Mathematical Language and Quantitative Reasoning

10 algorithms in Financial Mathematics, Statistics, and Data Foundations · 10 with asserted arithmetic.

In this family#

1. Variables, Constants, Expressions, and Equations verified

   Substitutes named quantities into a cash-balance equation and checks that the rearranged form still holds, returning the ending cash implied by startingCash, inflows and outflows.

   variablesConstantsExpressionsAndEquations(input)
2. Functions, Domains, Ranges, and Graphs verified

   Evaluates the straight-line function intercept + slope * value at every entry of values and reports the input span it was evaluated over alongside the output span it produced.

   functionsDomainsRangesAndGraphs(input)
3. Ratios, Proportions, Rates, and Percentages verified

   Turns a part-and-whole pair into a ratio and a percentage, and turns the same part spread over an elapsed span into a rate per period.

   ratiosProportionsRatesAndPercentages(input)
4. Percentage Change, Percentage Points, and Basis Points verified

   Expresses the move from an old level to a new one three ways: as a percent change relative to the old level, as a raw difference in percentage points, and as that difference scaled to basis points.

   percentageChangePercentagePointsAndBasisPoints(input)
5. Exponents, Roots, and Logarithms verified

   Applies the three operations that share one base: raising it to an exponent, taking its square root, and taking its natural logarithm.

   exponentsRootsAndLogarithms(input)
6. Summation, Products, and Index Notation verified

   Reduces a series to its sum and its product, and re-emits it as explicitly numbered terms so subscript notation can be read against real values.

   summationProductsAndIndexNotation(input)
7. Linear Equations and Systems verified

   Solves the two-equation system a*x + b*y = c and d*x + e*y = f by Cramer's rule, returning the solution and the determinant that decides whether one exists.

   linearEquationsAndSystems(input)
8. Inequalities, Bounds, and Constraints verified

   Tests a candidate number against a lower and upper bound, reporting whether it is admissible, what it becomes once clamped into range, and how far outside the range it sits.

   inequalitiesBoundsAndConstraints(input)
9. Units, Dimensions, Scale, and Normalization verified

   Rescales a series by subtracting an offset and dividing by a scale, so numbers recorded in one unit can be compared on a common footing.

   unitsDimensionsScaleAndNormalization(input)
10. Rounding, Precision, Tolerance, and Significant Digits verified

    Rounds a candidate to a fixed number of decimal places and measures it against a reference value and an allowed tolerance.

    roundingPrecisionToleranceAndSignificantDigits(input)

What they share#

Every topic here is a record-transform, so once you have called one the rest follow the same shape. Import paths differ only in the final segment:

import { variablesConstantsExpressionsAndEquations } from "fintech-algorithms/foundations/mathematical-language-and-quantitative-reasoning/variables-constants-expressions-and-equations";
import { functionsDomainsRangesAndGraphs } from "fintech-algorithms/foundations/mathematical-language-and-quantitative-reasoning/functions-domains-ranges-and-graphs";

Read them in the order above — the sequence is pedagogical, not alphabetical.

Where this sits#

Financial Mathematics, Statistics, and Data Foundations collects 120 algorithms across 12 families. For the concept behind this family rather than the call signatures, see the concept guides.