Symbols:Abbreviations
A
AC
- The axiom of choice.
Same as AoC.
ACC
a.e.
- Abbreviation for almost everywhere.
agm
- Abbreviation for arithmetic-geometric mean.
alg.
AoC
- The axiom of choice.
Same as AC.
arith.
- Abbreviation for arithmetic or arithmetical.
B
BNF
- Backus-Naur Form (previously Backus Normal Form until the syntax was simplified by Peter Naur).
It was Donald Knuth who suggested the name change, on the grounds that "normal" is an inaccurate description.
BPI
C
cdf or c.d.f.
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $X$ be a real-valued random variable on $\struct {\Omega, \Sigma, \Pr}$.
The cumulative distribution function (or c.d.f.) of $X$ is denoted $F_X$, and defined as:
- $\forall x \in \R: \map {F_X} x := \map \Pr {X \le x}$
CNF or cnf
D
D.C.
Some sources refer to a derivative as a differential coefficient, and abbreviate it D.C.
Some sources call it a derived function.
DCC
DNF or dnf
E
EE
Context: Predicate Logic.
- Rule of Existential Elimination, which is another term for the Rule of Existential Instantiation ($\text {EI}$).
EG
Context: Predicate Logic.
EI
Context: Predicate Logic.
Alternatively, Rule of Existential Introduction, which is another term for the Rule of Existential Generalisation ($\text {EG}$). Beware.
EMF
Context: Electromagnetism.
Electromotive force is a quantity that measures the source of potential energy in an electric circuit.
It is defined as the amount of work per unit electric charge.
F
FCF
G
GCD or g.c.d.
Also known as:
GCF
Also known as:
GCH
- The Generalized Continuum Hypothesis can be abbreviated $\operatorname {GCH}$.
glb
Another term for infimum.
H
HCF or h.c.f.
Also known as greatest common divisor (g.c.d.).
hex
hyp. $(1)$
hyp. $(2)$
I
iff
ICF
I.V.P.
I.V.P.: 1
I.V.P.: 2
J
K
L
LCM, lcm or l.c.m.
LHS
In an equation:
- $\text {Expression $1$} = \text {Expression $2$}$
the term $\text {Expression $1$}$ is the left hand side.
LQR
Let $p$ and $q$ be distinct odd primes.
Then:
- $\paren {\dfrac p q} \paren {\dfrac q p} = \paren {-1}^{\dfrac {\paren {p - 1} \paren {q - 1} } 4}$
where $\paren {\dfrac p q}$ and $\paren {\dfrac q p}$ are defined as the Legendre symbol.
An alternative formulation is: $\paren {\dfrac p q} = \begin{cases} \quad \paren {\dfrac q p} & : p \equiv 1 \lor q \equiv 1 \pmod 4 \\ -\paren {\dfrac q p} & : p \equiv q \equiv 3 \pmod 4 \end{cases}$
The fact that these formulations are equivalent is immediate.
This fact is known as the Law of Quadratic Reciprocity, or LQR for short.
lsb or l.s.b.
LSC
M
msb or m.s.b.
N
NNF
O
ODE
P
PCI
PCFI
PDE
A partial differential equation (abbreviated P.D.E. or PDE) is a differential equation which has:
- one dependent variable
- more than one independent variable.
The derivatives occurring in it are therefore partial.
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $X$ be an absolutely continuous random variable on $\struct {\Omega, \Sigma, \Pr}$.
Let $P_X$ be the probability distribution of $X$.
Let $\map \BB \R$ be the Borel $\sigma$-algebra of $\R$.
Let $\lambda$ be the Lebesgue measure on $\struct {\R, \map \BB \R}$.
We define the probability density function $f_X$ by:
- $\ds f_X = \frac {\d P_X} {\d \lambda}$
where $\dfrac {\d P_X} {\d \lambda}$ denotes the Radon-Nikodym derivative of $P_X$ with respect to $\lambda$.
PFI
PGF or p.g.f.
Let $X$ be a discrete random variable whose codomain, $\Omega_X$, is a subset of the natural numbers $\N$.
Let $p_X$ be the probability mass function for $X$.
