D00 / Foundation layer — under all 49 territories

Financial Mathematics, Statistics, and Data Foundations

The quantitative language, statistical judgment, and implementation discipline every later domain assumes.

105 released builds 12 algorithm familiesIn release

D00Canonical / Tested / Open

Published work

Released builds
in this territory.

Every card below is included in the current governed release with its article, sources, Python, TypeScript, and available labs.

Search the released library

D00-F01

Mathematical Language and Quantitative Reasoning

8 builds

D00-F02

Financial Arithmetic, Time Value, and Returns

10 builds

D00-F03

Data, Variables, Samples, and Measurement

8 builds

D00-F04

Location, Ranking, and Exploratory Summaries

10 builds

D00-F05

Dispersion, Shape, and Robust Statistics

10 builds

D00-F06

Probability and Random Variables

8 builds

D00-F07

Probability Distributions and Simulation Basics

8 builds

D00-F08

Sampling, Estimation, and Statistical Inference

10 builds

D00-F09

Dependence, Regression, and Model Foundations

9 builds

D00-F10

Financial Time-Series Foundations

7 builds

D00-F11

Financial Risk and Performance Statistics

9 builds

D00-F12

Statistical Computing and Reproducibility

8 builds

The foundation ladder

12 modules,
in dependency order.

This domain is a course, not a catalog: 120 topics that every later territory quietly assumes you already have. Read it in order and the rest of the atlas stops requiring leaps of faith.

D00-F01Mathematical Language and Quantitative Reasoning10 topics
D00-F02Financial Arithmetic, Time Value, and Returns10 topics
D00-F03Data, Variables, Samples, and Measurement10 topics
D00-F04Location, Ranking, and Exploratory Summaries10 topics
D00-F05Dispersion, Shape, and Robust Statistics10 topics
D00-F06Probability and Random Variables10 topics
D00-F07Probability Distributions and Simulation Basics10 topics
D00-F08Sampling, Estimation, and Statistical Inference10 topics
D00-F09Dependence, Regression, and Model Foundations10 topics
D00-F10Financial Time-Series Foundations10 topics
D00-F11Financial Risk and Performance Statistics10 topics
D00-F12Statistical Computing and Reproducibility10 topics

Territory coverage

What this domain
is mapped to cover.

The published builds above are the released slice of this map. Every subject below belongs to this territory's charter.

Mathematical notationrates and returnsdata types and measurementdescriptive and robust statisticsprobabilitydistributionsinferenceregressiontime seriesfinancial risk statisticsnumerical stabilityreproducibility

Financial Mathematics, Statistics, and Data Foundations

Released buildsin this territory.

Mathematical Language and Quantitative Reasoning

Variables, Constants, Expressions, and Equations

Functions, Domains, Ranges, and Graphs

Percentage Change, Percentage Points, and Basis Points

Exponents, Roots, and Logarithms

Linear Equations and Systems

Inequalities, Bounds, and Constraints

Units, Dimensions, Scale, and Normalization

Rounding, Precision, Tolerance, and Significant Digits

Financial Arithmetic, Time Value, and Returns

Simple Interest

Compound Interest

Present Value and Future Value

Discount Factors and Discount Rates

Cash-Flow Timelines and Net Present Value

Simple Return

Log Return

Holding-Period and Cumulative Return

Arithmetic versus Geometric Average Return

Return Annualization and Deannualization

Data, Variables, Samples, and Measurement

Observations, Entities, Variables, and Datasets

Numeric, Categorical, Ordinal, and Binary Variables

Population, Sample, Census, and Sampling Frame

Identifiers, Keys, Joins, and Data Grain

Timestamps, Time Zones, Calendars, and Observation Time

Missing, Nonfinite, Censored, and Truncated Values

Revisions, Vintages, and Point-in-Time Availability

Data Provenance, Lineage, Ownership, and Licensing

Location, Ranking, and Exploratory Summaries

Count, Sum, Minimum, Maximum, and Range

Arithmetic Mean

Weighted Mean

Median and Mode

Trimmed and Winsorized Means

Percentiles, Quantiles, and Quartiles

Ranks, Ties, and Percentile Rank

Frequency Tables and Relative Frequency

Histograms and Empirical Distribution Functions

Five-Number Summary and Box Plot

Dispersion, Shape, and Robust Statistics

Deviation, Absolute Deviation, and Squared Deviation

Range and Interquartile Range

Mean Absolute Deviation

Median Absolute Deviation

Population and Sample Variance

Population and Sample Standard Deviation

Coefficient of Variation and Scale Comparability

Z-Score, Robust Z-Score, and Standardization

Skewness and Tail Asymmetry

Kurtosis, Excess Kurtosis, and Tail Weight

Probability and Random Variables

Experiments, Outcomes, Sample Spaces, and Events

Probability Rules, Complements, Unions, and Intersections

Conditional Probability

Independence and Dependence

Expected Value

Variance, Moments, and Moment-Generating Intuition

Joint, Marginal, and Conditional Distributions

Covariance and Correlation of Random Variables

Probability Distributions and Simulation Basics

PMF, PDF, CDF, Survival, and Quantile Functions

Bernoulli and Binomial Distributions

Poisson Distribution and Event Counts

Lognormal Distribution and Positive Quantities

Student-t Distribution and Heavy Tails

Exponential, Gamma, and Weibull Waiting-Time Models

Mixture Distributions, Multimodality, and Fat Tails

Random Sampling and Monte Carlo Intuition

Sampling, Estimation, and Statistical Inference

Parameters, Statistics, Estimands, and Estimators

Sampling Distributions

Estimator Bias, Consistency, Efficiency, and Robustness

Law of Large Numbers

Central Limit Theorem

Standard Error

Confidence Intervals and Coverage

Null and Alternative Hypotheses

Released builds
in this territory.

12 modules,
in dependency order.

What this domain
is mapped to cover.