Index of Mathematical Symbols

Index of Mathematical Symbols

Greek Alphabet
$\alpha$ Alpha
$\beta$ Beta
$\gamma$ Gamma
$\delta, \Delta$ Delta
$\epsilon$ Epsilon
$\zeta$ Zeta
$\eta$ Eta
$\theta$ Theta
$\kappa$ Kappa
$\lambda$ Lambda
$\mu$ Mu
$\xi$ Xi
$\pi$ Pi
$\rho$ Rho
$\sigma$ Sigma
$\tau$ Tau
$\phi, \varphi$ Phi
$\chi$ Chi
$\psi, \Psi$ Psi
$\omega, \Omega$ Omega

Set/Logical Symbols
$\in$ In
$\cup, \bigcup$ Union
$\cap, \bigcap$ Intersection
$\subseteq, \subset$ Subset
$\supseteq, \supset$ Superset
$\setminus$ Set difference
$\triangle$ Symmetric difference
$\times$ Cartesian product
$A^c$ Complement of $A$
$\emptyset, \{ \}$ Empty set
$\mathbb{N}$ Set of natural numbers
$\mathbb{Z}$ Set of integers
$\mathbb{Q}$ Set of rational numbers
$\mathbb{R}$ Set of real numbers
$\mathbb{C}$ Set of complex numbers.
$\vee$ Or (connective)
$\wedge$ And (connective)
$\rightarrow, \Rightarrow$ Implication (connective)
$\leftrightarrow, \Leftrightarrow$ Logical equivalence (connective)
$\exists$ Existential quantifier
$\forall$ Universal quantifier
$\blacksquare$ End of proof

Calculus, Analysis, and Linear Algebra Symbols
$D(f)$, $\mathrm{dom} (f)$ Domain
$R(f)$, $\mathrm{ran} (f)$ Range
$C(f)$ Codomain
$(a, b)$ Bounded open interval
$[a, b]$ Bounded closed interval
$a_0 + a_1x + ... + a_nx^n$ Polynomial
$\sqrt{x}$ Squareroot function
$\sin x$, $\cos x$, $\tan x$ Sine, cosine, and tangent functions.
$\sec x$, $\csc x$, $\cot x$ Secant, cosecant, and cotangent functions.
$\sin^{-1} x$, $\cos^{-1} x$, $\tan^{-1} x$ Inverse sine, inverse cosine, and inverse tangent functions.
$a^x$, $e^x$ Exponential functions
$\log_a x$, $\ln x$ Logarithmic functions
$\lim$ Limit
$\limsup$ Limit superior
$\liminf$ Limit inferior
$\sup$ Supremum
$\inf$ Infimum
$dx$ Differential
$\displaystyle{\frac{d}{dx}}$ Differentiation operator
$\displaystyle{\int}$ Integral
$(a_n)_{n=1}^{\infty}, \{ a_n \}_{n=1}^{\infty}$ Sequence
$\to$ Convergence
$\uparrow$ Increasing
$\downarrow$ Decreasing
$(M, d)$ Metric space
$d$ Metric
$(X, \tau)$ Topological space
$B(x, r)$ Open ball
$\mathrm{int} (A)$ Interior
$\overline{A}$ Closure
$P = \{ a = x_0 < x_1 < ... < x_n = b \}$ Partition
$\mathscr{P} [a, b]$ Set of partitions
$V_f (P)$ Variation of $f$
$S(I)$ Set of step functions on $I$
$U(I)$ Set of upper functions on $I$
$L(I)$ Set of Lebesgue integrable functions on $I$
$\sum$ Summation
$\prod$ Product
$A_{m \times n}$ $m$ by $n$ Matrix
$I_n$ $n$ by $n$ Identity matrix
$0_{m \times n}$ $m$ by $n$ Zero matrix
$A^T$ Matrix transpose
$A^{-1}$ Matrix inverse
$\mathrm{adj} (A)$ Adjoint matrix
$\mathrm{cof} (A)$ Cofactor matrix
$\det$ Determinant
$\vec{x}, \mathbf{x}$ Vector
$\perp$ Perpendicular, orthogonal
$\mathrm{proj}$ Projection
$\parallel$ Parallel
$\| \cdot \|$ Norm
$\equiv$ Congruence (relation)
$\sim$ Equivalence (relation)
$<, \leq$ Less than, less than or equal (relation)
$>, \geq$ Greater than, greater than or equal (relation)
$=$ Equality
$\mod n$ Modulo

Abstract Algebra Symbols
$+$ Addition (binary operation)
$\cdot, *, \times$ Multiplication (binary operation)
$-$ Negation (unary operation)
$e$ Identity element
$0$ Additive identity
$1$ Multiplicative identity
$-a$ Additive inverse
$a^{-1}$ Multiplicative inverse
$(G, +), (G, \cdot)$ Additive group, multiplicative group
$(R, +, \cdot)$ Ring
$(F, +, \cdot)$ Field

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