A map of the symbols, not a substitute for the reasoning.
Notation & formulas · quick reference
Search a formula, inspect its assumptions, then open the matching lab.
∼PNegationLogic
P ∧ QConjunctionLogic
True only when both propositions are true.
P ∨ QInclusive disjunctionLogic
False only when both propositions are false.
P → QImplicationLogic
False only when P is true and Q is false.
P ↔ QBiconditionalLogic
P(n,r) = n! / (n − r)!Ordered selectionProbability
Counts selections without repetition when order creates distinct outcomes.
C(n,r) = n! / [r!(n − r)!]Unordered selectionProbability
Counts groups without repetition when rearranging a group does not create a new outcome.
|A ∪ B| = |A| + |B| − |A ∩ B|Two-set inclusion–exclusionProbability
Adds the two set counts and removes the overlap counted twice.
P(A|B) = P(A∩B) / P(B)Conditional probabilityProbability
When B is given, the active denominator becomes B.
P(A∩B) = P(A)P(B)Independence testProbability
Checks whether the occurrence of one event leaves the other probability unchanged.
A = P(1 + it)Simple interestFinancial Mathematics
Grows principal linearly using one rate on the original principal.
A = P(1 + i)ᵗCompound accumulationFinancial Mathematics
Accumulates each period’s balance at an effective rate i.
A = P(1 + j/m)ᵐᵗNominal conversionFinancial Mathematics
Uses nominal annual rate j convertible m times per year.
i = (1 + j/m)ᵐ − 1Annual effective rateFinancial Mathematics
Converts a nominal rate into the equivalent annual effective rate.
vⁿ = (1 + i)⁻ⁿDiscount factorFinancial Mathematics
Moves a value n periods backward to a focal date.
A + BMatrix additionMatrices
Adds corresponding entries of two matrices.
ABMatrix productMatrices
Combines rows of A with columns of B through dot products.
(AB)ᵢⱼProduct entryMatrices
Entry (i,j) is row i of A dotted with column j of B.
[A | I] → [I | A⁻¹]Gauss–Jordan inverseMatrices
Reduces the left block to the identity while transforming the right block.
RREF([A | b])Augmented systemMatrices
Reveals whether a system has a unique, infinite, or no solution.
ax + by ≤ cHalf-plane constraintLinear Programming
Describes one feasible side of a boundary line.
Z = c₁x + c₂yLinear objectiveLinear Programming
Assigns a value to each feasible point for maximization or minimization.
Evaluate feasible verticesCorner-point principleLinear Programming
A bounded two-variable LP reaches an optimum at a feasible vertex; an entire edge may also be optimal.
Z → ∞ (or −∞)Unbounded regionLinear Programming
A feasible improving direction lets the objective grow without a finite optimum.
max(row minima)MaximinGame Theory
The row player chooses the strategy with the largest guaranteed payoff.
min(column maxima)MinimaxGame Theory
The column player chooses the strategy with the smallest payoff they allow.
maximin = minimaxPure saddle pointGame Theory
Matching security levels identify a pure saddle-point value.
p + (1 − p) = 1Mixed strategyGame Theory
When no pure saddle exists, probabilities can make the opponent indifferent in supported 2×2 games.