book

The Statistics and Calculus with Python Workshop

Name: The Statistics and Calculus with Python Workshop
ISBN: 9781800209763

by Peter Farrell, Alvaro Fuentes, Ajinkya Sudhir Kolhe, Quan Nguyen, Alexander Joseph Sarver, Marios Tsatsos, Amit Chaurasia, Rohan Chikorde, Sanjin Dedic, Tim Hoolihan, Ravi Ranjan Prasad Karn, Alberto Manzini

August 2020

Beginner to intermediate

740 pages

13h 41m

English

Packt Publishing

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The Statistics and Calculus with Python Workshop
Preface
About the BookAudienceAbout the ChaptersConventionsCode PresentationSetting up Your EnvironmentSoftware RequirementsInstallation and SetupInstalling PythonProject JupyterInstalling LibrariesAccessing the Code Files
1. Fundamentals of Python
IntroductionControl Flow Methodsif StatementsExercise 1.01: Divisibility with ConditionalsLoopsThe while LoopThe for LoopExercise 1.02: Number Guessing GameData StructuresStringsListsExercise 1.03: Multi-Dimensional ListsTuplesSetsDictionariesExercise 1.04: Shopping Cart CalculationsFunctions and AlgorithmsFunctionsExercise 1.05: Finding the MaximumRecursionExercise 1.06: The Tower of HanoiAlgorithm DesignExercise 1.07: The N-Queens ProblemTesting, Debugging, and Version ControlTestingDebuggingExercise 1.08: Testing for ConcurrencyVersion ControlExercise 1.09: Version Control with Git and GitHubActivity 1.01: Building a Sudoku SolverSummary
2. Python's Main Tools for Statistics
IntroductionScientific Computing and NumPy BasicsNumPy ArraysVectorizationExercise 2.01: Timing Vectorized Operations in NumPyRandom SamplingWorking with Tabular Data in pandasInitializing a DataFrame ObjectAccessing Rows and ColumnsManipulating DataFramesExercise 2.02: Data Table ManipulationAdvanced Pandas FunctionalitiesExercise 2.03: The Student DatasetData Visualization with Matplotlib and SeabornScatter PlotsLine GraphsBar GraphsHistogramsHeatmapsExercise 2.04: Visualization of Probability DistributionsVisualization Shorthand from Seaborn and PandasActivity 2.01: Analyzing the Communities and Crime DatasetSummary
3. Python's Statistical Toolbox
IntroductionAn Overview of StatisticsTypes of Data in StatisticsCategorical DataExercise 3.01: Visualizing Weather PercentagesNumerical DataExercise 3.02: Min-Max ScalingOrdinal DataDescriptive StatisticsCentral TendencyDispersionExercise 3.03: Visualizing Probability Density FunctionsPython-Related Descriptive StatisticsInferential StatisticsT-TestsCorrelation MatrixExercise 3.04: Identifying and Testing Equality of MeansStatistical and Machine Learning ModelsExercise 3.05: Model SelectionPython's Other Statistics ToolsActivity 3.01: Revisiting the Communities and Crimes DatasetSummary
4. Functions and Algebra with Python
IntroductionFunctionsCommon FunctionsDomain and RangeFunction Roots and EquationsThe Plot of a FunctionExercise 4.01: Function Identification from PlotsFunction TransformationsShiftsScalingExercise 4.02: Function Transformation IdentificationEquationsAlgebraic ManipulationsFactoringUsing PythonExercise 4.03: Introduction to Break-Even AnalysisSystems of EquationsSystems of Linear EquationsExercise 4.04: Matrix Solution with NumPySystems of Non-Linear EquationsActivity 4.01: Multi-Variable Break-Even AnalysisSummary
5. More Mathematics with Python
IntroductionSequences and SeriesArithmetic SequencesGeneratorsExercise 5.01: Determining the nth Term of an Arithmetic Sequence and Arithmetic SeriesGeometric SequencesExercise 5.02: Writing a Function to Find the Next Term of the SequenceRecursive SequencesExercise 5.03: Creating a Custom Recursive SequenceTrigonometryBasic Trigonometric FunctionsExercise 5.04: Plotting a Right-Angled TriangleInverse Trigonometric FunctionsExercise 5.05: Finding the Shortest Way to the Treasure Using Inverse Trigonometric FunctionsExercise 5.06: Finding the Optimal Distance from an ObjectVectorsVector OperationsExercise 5.07: Visualizing VectorsComplex NumbersBasic Definitions of Complex NumbersPolar Representation and Euler's FormulaExercise 5.08: Conditional Multiplication of Complex NumbersActivity 5.01: Calculating Your Retirement Plan Using SeriesSummary
6. Matrices and Markov Chains with Python
IntroductionMatrix Operations on a Single MatrixBasic Operations on a MatrixInspecting a MatrixExercise 6.01: Calculating the Time Taken for Sunlight to Reach Earth Each DayOperations and Multiplication in MatricesAxes in a MatrixExercise 6.02: Matrix SearchMultiple MatricesBroadcastingOperations on Multiple MatricesIdentity MatrixThe eye FunctionInverse of a MatrixLogical OperatorsOuter Function or Vector ProductSolving Linear Equations Using MatricesExercise 6.03: Use of Matrices in Performing Linear EquationsTransition Matrix and Markov ChainsFundamentals of Markov ChainsStochastic versus Deterministic ModelsTransition State DiagramsTransition MatricesExercise 6.04: Finding the Probability of State Transitions Markov Chains and Markov PropertyActivity 6.01: Building a Text Predictor Using a Markov ChainSummary
7. Doing Basic Statistics with Python
IntroductionData PreparationIntroducing the DatasetIntroducing the Business ProblemPreparing the DatasetExercise 7.01: Using a String Column to Produce a Numerical ColumnCalculating and Using Descriptive StatisticsThe Need for Descriptive StatisticsA Brief Refresher of Statistical ConceptsUsing Descriptive StatisticsExercise 7.02: Calculating Descriptive StatisticsExploratory Data AnalysisWhat Is EDA?Univariate EDABi-variate EDA: Exploring Relationships Between VariablesExercise 7.03: Practicing EDAActivity 7.01: Finding Out Highly Rated Strategy GamesSummary
8. Foundational Probability Concepts and Their Applications
IntroductionRandomness, Probability, and Random VariablesRandomness and ProbabilityFoundational Probability ConceptsIntroduction to Simulations with NumPyExercise 8.01: Sampling with and without ReplacementProbability as a Relative FrequencyDefining Random VariablesExercise 8.02: Calculating the Average Wins in Roulette Discrete Random VariablesDefining Discrete Random VariablesThe Binomial DistributionExercise 8.03: Checking If a Random Variable Follows a Binomial DistributionContinuous Random VariablesDefining Continuous Random VariablesThe Normal DistributionSome Properties of the Normal DistributionExercise 8.04: Using the Normal Distribution in EducationActivity 8.01: Using the Normal Distribution in FinanceSummary

