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.