Fintech Math Bootcamp

We begin by learning to read a formula as a sentence about a quantity. A ledger balance, a processing fee, and a percentage comparison are enough to introduce variables, functions, units, and constraints. Our first discipline is simple: every symbol must mean something, and every operation must be allowed for its inputs. Module overview

1. 1Variables, Constants, Expressions, and EquationsA wallet reconciliation that actually balances2:34
2. 2Functions, Domains, Ranges, and GraphsA payment fee calculator with a valid input range2:34
3. 3Ratios, Proportions, Rates, and PercentagesComparing approval rates across merchants2:36
4. 4Percentage Change, Percentage Points, and Basis PointsA loan-rate change reported three different ways2:33
5. 5Exponents, Roots, and LogarithmsFinding the growth factor and the time it takes2:38
6. 6Summation, Products, and Index NotationA ledger sum and a return product are different loops2:33
7. 7Linear Equations and SystemsReconciling transaction counts and fee totals2:34
8. 8Inequalities, Bounds, and ConstraintsA lending limit that is a constraint, not an opinion2:34
9. 9Units, Dimensions, Scale, and NormalizationCents, currencies, and rates in the same pipeline2:43
10. 10Rounding, Precision, Tolerance, and Significant DigitsRounding a half-cent without guessing binary behavior2:41
11. Demo: Payment Fee & Rate CheckerA merchant payment dashboard2:38

Now money moves through time. Interest, discounting, cash flows, and returns will build on the ratios and exponents we already know. We will keep the timeline visible, distinguish price gains from external cash, and test why equal opposite percentage returns do not restore the original balance. Module overview

1. 11Simple InterestA fixed-rate invoice financing illustration2:30
2. 12Compound InterestWhen a savings balance earns on previous interest2:30
3. 13Present Value and Future ValueComparing money on two different dates2:31
4. 14Discount Factors and Discount RatesOne price today for one unit paid later2:33
5. 15Cash-Flow Timelines and Net Present ValueA project whose future receipts must repay its initial cost2:35
6. 16Simple ReturnA dividend can change the answer even when the price is known2:40
7. 17Log ReturnAdding changes in log space without confusing wealth2:49
8. 18Holding-Period and Cumulative ReturnA two-period performance report with changing bases2:43
9. 19Arithmetic versus Geometric Average ReturnChoosing an average that answers the actual return question2:36
10. 20Return Annualization and DeannualizationAn annual equivalent is not a prediction2:37
11. Demo: Loan & Investment CalculatorThe decision behind the calculator4:28

Before statistics, define the records. We will inspect what one row represents, how keys and timestamps preserve ownership, and why missing information cannot silently become zero. A correct formula cannot rescue an ambiguous data grain or a historical record that was not available at decision time. Module overview

1. 21Observations, Entities, Variables, and DatasetsThree payment rows are not three customers2:38
2. 22Numeric, Categorical, Ordinal, and Binary VariablesA risk grade is ordered, but not a measured distance2:27
3. 23Population, Sample, Census, and Sampling FrameA sample of approved loans cannot represent all applications2:34
4. 24Cross-Sectional, Time-Series, Panel, and Event DataCustomer histories and payment events have different grains2:43
5. 25Identifiers, Keys, Joins, and Data GrainA duplicate join can double the apparent money2:37
6. 26Timestamps, Time Zones, Calendars, and Observation TimeDifferent clock strings can describe the same instant2:38
7. 27Missing, Nonfinite, Censored, and Truncated ValuesUnknown, nonfinite, censored, and absent from the sample2:40
8. 28Measurement Error, Resolution, Accuracy, and PrecisionA clock can be consistent and still wrong2:38
9. 29Revisions, Vintages, and Point-in-Time AvailabilityBacktesting with the version that actually existed2:35
10. 30Data Provenance, Lineage, Ownership, and LicensingA useful feature needs a traceable origin2:36
11. Demo: Transaction Data Health CheckA revenue number nobody has checked5:20

Now we summarize observations without losing sight of what the summary preserves. A set of settlement delays will become counts, averages, weighted rates, ranks, percentiles, and distribution views. The same five numbers will repeatedly teach different questions; we will not declare one summary universally best. Module overview