9. Intermediate Statistics with Python
IntroductionLaw of Large NumbersPython and Random NumbersExercise 9.01: The Law of Large Numbers in ActionExercise 9.02: Coin Flipping Average over TimeA Practical Application of the Law of Large Numbers Seen in the Real WorldExercise 9.03: Calculating the Average Winnings for a Game of Roulette If We Constantly Bet on RedCentral Limit TheoremNormal Distribution and the CLTRandom Sampling from a Uniform DistributionExercise 9.04: Showing the Sample Mean for a Uniform DistributionRandom Sampling from an Exponential DistributionExercise 9.05: Taking a Sample from an Exponential DistributionConfidence IntervalsCalculating the Confidence Interval of a Sample MeanExercise 9.06: Finding the Confidence Interval of Polling FiguresSmall Sample Confidence IntervalConfidence Interval for a ProportionHypothesis TestingParts of a Hypothesis TestThe Z-TestExercise 9.07: The Z-Test in ActionProportional Z-TestThe T-TestExercise 9.08: The T-Test2-Sample T-Test or A/B TestingExercise 9.09: A/B Testing ExampleIntroduction to Linear RegressionExercise 9.10: Linear RegressionActivity 9.01: Standardized Test PerformanceSummary
10. Foundational Calculus with Python
IntroductionWriting the Derivative FunctionExercise 10.01: Finding the Derivatives of Other FunctionsFinding the Equation of the Tangent LineCalculating IntegralsUsing TrapezoidsExercise 10.02: Finding the Area Under a CurveUsing Integrals to Solve Applied ProblemsExercise 10.03: Finding the Volume of a Solid of RevolutionUsing Derivatives to Solve Optimization ProblemsExercise 10.04: Find the Quickest RouteExercise 10.05: The Box ProblemExercise 10.06: The Optimal CanExercise 10.07: Calculating the Distance between Two Moving ShipsActivity 10.01: Maximum Circle-to-Cone VolumeSummary
11. More Calculus with Python
IntroductionLength of a CurveExercise 11.01: Finding the Length of a CurveExercise 11.02: Finding the Length of a Sine WaveLength of a SpiralExercise 11.03: Finding the Length of the Polar Spiral CurveExercise 11.04: Finding the Length of Insulation in a RollExercise 11.05: Finding the Length of an Archimedean SpiralArea of a SurfaceThe FormulasExercise 11.06: Finding the Area of a 3D Surface – Part 1Exercise 11.07: Finding the Area of a 3D Surface – Part 2Exercise 11.08: Finding the Area of a Surface – Part 3Infinite SeriesPolynomial FunctionsSeriesConvergenceExercise 11.09: Calculating 10 Correct Digits of πExercise 11.10: Calculating the Value of π Using Euler's ExpressionA 20th Century FormulaInterval of ConvergenceExercise 11.11: Determining the Interval of Convergence – Part 1Exercise 11.12: Determining the Interval of Convergence – Part 2Exercise 11.13: Finding the ConstantActivity 11.01: Finding the Minimum of a SurfaceSummary
12. Intermediate Calculus with Python
IntroductionDifferential EquationsInterest CalculationsExercise 12.01: Calculating InterestExercise 12.02: Calculating Compound Interest – Part 1Exercise 12.03: Calculating Compound Interest – Part 2Exercise 12.04: Calculating Compound Interest – Part 3Exercise 12.05: Becoming a MillionairePopulation GrowthExercise 12.06: Calculating the Population Growth Rate – Part 1Exercise 12.07: Calculating the Population Growth Rate – Part 2Half-Life of Radioactive MaterialsExercise 12.08: Measuring Radioactive DecayExercise 12.09: Measuring the Age of a Historical ArtifactNewton's Law of CoolingExercise 12.10: Calculating the Time of DeathExercise 12.11: Calculating the Rate of Change in TemperatureMixture ProblemsExercise 