Book Image

Applying Math with Python - Second Edition

By : Sam Morley
Book Image

Applying Math with Python - Second Edition

By: Sam Morley

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.

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Table of Contents (13 chapters)
Preface
Preface
Who this book is for
What this book covers
To get the most out of this book
Download the example code files
Download the color images
Conventions used
Get in touch
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1
Chapter 1: An Introduction to Basic Packages, Functions, and Concepts
Chapter 1: An Introduction to Basic Packages, Functions, and Concepts
Technical requirements
Exploring Python numerical types
Understanding basic mathematical functions
Diving into the world of NumPy
Working with matrices and linear algebra
Summary
Further reading
Free Chapter
2
Chapter 2: Mathematical Plotting with Matplotlib
Chapter 2: Mathematical Plotting with Matplotlib
Technical requirements
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
Further reading
3
Chapter 3: Calculus and Differential Equations
Chapter 3: Calculus and Differential Equations
Technical requirements
Primer on calculus
Working with polynomials and calculus
Differentiating and integrating symbolically using SymPy
Solving equations
Integrating functions numerically using SciPy
Solving simple differential equations numerically
Solving systems of differential equations
Solving partial differential equations numerically
Using discrete Fourier transforms for signal processing
Automatic differentiation and calculus using JAX
Solving differential equations using JAX
Further reading
4
Chapter 4: Working with Randomness and Probability
Chapter 4: Working with Randomness and Probability
Technical requirements
Selecting items at random
Generating random data
Changing the random number generator
Generating normally distributed random numbers
Working with random processes
Analyzing conversion rates with Bayesian techniques
Estimating parameters with Monte Carlo simulations
Further reading
5
Chapter 5: Working with Trees and Networks
Chapter 5: Working with Trees and Networks
Technical requirements
Creating networks in Python
Visualizing networks
Getting the basic characteristics of networks
Generating the adjacency matrix for a network
Creating directed and weighted networks
Finding the shortest paths in a network
Quantifying clustering in a network
Coloring a network
Finding minimal spanning trees and dominating sets
Further reading
6
Chapter 6: Working with Data and Statistics
Chapter 6: Working with Data and Statistics
What is statistics?
Technical requirements
Creating Series and DataFrame objects
Loading and storing data from a DataFrame
Manipulating data in DataFrames
Plotting data from a DataFrame
Getting descriptive statistics from a DataFrame
Understanding a population using sampling
Performing operations on grouped data in a DataFrame
Testing hypotheses using t-tests
Testing hypotheses using ANOVA
Testing hypotheses for non-parametric data
Creating interactive plots with Bokeh
Further reading
7
Chapter 7: Using Regression and Forecasting
Chapter 7: Using Regression and Forecasting
Technical requirements
Using multilinear regression
Classifying using logarithmic regression
Modeling time series data with ARMA
Forecasting from time series data using ARIMA
Forecasting seasonal data using ARIMA
Using Prophet to model time series data
Using signatures to summarize time series data
Further reading
8
Chapter 8: Geometric Problems
Chapter 8: Geometric Problems
Technical requirements
Visualizing two-dimensional geometric shapes
Finding interior points
Finding edges in an image
Triangulating planar figures
Computing convex hulls
Constructing Bezier curves
Further reading
9
Chapter 9: Finding Optimal Solutions
Chapter 9: Finding Optimal Solutions
Technical requirements
Minimizing a simple linear function
Minimizing a non-linear function
Using gradient descent methods in optimization
Using least squares to fit a curve to data
Analyzing simple two-player games
Computing Nash equilibria
Further reading
10
Chapter 10: Improving Your Productivity
Chapter 10: Improving Your Productivity
Technical requirements
Keeping track of units with Pint
Accounting for uncertainty in calculations
Loading and storing data from NetCDF files
Working with geographical data
Executing a Jupyter notebook as a script
Validating data
Accelerating code with Cython
Distributing computing with Dask
Writing reproducible code for data science
11
Index
Index
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12
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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
Previous Section
End of Section 1
Next Section