book

Essential Math for Data Science

by Thomas Nield

May 2022

Intermediate to advanced

352 pages

9h 15m

English

O'Reilly Media, Inc.

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Conventions Used in This BookUsing Code ExamplesO’Reilly Online LearningHow to Contact UsAcknowledgments
Number TheoryOrder of OperationsVariablesFunctionsSummationsExponentsLogarithmsEuler’s Number and Natural LogarithmsEuler’s NumberNatural LogarithmsLimitsDerivativesPartial DerivativesThe Chain RuleIntegralsConclusionExercises
Understanding ProbabilityProbability Versus StatisticsProbability MathJoint ProbabilitiesUnion ProbabilitiesConditional Probability and Bayes’ TheoremJoint and Union Conditional ProbabilitiesBinomial DistributionBeta DistributionConclusionExercises
What Is Data?Descriptive Versus Inferential StatisticsPopulations, Samples, and BiasDescriptive StatisticsMean and Weighted MeanMedianModeVariance and Standard DeviationThe Normal DistributionThe Inverse CDFZ-ScoresInferential StatisticsThe Central Limit TheoremConfidence IntervalsUnderstanding P-ValuesHypothesis TestingThe T-Distribution: Dealing with Small SamplesBig Data Considerations and the Texas Sharpshooter FallacyConclusionExercises
What Is a Vector?Adding and Combining VectorsScaling VectorsSpan and Linear DependenceLinear TransformationsBasis VectorsMatrix Vector MultiplicationMatrix MultiplicationDeterminantsSpecial Types of MatricesSquare MatrixIdentity MatrixInverse MatrixDiagonal MatrixTriangular MatrixSparse MatrixSystems of Equations and Inverse MatricesEigenvectors and EigenvaluesConclusionExercises
A Basic Linear RegressionResiduals and Squared ErrorsFinding the Best Fit LineClosed Form EquationInverse Matrix TechniquesMatrix DecompositionGradient DescentOverfitting and VarianceStochastic Gradient DescentThe Correlation CoefficientStatistical SignificanceCoefficient of DeterminationStandard Error of the EstimatePrediction IntervalsTrain/Test SplitsMultiple Linear RegressionConclusionExercises
Understanding Logistic RegressionPerforming a Logistic RegressionLogistic FunctionFitting the Logistic CurveMultivariable Logistic RegressionUnderstanding the Log-OddsR-SquaredP-ValuesTrain/Test SplitsConfusion MatricesBayes’ Theorem and ClassificationReceiver Operator Characteristics/Area Under CurveClass ImbalanceConclusionExercises
When to Use Neural Networks and Deep LearningA Simple Neural NetworkActivation FunctionsForward PropagationBackpropagationCalculating the Weight and Bias DerivativesStochastic Gradient DescentUsing scikit-learnLimitations of Neural Networks and Deep LearningConclusionExercise
Redefining Data ScienceA Brief History of Data ScienceFinding Your EdgeSQL ProficiencyProgramming ProficiencyData VisualizationKnowing Your IndustryProductive LearningPractitioner Versus AdvisorWhat to Watch Out For in Data Science JobsRole DefinitionOrganizational Focus and Buy-InAdequate ResourcesReasonable ObjectivesCompeting with Existing SystemsA Role Is Not What You ExpectedDoes Your Dream Job Not Exist?Where Do I Go Now?Conclusion
Using LaTeX Rendering with SymPyBinomial Distribution from ScratchBeta Distribution from ScratchDeriving Bayes’ TheoremCDF and Inverse CDF from ScratchUse e to Predict Event Probability Over TimeHill Climbing and Linear RegressionHill Climbing and Logistic RegressionA Brief Intro to Linear ProgrammingMNIST Classifier Using scikit-learn

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About the Author

Thomas Nield is the founder of Nield Consulting Group as well as an instructor at O’Reilly Media and the University of Southern California. He enjoys making technical content relatable and relevant to those unfamiliar with or intimidated by it. Thomas regularly teaches classes on data analysis, machine learning, mathematical optimization, AI system safety, and practical artificial intelligence. He’s authored two books, Getting Started with SQL (O’Reilly) and Learning RxJava (Packt). He’s also the founder and inventor of Yawman Flight, a company that develops universal handheld controls for flight simulation and unmanned aerial vehicles.