The probability generating function for $X$, denoted $\map {\Pi_X} s$, is the formal power series defined by:
- $\ds \map {\Pi_X} s := \sum_{n \mathop = 0}^\infty \map {p_X} n s^n \in \R \sqbrk {\sqbrk s}$
PID or pid
A principal ideal domain is an integral domain in which every ideal is a principal ideal.
PMF or p.m.f.
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $X: \Omega \to \R$ be a discrete random variable on $\struct {\Omega, \Sigma, \Pr}$.
Then the (probability) mass function of $X$ is the (real-valued) function $p_X: \R \to \closedint 0 1$ defined as:
- $\forall x \in \R: \map {p_X} x = \begin{cases} \map \Pr {\set {\omega \in \Omega: \map X \omega = x} } & : x \in \Omega_X \\ 0 & : x \notin \Omega_X \end{cases}$
where $\Omega_X$ is defined as $\Img X$, the image of $X$.
That is, $\map {p_X} x$ is the probability that the discrete random variable $X$ takes the value $x$.
PMI
PNT
Poset
A partially ordered set is a relational structure $\struct {S, \preceq}$ such that $\preceq$ is a partial ordering.
The partially ordered set $\struct {S, \preceq}$ is said to be partially ordered by $\preceq$.
Q
QED
The initials of Quod Erat Demonstrandum, which is Latin for which was to be demonstrated.
These initials were traditionally added to the end of a proof, after the last line which is supposed to contain the statement that was to be proved.
QEF
The initials of Quod Erat Faciendum, which is Latin for which was to be done.
These initials were traditionally added to the end of a geometric construction.
QEI
The initials of Quod Erat Inveniendum, which is Latin for which was to be found.
These initials were traditionally added after the completion of a calculation (either arithmetic or algebraic).
R
RHS
In an equation:
- $\text {Expression $1$} = \text {Expression $2$}$
the term $\text {Expression $2$}$ is the right hand side.
S
SAA
SAS
SCF
SFCF
SHM
SICF
SSS
SUVAT
- A category of problems in elementary applied mathematics and Newtonian physics involving a body $B$ under constant acceleration $\mathbf a$.
- They consist of applications of the equations:
$(1):$ Velocity after Time
- $\mathbf v = \mathbf u + \mathbf a t$
$(2):$ Distance after Time
- $\mathbf s = \mathbf u t + \dfrac {\mathbf a t^2} 2$
$(3):$ Velocity after Distance
- $\mathbf v \cdot \mathbf v = \mathbf u \cdot \mathbf u + 2 \mathbf a \cdot \mathbf s$
where:
- $\mathbf u$ is the velocity at time $t = 0$
- $\mathbf v$ is the velocity at time $t$
- $\mathbf s$ is the displacement of $B$ from its initial position at time $t$
- $\cdot$ denotes the dot product.
The term SUVAT arises from the symbols used, $\mathbf s$, $\mathbf u$, $\mathbf v$, $\mathbf a$ and $t$.
T
U
UF
- Ultrafilter Lemma (also UL).
UFD
UL
- Ultrafilter Lemma (also UF).
URM
- Unlimited register machine: an abstraction of a computing device with certain particular characteristics.
V
W
WFF
WLOG
Suppose there are several cases which need to be investigated.
If the same argument can be used to dispose of two or more of these cases, then it is acceptable in a proof to pick just one of these cases, and announce this fact with the words: Without loss of generality, ..., or just WLOG.
WRT or w.r.t.
When performing calculus operations, that is differentiation or integration, one needs to announce which variable one is "working with".
Thus the phrase with respect to is (implicitly or explicitly) part of every statement in calculus.
X
Y
Z
Zermelo-Fraenkel Set Theory
- ZF
An abbreviation for Zermelo-Fraenkel Set Theory, a system of axiomatic set theory upon which most of conventional mathematics can be based.
Zermelo-Fraenkel Set Theory with the Axiom of Choice
- ZFC
An abbreviation for Zermelo-Fraenkel Set Theory with the Axiom of Choice, a system of axiomatic set theory upon which the whole of (at least conventional) mathematics can be based.