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Computational Mathematics — Glossary
| Term | Meaning |
|---|---|
| Acyclic graph | A graph with no cycles |
| Adjacency matrix | Matrix A with A[i][j] = 1/edge-info between i and j |
| Adjugate (adjugate matrix) | Transpose of the cofactor matrix; used in inverse |
| Algorithm | A finite, unambiguous sequence of steps |
| Anonymous predicate | A predicate used without naming (rare here) |
| Argument | Input value to a function/predicate |
| Arity | Number of inputs a function/predicate takes |
| Arrow (→) | Implication connective |
| Asymmetric | Not symmetric; irreflexive relation |
| Basis | A linearly independent spanning set of a vector space |
| Basis vector | One vector in a basis |
| Biconditional | p iff q (↔); true when both same truth value |
| Bijection | One-to-one and onto function |
| Binary operation | Operation taking two operands |
| Binary relation | A set of ordered pairs |
| Block matrix | Matrix partitioned into submatrices |
| Bridge | An edge whose removal disconnects a graph |
| C (big-O related) | Complexity class of P problems solvable in poly-time |
| Cardinality | Number of elements in a set |
| Carry (ripple) | Overflow bit added to the next column in addition |
| CNF (conjunctive normal form) | AND of clauses (ORs of literals) |
| Column space | Span of the columns of a matrix |
| Combinatorics | Counting and arrangement mathematics |
| Combination | Selection without regard to order |
| Complete graph Kₙ | Every pair of vertices joined by an edge |
| Complete theory | A theory deciding every sentence |
| Complete type system | Accepts every safe program (see soundness) |
| Complete graph | Every pair of distinct vertices joined |
| Completeness (logic) | All logical validities are provable |
| Composite (number) | A natural number >1 with divisors other than 1 and itself |
| Concurrency | Multiple processes/edges interacting |
| Connection (database) | A session with a data source |
| Consistency (logic) | Not both φ and ¬φ provable |
| Consistency (graph) | A graph property name, not the logic term |
| Constraint | A condition that must hold |
| Contradiction | A formula true in no row of a truth table |
| Controlled variable | Variable held constant in an experiment |
| Coset | Translate of a subgroup (group theory) |
| CPA (complexity) | Constraint satisfiability class |
| Cycle (graph) | A closed walk with no repeated vertices except start/end |
| Cycle (matrix) | Permutation cycle |
| Cypher | A cipher (alternate spelling) |
| DAG | Directed acyclic graph |
| Degree (graph) | Number of edges incident to a vertex |
| Degree (polynomial) | Highest power of the variable |
| Deterministic | Having a single determined next state |
| Determinant | Scalar det(A) summarising scaling & invertibility |
| Derivation / Derivation tree | Proof tree / parse tree |
| Descent | A step down |
| DFA (deterministic finite automaton) | Automata theory (Module 2 adjacent) |
| Diagonal matrix | a_ij = 0 for i ≠ j |
| Diagonalisation | A = PDP⁻¹ decomposition |
| Digraph | Directed graph |
| Dimensional analysis | Technique with dimensions (adjacent) |
| Dimension (vector space) | Number of vectors in a basis |
| Disjunction | p ∨ q (or) |
| Divide (÷) | Arithmetic operation |
| DNF (disjunctive normal form) | OR of monomials (ANDs of literals) |
| Domain (function) | Set of inputs |
| Domain (relation) | Set of first elements |
| Dominant | Of great effect or power |
| Dominate | A vertex adjacent to all others |
| Dual graph | Graph whose vertices are faces of original |
| Dual of a Boolean algebra | Swap ∧/∨, 0/1 |
| Edge (graph) | Link between two vertices |
| Eigenvalue | λ in Av = λv |
| Eigenvector | Non-zero v in Av = λv |
| Elementary matrix | Identity with one row op; row ops = left mult |
| Elementary row operation | Swap/scale/add rows in Gaussian elim |
| Enumerable | Countable |
| Equivalence relation | Reflexive, symmetric, transitive |
| Exclusive or (XOR) | p ⊕ q: true exactly when exactly one true |
| Existential quantifier | ∃x (there exists x) |
| Field | Algebraic structure (e.g., ℝ, ℂ) |
| Filter (SQL) | Data retrieval clause |
| Formula (logic) | A well-formed formula |
| Four-color theorem | Planar graphs need 4 colors (adjacent) |
| Free group | Group with no relations |
| Function | Mapping from domain to codomain |
| Functional dependency | Database constraint |
| GCD | Greatest common divisor |
| Generator | Element generating a group |
