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Applying Math with Python - Second Edition

Name: Applying Math with Python - Second Edition
Author: Sam Morley
ISBN: 9781804618370

by Sam Morley

December 2022

Intermediate to advanced

376 pages

10h 8m

English

Packt Publishing

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Applying Math with Python
ContributorsAbout the authorAbout the reviewer
Preface
Who this book is forWhat this book coversTo get the most out of this bookDownload the example code filesDownload the color imagesConventions usedGet in touchShare your thoughtsDownload a free PDF copy of this book
Chapter 1: An Introduction to Basic Packages, Functions, and Concepts
Technical requirementsExploring Python numerical typesDecimal typeFraction typeComplex typeUnderstanding basic mathematical functionsDiving into the world of NumPyElement accessArray arithmetic and functionsUseful array creation routinesHigher-dimensional arraysWorking with matrices and linear algebraBasic methods and propertiesMatrix multiplicationDeterminants and inversesSystems of equationsEigenvalues and eigenvectorsSparse matricesSummaryFurther reading
Chapter 2: Mathematical Plotting with Matplotlib
Technical requirementsBasic plotting with MatplotlibGetting readyHow to do it...How it works…There’s more…Adding subplotsGetting readyHow to do it...How it works...There’s more...See alsoPlotting with error barsGetting readyHow to do it…How it works…There’s more...Saving Matplotlib figuresGetting readyHow to do it...How it works...There’s more...See alsoSurface and contour plotsGetting readyHow to do it...How it works...There’s more...See alsoCustomizing three-dimensional plotsGetting readyHow to do it...How it works...There’s more...Plotting vector fields with quiver plotsGetting readyHow to do it…How it works…There’s more…Further reading
Chapter 3: Calculus and Differential Equations
Technical requirementsPrimer on calculusWorking with polynomials and calculusGetting readyHow to do it...How it works...There’s more...See alsoDifferentiating and integrating symbolically using SymPyGetting readyHow to do it...How it works...There’s more...Solving equationsGetting readyHow to do it...How it works...There’s more...Integrating functions numerically using SciPyGetting readyHow to do it...How it works...There’s more...Solving simple differential equations numericallyGetting readyHow to do it...How it works...There’s more...See alsoSolving systems of differential equationsGetting readyHow to do it...How it works...There’s more...Solving partial differential equations numericallyGetting readyHow to do it...How it works...There’s more...See alsoUsing discrete Fourier transforms for signal processingGetting readyHow to do it...How it works...There’s more...See alsoAutomatic differentiation and calculus using JAXGetting readyHow to do it…How it works…There’s more…See alsoSolving differential equations using JAXGetting readyHow to do it…How it works…See alsoFurther reading
Chapter 4: Working with Randomness and Probability
Technical requirementsSelecting items at randomGetting readyHow to do it...How it works...There’s more...Generating random dataGetting readyHow to do it...How it works...There’s more...Changing the random number generatorGetting readyHow to do it...How it works...There’s more...Generating normally distributed random numbersGetting readyHow to do it...How it works...There’s more...Working with random processesGetting readyHow to do it...How it works...There’s more...Analyzing conversion rates with Bayesian techniquesGetting readyHow to do it...How it works...There’s more...Estimating parameters with Monte Carlo simulationsGetting readyHow to do it...How it works...There’s more...See alsoFurther reading
Chapter 5: Working with Trees and Networks
Technical requirementsCreating networks in PythonGetting readyHow to do it...How it works...There’s more...Visualizing networksGetting readyHow to do it...How it works...There’s more...Getting the basic characteristics of networksGetting readyHow to do it...How it works...There’s more...Generating the adjacency matrix for a networkGetting readyHow to do it...How it works...There’s more...Creating directed and weighted networksGetting readyHow to do it...How it works...There’s more...Finding the shortest paths in a networkGetting readyHow to do it...How it works...There’s more...Quantifying clustering in a networkGetting readyHow to do it...How it works...There’s more...Coloring a networkGetting readyHow to do it...How it works...There’s more...Finding minimal spanning trees and dominating setsGetting readyHow to do it...How it works...Further reading
Chapter 6: Working with Data and Statistics
What is statistics?Technical requirementsCreating Series and DataFrame objectsGetting readyHow to do it...How it works...There’s more...See alsoLoading and storing data from a DataFrameGetting readyHow to do it...How it works...See alsoManipulating data in DataFramesGetting readyHow to do it...How it works...There’s more...Plotting data from a DataFrameGetting readyHow to do it...How it works...There’s more...Getting descriptive statistics from a DataFrameGetting readyHow to do it...How it works...There’s more...Understanding a population using samplingGetting readyHow to do it...How it works...See alsoPerforming operations on grouped data in a DataFrameGetting readyHow to do it...How it works...Testing hypotheses using t-testsGetting readyHow to do it...How it works...There’s more...Testing hypotheses using ANOVAGetting readyHow to do it...How it works...There’s more...Testing hypotheses for non-parametric dataGetting readyHow to do it...How it works...Creating interactive plots with BokehGetting readyHow to do it...How it works...There’s more...Further reading
Chapter 7: Using Regression and Forecasting
Technical requirementsGetting readyHow to do it...How it works...There’s more...Using multilinear regressionGetting readyHow to do it...How it works...Classifying using logarithmic regressionGetting readyHow to do it...How it works...There’s more...Modeling time series data with ARMAGetting readyHow to do it...How it works...There’s more...Forecasting from time series data using ARIMAGetting readyHow to do it...How it works...Forecasting seasonal data using ARIMAGetting readyHow to do it...How it works...There’s more...Using Prophet to model time series data Getting readyHow to do it...How it works...There’s more...Using signatures to summarize time series dataGetting readyHow to do it…How it works…There’s more…See alsoFurther reading
Chapter 8: Geometric Problems
Technical requirementsVisualizing two-dimensional geometric shapesGetting readyHow to do it...How it works...There’s more...See alsoFinding interior pointsGetting readyHow to do it...How it works...Finding edges in an imageGetting readyHow to do it…How it works...Triangulating planar figuresGetting readyHow to do it...How it works...There’s more...See alsoComputing convex hullsGetting readyHow to do it...How it works...Constructing Bezier curvesGetting readyHow to do it...How it works...There’s more...Further reading