12.12: Solving Mixture Problems – Part 1Exercise 12.13: Solving Mixture Problems – Part 2Exercise 12.14: Solving Mixture Problems – Part 3Exercise 12.15: Solving Mixture Problems – Part 4Euler's MethodExercise 12.16: Solving Differential Equations with Euler's MethodExercise 12.17: Using Euler's Method to Evaluate a FunctionRunge-Kutta MethodExercise 12.18: Implementing the Runge-Kutta MethodPursuit CurvesExercise 12.19: Finding Where the Predator Catches the PreyExercise 12.20: Using Turtles to Visualize Pursuit CurvesPosition, Velocity, and AccelerationExercise 12.21: Calculating the Height of a Projectile above the GroundAn Example of Calculating the Height of a Projectile with Air ResistanceExercise 12.22: Calculating the Terminal VelocityActivity 12.01: Finding the Velocity and Location of a ParticleSummary
Appendix
1. Fundamentals of PythonActivity 1.01: Building a Sudoku Solver2. Python's Main Tools for StatisticsActivity 2.01: Analyzing the Communities and Crime Dataset3. Python's Statistical ToolboxActivity 3.01: Revisiting the Communities and Crimes Dataset4. Functions and Algebra with PythonActivity 4.01: Multi-Variable Break-Even Analysis5. More Mathematics with PythonActivity 5.01: Calculating Your Retirement Plan Using Series6. Matrices and Markov Chains with PythonActivity 6.01: Building a Text Predictor Using a Markov Chain7. Doing Basic Statistics with PythonActivity 7.01: Finding Out Highly Rated Strategy Games8. Foundational Probability Concepts and Their ApplicationsActivity 8.01: Using the Normal Distribution in Finance9. Intermediate Statistics with PythonActivity 9.01: Standardized Test Performance10. Foundational Calculus with PythonActivity 10.01: Maximum Circle-to-Cone Volume11. More Calculus with PythonActivity 11.01: Finding the Minimum of a Surface12. Intermediate Calculus with PythonActivity 12.01: Finding the Velocity and Location of a Particle

Overview

The Statistics and Calculus with Python Workshop provides an in-depth exploration of essential mathematical concepts in the context of Python programming, aimed specifically at applications in artificial intelligence. Through real-world examples and exercises, you'll learn to implement statistics and calculus in Python.

What this Book will help me do

Understand and use Python libraries for statistical analysis.
Analyze and visualize data to answer key questions.
Solve calculus problems like derivatives and integrals computationally.
Apply statistical and probabilistic concepts to practical situations.
Use numerical methods for differential equations in Python.

Author(s)

Peter Farrell, Alvaro Fuentes, Ajinkya Sudhir Kolhe, Quan Nguyen, Alexander Joseph Sarver, and Marios Tsatsos are seasoned professionals and educators in mathematics, statistics, and programming. Their extensive background spans education, practical application, and teaching Python in technical contexts. They bring a hands-on, approachable style to this comprehensive guide.

Who is it for?

This book is perfect for Python programmers looking to deepen their understanding of statistics and calculus, particularly in AI applications. It suits intermediate learners who are familiar with basic programming and concepts in mathematics. If you are looking for a practical way to connect coding with advanced math to solve real-world problems, this book is ideal. The content assumes some prior mathematical knowledge but guides you in applying it effectively with Python.

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