Discover easy-to-follow solutions and techniques to help you to implement applied mathematical concepts such as probability, calculus, and equations using Python's numeric and scientific libraries
Key Features
• Compute complex mathematical problems using programming logic with the help of step-by-step recipes
• Learn how to use Python libraries for computation, mathematical modeling, and statistics
• Discover simple yet effective techniques for solving mathematical equations and apply them in real-world statistics
Book Description
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.
What you will learn
• Become familiar with basic Python packages, tools, and libraries for solving mathematical problems
• Explore real-world applications of mathematics to reduce a problem in optimization
• Understand the core concepts of applied mathematics and their application in computer science
• Find out how to choose the most suitable package, tool, or technique to solve a problem
• Implement basic mathematical plotting, change plot styles, and add labels to plots using Matplotlib
• Get to grips with probability theory with the Bayesian inference and Markov Chain Monte Carlo (MCMC) methods
Who this book is for
Whether you are a professional programmer or a student looking to solve mathematical problems computationally using Python, this is the book for you. Advanced mathematics proficiency is not a prerequisite, but basic knowledge of mathematics will help you to get the most out of this Python math book. Familiarity with the concepts of data structures in Python is assumed.
Author(s): Sam Morley
Edition: 2
Publisher: Packt Publishing
Year: 2022
Language: English
Commentary: Publisher's PDF
Pages: 376
City: Birmingham, UK
Tags: Data Analysis;Regression;Python;Bayesian Inference;Game Theory;Ordinary Differential Equations;Data Visualization;Statistics;Numerical Methods;Optimization;Partial Differential Equations;Random Number Generation;NumPy;matplotlib;pandas;Graph Theory;Jupyter;NetworkX;Networks;Geospatial Data;Linear Algebra;SciPy;Probability Theory;Fourier Transform;SymPy;Integration;Cython;Calculus;Bokeh;Dask;Analysis of Variance;Prophet;Symbolic Computations;Productivity;Nonparametric Models;Geometry;ARIMA;JAX
Cover
Title Page
Copyright
Dedication
Contributors
Table of Contents
Preface
Chapter 1: An Introduction to Basic Packages, Functions, and Concepts
Technical requirements
Exploring Python numerical types
Decimal type
Fraction type
Complex type
Understanding basic mathematical functions
Diving into the world of NumPy
Element access
Array arithmetic and functions
Useful array creation routines
Higher-dimensional arrays
Working with matrices and linear algebra
Basic methods and properties
Matrix multiplication
Determinants and inverses
Systems of equations
Eigenvalues and eigenvectors
Sparse matrices
Summary
Further reading
Chapter 2: Mathematical Plotting with Matplotlib
Technical requirements
Basic plotting with Matplotlib
Getting ready
How to do it...
How it works…
There’s more…
Adding subplots
Getting ready
How to do it...
How it works...
There’s more...
See also
Plotting with error bars
Getting ready
How to do it…
How it works…
There’s more...
Saving Matplotlib figures
Getting ready
How to do it...
How it works...
There’s more...
See also
Surface and contour plots
Getting ready
How to do it...
How it works...
There’s more...
See also
Customizing three-dimensional plots
Getting ready
How to do it...
How it works...
There’s more...
Plotting vector fields with quiver plots
Getting ready
How to do it…
How it works…
There’s more…
Further reading
Chapter 3: Calculus and Differential Equations
Technical requirements
Primer on calculus
Working with polynomials and calculus
Getting ready
How to do it...
How it works...
There’s more...
See also
Differentiating and integrating symbolically using SymPy
Getting ready
How to do it...
How it works...
There’s more...
Solving equations
Getting ready
How to do it...
How it works...
There’s more...
Integrating functions numerically using SciPy
Getting ready
How to do it...
How it works...
There’s more...
Solving simple differential equations numerically
Getting ready
How to do it...
How it works...
There’s more...
See also
Solving systems of differential equations
Getting ready
How to do it...
How it works...
There’s more...
Solving partial differential equations numerically
Getting ready
How to do it...
How it works...
There’s more...
See also
Using discrete Fourier transforms for signal processing
Getting ready
How to do it...
How it works...
There’s more...
See also
Automatic differentiation and calculus using JAX
Getting ready
How to do it…
How it works…
There’s more…
See also
Solving differential equations using JAX
Getting ready
How to do it…
How it works…
See also
Further reading
Chapter 4: Working with Randomness and Probability
Technical requirements
Selecting items at random
Getting ready
How to do it...
How it works...
There’s more...
Generating random data
Getting ready
How to do it...
How it works...
There’s more...
Changing the random number generator
Getting ready
How to do it...
How it works...
There’s more...
Generating normally distributed random numbers
Getting ready
How to do it...
How it works...
There’s more...
Working with random processes
Getting ready
How to do it...
How it works...
There’s more...
Analyzing conversion rates with Bayesian techniques
Getting ready
How to do it...