Chapter 9: Finding Optimal Solutions
Technical requirementsMinimizing a simple linear functionGetting readyHow to do it...How it works...There’s more...Minimizing a non-linear functionGetting readyHow to do it...How it works...There’s more...Using gradient descent methods in optimizationGetting readyHow to do it...How it works...There’s more...Using least squares to fit a curve to dataGetting readyHow to do it...How it works...There’s more...Analyzing simple two-player gamesGetting readyHow to do it...How it works...There’s more...Computing Nash equilibriaGetting readyHow to do it...How it works...There’s more...See alsoFurther reading
Chapter 10: Improving Your Productivity
Technical requirementsKeeping track of units with PintGetting readyHow to do it...How it works...There’s more...Accounting for uncertainty in calculationsGetting readyHow to do it...How it works...There’s more...Loading and storing data from NetCDF filesGetting readyHow to do it...How it works...There’s more...Working with geographical dataGetting readyHow to do it...How it works...Executing a Jupyter notebook as a scriptGetting readyHow to do it...How it works...There’s more...Validating dataGetting readyHow to do it...How it works...Accelerating code with CythonGetting readyHow to do it...How it works...There’s more...Distributing computing with DaskGetting readyHow to do it...How it works...There’s more...Writing reproducible code for data scienceGetting readyHow to do it…How it works…There’s more…See also...
Index
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Content preview from Applying Math with Python - Second Edition

4 Working with Randomness and Probability

In this chapter, we will discuss randomness and probability. We will start by briefly exploring the fundamentals of probability by selecting elements from a set of data. Then, we will learn how to generate (pseudo) random numbers using Python and NumPy, and how to generate samples according to a specific probability distribution. We will conclude the chapter by looking at a number of advanced topics covering random processes and Bayesian techniques and using Markov Chain Monte Carlo (MCMC) methods to estimate the parameters of a simple model.

Probability is a quantification of the likelihood of a specific event occurring. We use probabilities intuitively all of the time, although sometimes the formal ...

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Applying Math with Python - Second Edition

by Sam Morley

4

Working with Randomness and Probability

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