1. 31Count, Sum, Minimum, Maximum, and RangeInspecting settlement delays before modeling them2:25
2. 32Arithmetic MeanThe mean as a balance point, not a typical actual observation2:29
3. 33Weighted MeanPooling merchant approval rates by exposure2:32
4. 34Median and ModeA typical settlement delay by order and frequency2:22
5. 35Trimmed and Winsorized MeansReducing outlier influence without pretending data vanished2:34
6. 36Percentiles, Quantiles, and QuartilesA percentile is incomplete without its interpolation rule2:34
7. 37Ranks, Ties, and Percentile RankTied scores need a fair, explicit rank convention2:38
8. 38Frequency Tables and Relative FrequencyTurning payment status counts into a denominator-aware summary2:39
9. 39Histograms and Empirical Distribution FunctionsA histogram changes with bins; an ECDF preserves sample order2:29
10. 40Five-Number Summary and Box PlotA box-plot fence is not an observed whisker2:30
11. Demo: Settlement Delay DashboardWhere the payouts wait5:39

A typical value is only part of the story. Spread and shape explain how customer experiences or returns differ around that center. We will preserve units while taking absolute values, squares, and roots, and distinguish robustness from permission to ignore serious tail outcomes. Module overview

1. 41Deviation, Absolute Deviation, and Squared DeviationExplaining inconsistent settlement time2:37
2. 42Range and Interquartile RangeSeparating the overall spread from the typical middle spread2:23
3. 43Mean Absolute DeviationAn interpretable average distance from a central delay2:22
4. 44Median Absolute DeviationRobust central spread without confusing two MADs2:32
5. 45Population and Sample VarianceVariance as a ledger of squared deviations2:35
6. 46Population and Sample Standard DeviationReturning risk or service spread to the original unit2:29
7. 47Coefficient of Variation and Scale ComparabilityComparing relative spread across positive-scale services2:35
8. 48Z-Score, Robust Z-Score, and StandardizationStandardizing alerts without turning unusual into fraudulent2:32
9. 49Skewness and Tail AsymmetryRecognizing the direction of a service-delay tail2:41
10. 50Kurtosis, Excess Kurtosis, and Tail WeightInterpreting fourth moments without declaring a tail safe2:44
11. Demo: Anomaly Alert EngineAn engine that scores every settlement6:13

Observed data describes what happened. Probability gives us a language for uncertain outcomes and explicitly assumed models. Payment events, fraud flags, and claim losses will introduce conditioning, base rates, expectation, and dependence. Watch the denominator: changing the conditioning population changes the question. Module overview

1. 51Experiments, Outcomes, Sample Spaces, and EventsDefining what can happen to a payment2:31
2. 52Probability Rules, Complements, Unions, and IntersectionsAvoiding double-counting fraud rules2:25
3. 53Conditional ProbabilityChanging the denominator after a fraud flag2:30
4. 54Independence and DependenceChecking whether two failure mechanisms share information2:38
5. 55Bayes’ Theorem and Base RatesWhy a good fraud detector can still generate many false alarms2:35
6. 56Discrete and Continuous Random VariablesDistinguishing uncertain counts from uncertain amounts2:36
7. 57Expected ValueBudgeting expected insurance loss without promising the average2:35
8. 58Variance, Moments, and Moment-Generating IntuitionMeasuring uncertainty around an expected claim count2:39
9. 59Joint, Marginal, and Conditional DistributionsSeeing default risk inside customer segments2:29
10. 60Covariance and Correlation of Random VariablesDependence in shared credit or insurance losses2:38
11. Demo: Fraud Alert Triage SimulatorOne alert, one question5:59

We can now read distributions as models rather than decorative curves. Counts, positive amounts, waiting times, and simulated outcomes each have different support and assumptions. Our goal is not to memorize a catalogue of names, but to understand which mechanism a distribution represents and where it can fail. Module overview