| Geometry (computational) | Algorithm design paradigm |
| Glb / lub | Greatest lower bound / least upper bound |
| Graph colouring | Assigning colours to vertices (adjacent differ) |
| Greatest common divisor | Largest divisor of two integers |
| Group | Set with one associative op, identity, inverses |
| Group action | Group "acting" on a set |
| Hadamard product | Entry-wise matrix product |
| Hamiltonian path/cycle | Visits every vertex once |
| Hasse diagram | Diagram of a partial order |
| Hex | Hexadecimal (base 16) |
| Homogeneous | Linear system Ax=0; or same dimension |
| Hoare logic | Axiomatic semantics for programs |
| Homomorphism | Structure-preserving map |
| Idempotent | x·x = x; or P ∪ P = P |
| Identity (elem) | e with e·x = x·e = x |
| Identity matrix I | Diagonal of 1s, rest 0 |
| Identity of | Equal in value |
| If and only if (iff) | Bidirectional implication (↔) |
| Image (linear map) | Range; set {T(v): v∈V} |
| Image (relation/graph) | Neighbourhood of a vertex set |
| Implication | p → q (if p then q) |
| Imprimitive | A block system |
| Inconsistent | No model (logic) / no solution (linear system) |
| Increasing | Non-decreasing sequence |
| Inductive step | Second part of a proof by induction |
| Inference rule | Logical step (e.g., modus ponens) |
| Infinite | Without bound |
| Info (information) | Data with context |
| Inherited | Inherited from |
| Inner product | u·v = Σu_i v_i ; also dot product |
| Instance | Occurrence |
| Integer | Whole number ℤ |
| Integration | Area under a curve |
| Integrity | Data unchanged; also database consistency |
| Intersect / intersection | Common elements (∩) |
| Intersection (graphs) | Common edges/vertices |
| Inverse (function) | f⁻¹ undoes f |
| Inverse (matrix) | A⁻¹ with AA⁻¹ = A⁻¹A = I (if exists) |
| Involution | Function that is its own inverse |
| Isomorphic graphs | Same structure (renaming of vertices) |
| Isomorphism (groups) | Structure-preserving bijection of groups |
| Kernel (linear map) | {v : T(v) = 0} (null space) |
| Kernel (graph) | (Not standard usage) |
| Kripke model | Semantics for modal logic |
| Lambda calculus | Function calculus (adjacent to logic) |
| Lattice | Poset where every pair has a join/meet |
| Lattice (matrix) | A matrix viewed as a grid |
| Leaf | Vertex of degree 1; pendant vertex |
| Length (walk/edge) | Number of edges in walk; magnitude for edge |
| Less than or equal (≤) | Order relation |
| Linear combination | Σ c_i v_i |
| Linear dependence | Non-trivial combination = 0 |
| Linear independence | Only trivial combination = 0 |
| Linear map / transformation | T(u+v)=T(u)+T(v), T(cu)=cT(u) |
| Linear ordering | Total order |
| Linear program | Optimization with linear constraints |
| Line graph | Nodes = edges of original |
| Linked list | Linear data structure |
| LUB | Least upper bound (supremum) |
| Loop | Edge from a vertex to itself |
| Maximum | Largest element |
| Max-flow min-cut theorem | Network flows optimization |
| Mealy / Moore machine | Finite-state machine types |
| Meet | Greatest lower bound (∧) |
| Member | Element x ∈ S |
| Mersenne prime | 2ᵖ−1 prime |
| Min / min-cut | Minimum / minimum cut |
| Minimal | Minimal element (no smaller) |
| Minimal polynomial | Monic polynomial of least degree for an element |
| Minimum | Smallest element |
| Minor (graph) | Graph obtained by edge/vertex deletions/contractions |
| Minor (matrix) | Determinant |
| Minus | Subtraction |
| Modus ponens | p→q, p ⊢ q |
| Modus tollens | p→q, ¬q ⊢ ¬p |
| Monomial | Product of powers of variables (single term) |
| Moore matrix | (Rare: finite-field matrix) |
| Multiset | Set with repetition |
| Morphism | Structure-preserving map |
| Negation | ¬p (not p) |
| Neighbour | Adjacent vertex |
| Nested quantifier | ∀∃ or ∃∀ mix |
| Network | A weighted directed graph (often) |
| Node | Vertex of a graph |
| Non-deterministic | Multiple possible next states |
| Non sequitur | "does not follow" (logical fallacy) |
| Normal form | Standardized representation |
| Not (¬) | Logical negation |
| Null space | Kernel of A; {x : Ax = 0}; solutions to homogeneous system |
| Nullity | dim(null space) |
| Number | Mathematical object |
| Number theory | Study of integers |
| Object | Element being described |
| Octet | Group of eight |
| Open set | Topology (adjacent) |
| Operation | A function mapping elements |
| Operator | Symbol for an operation |
| Optimal | Best possible |
| Order (group) | Number of elements in a group |
| Order (relation) | Total/preorder relation |