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 8. Career Advice and the Path Forward

As we come to a close with this book, it is a good idea to evaluate where to go from here. You learned and integrated a wide survey of applied mathematical topics: calculus, probability, statistics, and linear algebra. Then you applied these techniques to practical applications, including linear regression, logistic regression, and neural networks. In this chapter, we will cover how to use this knowledge going forward while navigating the strange, exciting, and oddly diverse landscape of a data science career. I will emphasize the importance of having direction and a tangible objective to work toward, rather than memorizing tools and techniques without an actual problem in mind.

Since we’re moving away from foundational concepts and applied methods, this chapter will have a different tone than the rest of the book. You might be expecting to learn how you can apply these mathematical modeling skills to your career in focused and tangible ways. However, if you want to be successful in a data science career, you will have to learn a few more hard skills like SQL and programming, as well as soft skills to develop professional awareness. The latter are especially important so you do not become lost in the shape-shifting profession that is data science and unseen market forces blindside you.

I am not going to presume to know your career goals or what you hope to achieve with this information. I will make a few safe bets, though, since you ...