1. 61PMF, PDF, CDF, Survival, and Quantile FunctionsTurning a loss model into probabilities and thresholds2:38
2. 62Bernoulli and Binomial DistributionsCounting failures across a fixed number of comparable attempts2:37
3. 63Poisson Distribution and Event CountsModeling event counts over a stated exposure interval2:35
4. 64Uniform Distribution and Random SamplingScaling random draws for simulation without claiming uniform market behavior2:43
5. 65Normal Distribution and Standard NormalStandardizing a processing-time model and reading density correctly2:34
6. 66Lognormal Distribution and Positive QuantitiesModeling positive amounts in log space2:37
7. 67Student-t Distribution and Heavy TailsAllowing heavier tails without assuming all moments exist2:38
8. 68Exponential, Gamma, and Weibull Waiting-Time ModelsWaiting for an event, several stages, or an aging failure process2:36
9. 69Mixture Distributions, Multimodality, and Fat TailsSeparating customer groups instead of forcing one average distribution2:41
10. 70Random Sampling and Monte Carlo IntuitionEstimating a quantity by simulation and checking the uncertainty2:45
11. Demo: Insurance Claims SimulatorA year of claims5:37

An estimate changes when the sample changes. This module turns that fact into sampling distributions, standard errors, confidence intervals, and tests. We will separate uncertainty in an average from variation in individual customers, and avoid turning significance thresholds into certainty or business-value scores. Module overview

1. 71Parameters, Statistics, Estimands, and EstimatorsChoosing the population question before calculating an answer2:32
2. 72Sampling DistributionsSeparating variation in customers from variation in an estimate2:29
3. 73Estimator Bias, Consistency, Efficiency, and RobustnessComparing estimators on error rather than a fashionable label2:44
4. 74Law of Large NumbersWhy more observations can stabilize a rate without a monotone path2:44
5. 75Central Limit TheoremWhy averages may look normal when individual amounts do not2:40
6. 76Standard ErrorMeasuring uncertainty in a mean rather than variation among payments2:38
7. 77Confidence Intervals and CoverageInterpreting interval uncertainty as repeated coverage2:39
8. 78Null and Alternative HypothesesTesting an explicit baseline rather than a vague improvement claim2:36
9. 79P-Values, Significance, Type I/II Errors, and PowerPreventing p-values from becoming certainty scores2:36
10. 80Effect Size, Practical Significance, and Multiple ComparisonsSeparating a detectable effect from a worthwhile change2:56
11. Demo: A/B Test AnalyzerA new checkout button6:26

Next we connect variables without claiming every relationship is causal. Paired observations become scatter plots, centered products, ranks, and a fitted line. We will inspect residuals and group composition, then test the boundary between a useful predictive summary and a justified explanation of an intervention. Module overview

1. 81Scatter Plots, Association, and Nonlinear PatternsLooking at paired observations before compressing them2:34
2. 82Sample Covariance Calculation and InterpretationConstructing a covariance rather than trusting a matrix cell2:27
3. 83Pearson Correlation Calculation and InterpretationNormalizing linear association without claiming independence2:33
4. 84Spearman Rank Correlation and Kendall TauComparing monotone rankings and pair ordering2:40
5. 85Correlation, Causation, Confounding, and Spurious RelationshipsA pooled recovery-rate comparison that reverses within difficulty groups2:35
6. 86Simple Ordinary Least Squares RegressionFitting a line to paired operational measurements2:36
7. 87Intercepts, Slopes, Coefficients, and PredictionsInterpreting a coefficient before using it for extrapolation2:37
8. 88Residuals, MAE, MSE, and RMSEChoosing an error metric that reflects the cost of mistakes2:34
9. 89R-Squared and Adjusted R-SquaredComparing a regression with a mean-only baseline2:33
10. 90Regression Assumptions, Heteroskedasticity, and MulticollinearityDiagnosing unstable uncertainty and redundant predictors2:56
11. Demo: Credit Limit Scoring ModelIncome, spending and a limit6:35

Financial data has an information clock. We will distinguish levels from changes, lags from leads, rolling memory from expanding memory, and an event date from its release date. Every forecast and backtest inherits these timing choices, even when the final model looks mathematically sophisticated. Module overview

