cheat-sheet.md

Maths Symbol Cheat Sheet

Before we start, here is a helpful Maths cheat sheet you can download and refer to when exploring the different maths concepts in Cryptography:

Symbol	Description	Explanation
$P, Q, R, S, ...$	Propositional (sentential) variables	These are placeholders for statements that can be either true or false.
$\rightarrow$	Implies	Indicates that one statement follows logically from another.
$\leftrightarrow$	If and only if	Represents a two-way implication; both statements are true or false together.
$>$	Greater than	Indicates that one value is larger than another.
$<$	Less than	Indicates that one value is smaller than another.
$\geq$	Greater than or equal to	Indicates that one value is greater than or equal to another.
$\leq$	Less than or equal to	Indicates that one value is less than or equal to another.
$\neq$	Not equal to	Denotes inequality between two values or expressions.
$\equiv$	Triple bar equal sign	Indicates equal or identical expressions.
$\land$	Logical “and” (conjunction)	It represents the idea that two statements must both be true for the combined statement to be true.
$\lor$	Logical “or” (disjunction)	It indicates that at least one of the connected statements needs to be true for the combined statement to be true.
$\lnot$	Logical negation	This symbol negates or reverses the truth value of a statement.
$\exists$	Existential quantifier	It asserts that there exists at least one element in a set that satisfies a given condition.
$\forall$	Universal quantifier	It states that a certain condition is true for every element in a set.
$\in$	“Is an element of”	Shows that an element belongs to a particular set.
$\subseteq$	“Is a subset of”	Denotes that one set's elements are entirely contained within another set.
$\subset$	“Is a proper subset of”	Implies a subset relationship where the sets are not equal.
$\cap$	Set intersection	Represents the elements common to two or more sets.
$\cup$	Set union	Represents the combination of elements from multiple sets.
$\times$	Cartesian product	Denotes combining elements from different sets to create ordered pairs.
$\setminus$	Set difference	Shows the elements present in one set but not in another.
$\overline{A}$	The complement of $A$	Contains all elements not in set A within the universal set.
$|A|$	Cardinality (size) of $A$	Shows the number of elements in a set.
$A \times B$	The Cartesian product of $A$ and $B$	Represents all possible ordered pairs of elements from sets $A$ and $B$.
$\vert C_{n}^{k} \vert$	Cardinality	Denotes the size of set $\vert C_{n}^{k} \vert$.
$\sum$	Summation	Represents the sum of a sequence of numbers or terms.
$\infty$	Infinity	Represents a quantity without bound or limit.
$p \in P$	Membership	States that variable $p$ belongs to set $P$.
$y'$	Variable	Indicates a specific variable, potentially modified.
$\log(x)$	Logarithm	Represents the logarithm of $x$.
$C1, C2, …$	Constraints	These are constraints that can be specified as different letters.
$(a, b)$	Interval	Represents the range of values between $a$ and $b$.
$\mathbb{R}$	Real numbers	Represents the set of all real numbers.
$\mathbb{Z}$	Integers	Represents the set of all integers.
$\mathbb{N}$	Natural numbers	Represents the set of all natural numbers.
$\mathbb{Q}$	Rational numbers	Represents the set of all rational numbers.
$\mathbb{C}$	Complex numbers	Represents the set of all complex numbers.
$\lambda_h$	Lambda parameter	A specific parameter indexed by $h$.
$\lambda$	Lambda / Wavelength	A Greek letter commonly used in mathematics to represent eigenvalues, parameters, or constants. Denotes the distance between two successive points in a wave.
$\alpha_i$	Alpha parameter	A specific parameter indexed by $i$.
$\alpha$	Alpha	A Greek letter frequently used in mathematics and science to denote various quantities such as angles, constants, or coefficients.
$\psi$	Psi / Wave function	Represents a mathematical description of the quantum state of a system.
$\beta$	Beta	A Greek letter often used to represent various concepts, such as coefficients, angles, or constants.
$\gamma$	Gamma / Lorentz factor	Indicates the factor by which time, length, and relativistic mass change for an object moving relative to an observer.
$\text{OP max}$	Optimization objective	A function being maximised to find the average sum.
$\emptyset$	Empty set	Represents a set with no elements.
$R_{\text{min}}^{k,i}$	Minimum value	Represents a minimum value indexed by $k$ and $i$.
$R_{\text{max}}^{k,i}$	Maximum Value	Represents a maximum value indexed by $k$ and $i$.
$l$ or $L$	Length	Represents the extent of something from one end to another.
$\omega$	Angular frequency	Measures the rate of change of angular displacement with respect to time.
$f$	Frequency	Represents the number of occurrences of a repeating event per unit of time.
$v$	Velocity	Indicates the rate of change of position of an object in a particular direction.
$\eta$	Efficiency	Represents the effectiveness of a process in converting inputs into useful outputs.
$N$	Ways symbol	Denotes the number of ways or possibilities in a particular scenario.
$W$	Work function	Represents the minimum energy needed to remove an electron from a solid to a point just outside the solid surface.
$\Delta$	Incremental change	Denotes a change or difference between two values.
$\int$	Integral	Represents the mathematical concept of an integral, involving the accumulation of quantities.
$\Omega$	Omega	Often used to represent various concepts in different contexts, such as solid angles or angular velocity.
$\partial$	Partial derivative	Represents the derivative of a function with respect to one of its variables, holding the others constant.
$\nabla$	Nabla / Del operator	Represents the gradient, divergence, or curl of a field.
$\approx$	Approximately equal	Indicates that two values are nearly equal.
$\propto$	Proportional to	Indicates that one quantity is proportional to another.
$\sum_{i=1}^{n}$	Summation notation	Represents the sum of a sequence of terms from $i=1$ to $n$.
$\prod_{i=1}^{n}$	Product notation	Represents the product of a sequence of terms from $i=1$ to $n$.
$\int_{a}^{b}$	Definite integral	Represents the integral of a function from $a$ to $b$.
$\oint$	Contour integral	Represents the integral of a function over a closed curve.
$\lim_{x \to a}$	Limit	Represents the value that a function approaches as the variable approaches a specified value.
$\frac{dy}{dx}$	Derivative	Represents the rate of change of $y$ with respect to $x$.
$\binom{n}{k}$	Binomial coefficient	Represents the number of ways to choose $k$ elements from a set of $n$ elements.