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

Chapter 1Chapter 2Chapter 3Chapter 4Chapter 5Chapter 6Chapter 7

Content preview from Essential Math for Data Science

Chapter 1. Basic Math and Calculus Review

We will kick off the first chapter covering what numbers are and how variables and functions work on a Cartesian system. We will then cover exponents and logarithms. After that, we will learn the two basic operations of calculus: derivatives and integrals.

Before we dive into the applied areas of essential math such as probability, linear algebra, statistics, and machine learning, we should probably review a few basic math and calculus concepts. Before you drop this book and run screaming, do not worry! I will present how to calculate derivatives and integrals for a function in a way you were probably not taught in college. We have Python on our side, not a pencil and paper. Even if you are not familiar with derivatives and integrals, you still do not need to worry.

I will make these topics as tight and practical as possible, focusing only on what will help us in later chapters and what falls under the “essential math” umbrella.

This Is Not a Full Math Crash Course!

This is by no means a comprehensive review of high school and college math. If you want that, a great book to check out is No Bullshit Guide to Math and Physics by Ivan Savov (pardon my French). The first few chapters contain the best crash course on high school and college math I have ever seen. The book Mathematics 1001 by Dr. Richard Elwes has some great content as well, and in bite-sized explanations.