1. 91Time Order, Frequency, Regularity, and Financial CalendarsA trading calendar is not an evenly spaced stopwatch2:33
2. 92Levels, Changes, Differences, and ReturnsSeparating account levels, cash changes, and relative returns2:35
3. 93Lags, Leads, and Temporal DependenceKeeping past features separate from future labels2:22
4. 94Rolling and Expanding WindowsChoosing how much history a monitoring statistic remembers2:26
5. 95Resampling, Aggregation, and Time AlignmentAggregating event payments without double-counting a boundary2:33
6. 96Trend, Seasonality, Cycles, and RemainderSeparating a growing business from a repeating weekly pattern2:38
7. 97Autocovariance and AutocorrelationMeasuring lagged similarity on a declared finite-sample convention2:29
8. 98Stationarity and Differencing IntuitionRemoving a changing level without declaring stationarity solved2:39
9. 99Smoothing, Baselines, and Naive ForecastsGiving an advanced forecast a simple baseline to beat2:31
10. 100Look-Ahead Leakage and Time-Aware Data SplitsBlocking late information even when its event date is old2:30
11. Demo: Daily Payment Volume ForecasterA calendar, not a stopwatch5:55

Now the earlier pieces assemble into risk and performance statistics. We will read volatility, downside, drawdown, loss quantiles, beta, and portfolio variance as different lenses. Every attractive number gets the same question: which observations, which units, which assumptions, and what does this measure leave out? Module overview

1. 101Volatility and Annualized VolatilityExpressing return dispersion without promising a future range2:42
2. 102Downside Deviation and Target ShortfallMeasuring shortfall below a required return2:35
3. 103Drawdown and Maximum DrawdownTracking loss from a running wealth peak2:30
4. 104Loss Distributions and Loss QuantilesBuilding the loss tail with an explicit sign convention2:31
5. 105Value at Risk IntuitionA quantile threshold is not a worst-case promise2:29
6. 106Expected Shortfall IntuitionAveraging the source-defined exceedance slice and auditing its probability mass2:43
7. 107Beta and Market-Relative RiskMarket sensitivity is not total portfolio risk2:33
8. 108Sharpe, Sortino, and Information Ratio IntuitionReading performance ratios without mixing risk definitions2:46
9. 109Active Return and Tracking ErrorMeasuring benchmark-relative consistency on matched observations2:38
10. 110Covariance Matrices, Portfolio Variance, and DiversificationWhy two individually quiet holdings can become a risky combination2:53
11. Demo: Portfolio Risk ReportA tear sheet for two quiet funds6:21

Our final module makes the implementation trustworthy enough to inspect. Floating-point limits, online state, random seeds, shape alignment, and train-only preprocessing can change an answer without changing the displayed formula. We finish by testing properties and preserving an audit trail, not by assuming that runnable code is correct code. Module overview

1. 111Floating-Point Representation, Overflow, and UnderflowWhy a familiar decimal can fail exact equality2:47
2. 112Stable Summation and Mean CalculationRecovering low-order contributions during accumulation2:37
3. 113Stable Online Variance and Welford’s AlgorithmUpdating variance as records arrive without unstable raw subtraction2:38
4. 114Batch, Rolling, and Streaming Statistic EquivalenceMaking different execution styles compute the same statistic2:41
5. 115Missing, Infinite, Invalid, and Unsupported-State PoliciesRefusing to make invalid inputs look like calm markets2:36
6. 116Pseudorandom Numbers, Seeds, and ReproducibilityReplaying a simulation without confusing reproducibility with security2:33
7. 117Vectorization, Index Alignment, and Shape SafetyPreventing a dimensionally valid but semantically wrong dot product2:27
8. 118Leakage-Free Fitting, Scaling, and PreprocessingFitting a scaler without teaching it the test distribution2:37
9. 119Fixtures, Numerical Tolerances, and Property TestsTesting mathematical behavior, not just one screenshot2:43
10. 120Reproducible Analysis, Metadata, and Audit TrailsMaking a result reproducible without confusing metadata with truth2:57
11. Demo: Production-Grade Metrics ServiceSame data, run twice6:26