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Applying Math with Python

Applying Math with Python - Second Edition

By : Morley
5 (8)
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Applying Math with Python

Applying Math with Python

5 (8)
By: Morley
Buy this Book

Overview of this book

The updated edition of Applying Math with Python will help you solve complex problems in a wide variety of mathematical fields in simple and efficient ways. Old recipes have been revised for new libraries and several recipes have been added to demonstrate new tools such as JAX. You'll start by refreshing your knowledge of several core mathematical fields and learn about packages covered in Python's scientific stack, including NumPy, SciPy, and Matplotlib. As you progress, you'll gradually get to grips with more advanced topics of calculus, probability, and networks (graph theory). Once you’ve developed a solid base in these topics, you’ll have the confidence to set out on math adventures with Python as you explore Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science.
Table of Contents (13 chapters)
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Preface
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Preface
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Who this book is for
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What this book covers
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To get the most out of this book
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Download the example code files
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Download the color images
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Conventions used
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Get in touch
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Download a free PDF copy of this book
1
Chapter 1: An Introduction to Basic Packages, Functions, and Concepts
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Chapter 1: An Introduction to Basic Packages, Functions, and Concepts
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Technical requirements
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Exploring Python numerical types
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Understanding basic mathematical functions
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Diving into the world of NumPy
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Working with matrices and linear algebra
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Summary
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Further reading
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Chapter 2: Mathematical Plotting with Matplotlib
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Chapter 2: Mathematical Plotting with Matplotlib
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Technical requirements
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Basic plotting with Matplotlib
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Adding subplots
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Plotting with error bars
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Saving Matplotlib figures
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Surface and contour plots
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Customizing three-dimensional plots
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Plotting vector fields with quiver plots
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Further reading
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Chapter 3: Calculus and Differential Equations
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Chapter 3: Calculus and Differential Equations
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Technical requirements
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Primer on calculus
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Working with polynomials and calculus
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Differentiating and integrating symbolically using SymPy
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Solving equations
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Integrating functions numerically using SciPy
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Solving simple differential equations numerically
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Solving systems of differential equations
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Solving partial differential equations numerically
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Using discrete Fourier transforms for signal processing
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Automatic differentiation and calculus using JAX
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Solving differential equations using JAX
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Further reading
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Chapter 4: Working with Randomness and Probability
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Chapter 4: Working with Randomness and Probability
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Technical requirements
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Selecting items at random
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Generating random data
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Changing the random number generator
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Generating normally distributed random numbers
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Working with random processes
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Analyzing conversion rates with Bayesian techniques
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Estimating parameters with Monte Carlo simulations
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Further reading
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Chapter 5: Working with Trees and Networks
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Chapter 5: Working with Trees and Networks
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Technical requirements
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Creating networks in Python
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Visualizing networks
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Getting the basic characteristics of networks
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Generating the adjacency matrix for a network
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Creating directed and weighted networks
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Finding the shortest paths in a network
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Quantifying clustering in a network
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Coloring a network
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Finding minimal spanning trees and dominating sets
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Further reading
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Chapter 6: Working with Data and Statistics
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Chapter 6: Working with Data and Statistics
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What is statistics?
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Technical requirements
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Creating Series and DataFrame objects
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Loading and storing data from a DataFrame
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Manipulating data in DataFrames
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Plotting data from a DataFrame
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Getting descriptive statistics from a DataFrame
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Understanding a population using sampling
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Performing operations on grouped data in a DataFrame
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Testing hypotheses using t-tests
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Testing hypotheses using ANOVA
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Testing hypotheses for non-parametric data
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Creating interactive plots with Bokeh
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Further reading
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Chapter 7: Using Regression and Forecasting
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Chapter 7: Using Regression and Forecasting
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Technical requirements
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Using multilinear regression
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Classifying using logarithmic regression
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Modeling time series data with ARMA
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Forecasting from time series data using ARIMA
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Forecasting seasonal data using ARIMA
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Using Prophet to model time series data
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Using signatures to summarize time series data
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Further reading
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Chapter 8: Geometric Problems
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Chapter 8: Geometric Problems
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Technical requirements
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Visualizing two-dimensional geometric shapes
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Finding interior points
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Finding edges in an image
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Triangulating planar figures
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Computing convex hulls
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Constructing Bezier curves
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Further reading
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Chapter 9: Finding Optimal Solutions
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Chapter 9: Finding Optimal Solutions
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Technical requirements
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Minimizing a simple linear function
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Minimizing a non-linear function
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Using gradient descent methods in optimization
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Using least squares to fit a curve to data
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Analyzing simple two-player games
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Computing Nash equilibria
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Further reading
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Chapter 10: Improving Your Productivity
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Chapter 10: Improving Your Productivity
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Technical requirements
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Keeping track of units with Pint
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Accounting for uncertainty in calculations
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Loading and storing data from NetCDF files
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Working with geographical data
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Executing a Jupyter notebook as a script
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Validating data
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Accelerating code with Cython
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Distributing computing with Dask
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Writing reproducible code for data science
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Index
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Index
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Why subscribe?
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Other Books You May Enjoy
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Other Books You May Enjoy
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Packt is searching for authors like you
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Mathematical Plotting with Matplotlib

Plotting is a fundamental tool in all of mathematics. A good plot can reveal hidden details, suggest future directions, verify results, or reinforce an argument. It is no surprise, then, that the scientific Python stack features a powerful and flexible plotting library called Matplotlib.

In this chapter, we will plot functions and data in a variety of styles and create figures that are fully labeled and annotated. We will create three-dimensional plots, customize the appearance of figures, create figures that contain multiple plots using subplots, and save figures directly to files for applications that are not running in an interactive environment.

Plotting is one of the most important aspects covered in this book. Plotting data, functions, or solutions can often help you gain an understanding of a problem that can really help to reason about your methods. We will see plotting again in every chapter of this book.

In this chapter, we will cover the following recipes:

  • Basic plotting with Matplotlib
  • Adding subplots
  • Plotting with error bars
  • Saving Matplotlib figures
  • Surface and contour plots
  • Customizing three-dimensional plots
  • Plotting vector fields with quiver plots
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Programming languages
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