Notation

+, -, ×, ÷        Basic operations
·                  Multiplication (dot)
a^n                Exponentiation
sqrt(x), ∛x       Square root, cube root
|x|                Absolute value
⌊x⌋               Floor (round down)
⌈x⌉               Ceiling (round up)
n!                 Factorial: n × (n-1) × ... × 1
±                  Plus or minus
≈                  Approximately equal
∝                  Proportional to

=                  Equal
≠                  Not equal
<, >               Less than, greater than
≤, ≥               Less/greater than or equal
≡                  Identical / congruent (mod n)
:=  or  ≜          Defined as
~                  Approximately / distributed as

∀                  For all (universal quantifier)
∃                  There exists (existential)
∃!                 There exists exactly one
∈                  Element of
∉                  Not element of
⊆, ⊂              Subset, proper subset
∪                  Union
∩                  Intersection
∅                  Empty set
¬, ∧, ∨           Not, and, or
→, ↔               Implies, if and only if
∴                  Therefore
∵                  Because
□, QED             End of proof

Letter   Name       Common usage
──────────────────────────────────────────────
α alpha    Significance level, angles, learning rate
β beta     Type II error, angles, coefficients
γ gamma    Euler-Mascheroni constant, discount factor
δ delta    Small change, Kronecker delta, tolerance
ε epsilon  Small positive number, machine epsilon
ζ zeta     Riemann zeta function
η eta      Learning rate, efficiency
θ theta    Angle, parameters (ML)
ι iota     (rare in math)
κ kappa    Curvature, condition number
λ lambda   Eigenvalue, Poisson rate, anonymous functions
μ mu       Mean, micro (10^-6)
ν nu       Degrees of freedom, frequency
ξ xi       Random variable, dummy variable
π pi       3.14159..., projection
ρ rho      Correlation, density, resistivity
σ sigma    Standard deviation, summation (Σ)
τ tau      Time constant, Kendall's tau
υ upsilon  (rare)
φ phi      Euler's totient, golden ratio, angle
χ chi      Chi-squared test
ψ psi      Wave function, digamma
ω omega    Angular frequency, Big-Omega (Ω)

Σ (sigma)   Summation:  sum_{i=1}^{n} i = 1 + 2 + ... + n
Π (pi)      Product:    prod_{i=1}^{n} i = n!

∫             Integral:   ∫_a^b f(x) dx
∂             Partial derivative: ∂f/∂x
∇             Gradient (nabla): ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)
∞             Infinity
lim           Limit:      lim_{x→a} f(x)
→             Approaches: x → ∞
d/dx          Derivative with respect to x
f'(x)         First derivative of f
f''(x)        Second derivative

O(f(n))       Big-O:      upper bound (worst case)
Ω(f(n))       Big-Omega:  lower bound (best case)
Θ(f(n))       Big-Theta:  tight bound (exact order)
o(f(n))       Little-o:   strictly less than
ω(f(n))       Little-omega: strictly greater than

⊤, ⊥          True, False (top, bottom)
⊢             Proves / entails: Γ ⊢ A
⊨             Models / satisfies
λ             Lambda (function abstraction)
→             Function type: A → B
×             Product type: A × B
+             Sum type: A + B
∘             Function composition: (f ∘ g)(x) = f(g(x))

{x | P(x)}    Set of x satisfying P
{x ∈ S | P(x)} Set of x in S satisfying P
[a, b]        Closed interval
(a, b)        Open interval
[a, b)        Half-open interval
(a, ∞)        All reals greater than a

Category         Typical variables
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Integers         i, j, k, m, n
Real numbers     x, y, z, t
Complex          z, w
Matrices         A, B, C, M
Vectors          u, v, w, x (bold or arrow)
Sets             A, B, C, S, T, U (capitals)
Functions        f, g, h
Primes           p, q
Angles           α, β, θ, φ
Small quantities ε, δ
Constants        c, k, C, K
Probability      P, p, q
Statistics       μ (mean), σ (SD), ρ (correlation)
Parameters       α, β, θ, λ