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Greek Letters: List and Mathematical Use

This article aims to list the Greek letters and suggest some fairly standard uses in mathematics. As these letters are used a lot from high school and even more in higher education, we thought it was useful to make a reminder about it.

List of letters of the Greek alphabet

The Greek alphabet is made up of 24 letters, the first of which is alpha and the last is omega. Here is the list of these 24 letters:

Name
French
Letters
tiny
Letters
case
alphaαA
betaβB
gammaγΓ
deltaδΔ
epsilonεE
zetaζZ
etaηH
thetaθΘ
iotaιI
kappaκK
lambdaλΛ
muμM
nuνN
ksi or xiξΞ
omicronοΟ
piπΠ
rhoρP
sigmaσΣ
tauτT
upsilonυY
phiφ/ϕΦ
khi or chiχX
psiψΨ
omegaωΩ
List of 24 Greek letters

You will have noticed, a lot of capital letters are the same as those we currently use

Mathematical use of Greek letters

The list below is surely not exhaustive but here are some conventions of Greek letters used for mathematics

Alpha, beta, gamma, lambda, mu

These three letters are often used as parameters: a power, a scalar for linear maps, including lambda and mu.
We usually start by using alpha. Then, if we need a second parameter, we add beta, then gamma.

Delta

Delta can also be used as a parameter. But this Greek letter also has several other uses:

  • Δ is the famous discriminant to solve to solve the quadratic equations
  • Δ and δ are used to represent differences. This is especially the case in economics and physics, it is less something we do in math
  • Δ is also the symbol used for the Laplacian
  • δ is the Kronecker symbol: δA (x) = 1 if x belongs to A, 0 otherwise

Epsilon

ε represents in analysis a small quantity taken arbitrarily. It is the enemy of many students in higher education.

Zeta

The best known of these: The Riemann zeta function. Zeta is defined by

\zeta(s) = \displaystyle \sum_{n=1}^{+\infty}n^{-s}

There is moreover a conjecture known about the Riemann zeta function, I'll let you look for it.

Theta

The letter θ is often used to define angles: cos(θ), sin(θ) or even θ on its own.

Pi

There is a use that you necessarily know and one that you do not necessarily think of:

  • π is the irrational and even transcendent number known to almost everyone. We have done everything an article above, go ahead I'm sure you have things to learn. And we also have this article to demonstrate its irrationality.
  • Π is the symbol for products, did you think of this one? Here is an example of using capital pi with the factorials :
not! =1\times \ldots \times n= \prod_{k=1}^nk 

Sigma

For sigma, we can also differentiate 2 uses of this Greek letter in mathematics:

  • σ is what is called the standard deviation in probability that follows from σ2, the variance
  • Σ is the symbol used for sums. Example with the sum of the first n integers:
\sum_{k=1}^nk = \dfrac{n(n+1)}{2}

Dew

τ is the letter used to define a topology.

Phi and psi

These two Greek letters are often used for application names. If phi is already taken then we take psi.

when the

  • Khi (also called chi) is used in statistics to make in particular what is called the text of the "chi-square" and we therefore take the lowercase chi, χ.
  • χ is also used in linear algebra, χA is the characteristic polynomial of the matrix A

Omega

Two main uses are made of Omega:

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