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Applying Math with Python

Applying Math with Python

By : Sam Morley
4.3 (4)
Buy this Book
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Applying Math with Python

Applying Math with Python

4.3 (4)
By: Sam Morley
Buy this Book

Overview of this book

Python, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python’s scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover 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 (12 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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Code in Action
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Conventions used
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Sections
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Getting ready
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How to do it…
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How it works…
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There's more…
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See also
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Get in touch
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Reviews
1
Basic Packages, Functions, and Concepts
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Basic Packages, Functions, and Concepts
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Technical requirements
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Python numerical types
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Basic mathematical functions
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NumPy arrays
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Matrices
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Summary
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Further reading
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2
Mathematical Plotting with Matplotlib
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Mathematical Plotting with Matplotlib
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Technical requirements
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Basic plotting with Matplotlib
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Changing the plotting style
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Adding labels and legends to plots
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Adding subplots
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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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Further reading
3
Calculus and Differential Equations
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Calculus and Differential Equations
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Technical requirements
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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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Further reading
4
Working with Randomness and Probability
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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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Working with Trees and Networks
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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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Working with Data and Statistics
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Working with Data and 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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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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Regression and Forecasting
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Regression and Forecasting
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Technical requirements
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Using basic linear regression
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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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Further reading
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Geometric Problems
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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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Finding Optimal Solutions
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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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Miscellaneous Topics
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Miscellaneous Topics
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Technical requirements
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Keeping track of units with Pint
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Getting ready
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How to do it...
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How it works...
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There's more...
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Accounting for uncertainty in calculations
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Getting ready
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How to do it...
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How it works...
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There's more...
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Loading and storing data from NetCDF files
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Getting ready
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How to do it...
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How it works...
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Working with geographical data
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Getting ready
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How to do it...
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How it works...
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Executing a Jupyter notebook as a script
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Getting ready
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How to do it...
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How it works...
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Validating data
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Getting ready
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How to do it...
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How it works...
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Working with data streams
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Getting ready
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How to do it...
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How it works...
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See also
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Accelerating code with Cython
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Getting ready
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How to do it...
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How it works...
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There's more...
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Distributing computing with Dask
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Getting ready
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How to do it...
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How it works...
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There's more...
11
Other Books You May Enjoy
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Other Books You May Enjoy
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Preface

Python is a powerful and flexible programming language that is fun and easy to learn. It is the programming language of choice for many professionals, hobbyists, and scientists. The power of Python comes from its large ecosystem of packages and a friendly community, and its ability to communicate seamlessly with compiled extension modules. This means that Python is ideal for solving problems of all kinds, especially mathematical problems.

Mathematics is usually associated with calculations and equations but, in reality, these are very small parts of a much larger subject. At its core, mathematics is about solving problems, and the logically structured approach to solutions. Once you explore past the equations, calculations, derivatives, and integrals, you discover a vast world of beautiful, elegant structures.

This book is an introduction to solving mathematical problems using Python. It introduces some of the basic concepts of mathematics and how to use Python to work with these concepts. It also introduces some basic templates for solving a variety of mathematical problems across a large number of topics within mathematics. The first few chapters focus on core skills such as working with NumPy arrays, plotting, calculus, and probability. These topics are very important throughout mathematics and act as a foundation for the rest of the book. In the remaining chapters, we discuss more practical problems, covering topics such as data analysis and statistics, networks, regression and forecasting, optimization, and game theory. We hope that this book provides a basis for solving mathematical problems and the tools for you to further explore the world of mathematics.

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