In some older fonts that are not yet compatible with Unicode 3.0 from 1998, the
U+03D5 GREEK PHI SYMBOL might be represented by the "loopy" symbol
instead.[3]
This is no longer a correct representation. The U+03C6 GREEK SMALL
LETTER PHI may be presented as either the "stroked" glyph, but preferably as the
"loopy" glyph.[3]
In HTML/XHTML, the upper and lower case phi character entity
references are Φ (Φ) and φ (φ) respectively.
In LaTeX, the math symbols are Phi ( ), phi ( ), and varphi ( ).