How it works...
There’s more...
Estimating parameters with Monte Carlo simulations
Getting ready
How to do it...
How it works...
There’s more...
See also
Further reading
Chapter 5: Working with Trees and Networks
Technical requirements
Creating networks in Python
Getting ready
How to do it...
How it works...
There’s more...
Visualizing networks
Getting ready
How to do it...
How it works...
There’s more...
Getting the basic characteristics of networks
Getting ready
How to do it...
How it works...
There’s more...
Generating the adjacency matrix for a network
Getting ready
How to do it...
How it works...
There’s more...
Creating directed and weighted networks
Getting ready
How to do it...
How it works...
There’s more...
Finding the shortest paths in a network
Getting ready
How to do it...
How it works...
There’s more...
Quantifying clustering in a network
Getting ready
How to do it...
How it works...
There’s more...
Coloring a network
Getting ready
How to do it...
How it works...
There’s more...
Finding minimal spanning trees and dominating sets
Getting ready
How to do it...
How it works...
Further reading
Chapter 6: Working with Data and Statistics
What is statistics?
Technical requirements
Creating Series and DataFrame objects
Getting ready
How to do it...
How it works...
There’s more...
See also
Loading and storing data from a DataFrame
Getting ready
How to do it...
How it works...
See also
Manipulating data in DataFrames
Getting ready
How to do it...
How it works...
There’s more...
Plotting data from a DataFrame
Getting ready
How to do it...
How it works...
There’s more...
Getting descriptive statistics from a DataFrame
Getting ready
How to do it...
How it works...
There’s more...
Understanding a population using sampling
Getting ready
How to do it...
How it works...
See also
Performing operations on grouped data in a DataFrame
Getting ready
How to do it...
How it works...
Testing hypotheses using t-tests
Getting ready
How to do it...
How it works...
There’s more...
Testing hypotheses using ANOVA
Getting ready
How to do it...
How it works...
There’s more...
Testing hypotheses for non-parametric data
Getting ready
How to do it...
How it works...
Creating interactive plots with Bokeh
Getting ready
How to do it...
How it works...
There’s more...
Further reading
Chapter 7: Using Regression and Forecasting
Technical requirements
Getting ready
How to do it...
How it works...
There’s more...
Using multilinear regression
Getting ready
How to do it...
How it works...
Classifying using logarithmic regression
Getting ready
How to do it...
How it works...
There’s more...
Modeling time series data with ARMA
Getting ready
How to do it...
How it works...
There’s more...
Forecasting from time series data using ARIMA
Getting ready
How to do it...
How it works...
Forecasting seasonal data using ARIMA
Getting ready
How to do it...
How it works...
There’s more...
Using Prophet to model time series data
Getting ready
How to do it...
How it works...
There’s more...
Using signatures to summarize time series data
Getting ready
How to do it…
How it works…
There’s more…
See also
Further reading
Chapter 8: Geometric Problems
Technical requirements
Visualizing two-dimensional geometric shapes
Getting ready
How to do it...
How it works...
There’s more...
See also
Finding interior points
Getting ready
How to do it...
How it works...
Finding edges in an image
Getting ready
How to do it…
How it works...
Triangulating planar figures
Getting ready
How to do it...
How it works...
There’s more...
See also
Computing convex hulls
Getting ready
How to do it...
How it works...
Constructing Bezier curves
Getting ready
How to do it...
How it works...
There’s more...
Further reading
Chapter 9: Finding Optimal Solutions
Technical requirements
Minimizing a simple linear function
Getting ready
How to do it...
How it works...
There’s more...
Minimizing a non-linear function
Getting ready
How to do it...
How it works...
There’s more...
Using gradient descent methods in optimization
Getting ready
How to do it...
How it works...
There’s more...
Using least squares to fit a curve to data
Getting ready
How to do it...
How it works...
There’s more...
Analyzing simple two-player games
Getting ready
How to do it...
How it works...
There’s more...
Computing Nash equilibria
Getting ready
How to do it...
How it works...
There’s more...
See also
Further reading
Chapter 10: Improving Your Productivity
Technical requirements
Keeping track of units with Pint
Getting ready
How to do it...
How it works...
There’s more...
Accounting for uncertainty in calculations
Getting ready
How to do it...
How it works...
There’s more...
Loading and storing data from NetCDF files
Getting ready
How to do it...
How it works...
There’s more...
Working with geographical data
Getting ready
How to do it...
How it works...
Executing a Jupyter notebook as a script
Getting ready
How to do it...
How it works...
There’s more...
Validating data
Getting ready
How to do it...
How it works...
Accelerating code with Cython
Getting ready
How to do it...
How it works...
There’s more...
Distributing computing with Dask
Getting ready
How to do it...
How it works...
There’s more...
Writing reproducible code for data science
Getting ready
How to do it…
How it works…
There’s more…
See also...
Index
About Packt
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