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Sam Morley - Applying Math with Python: Practical recipes for solving computational math problems using Python programming and its libraries

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Applying Math with Python: Practical recipes for solving computational math problems using Python programming and its libraries: summary, description and annotation

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Discover easy-to-follow solutions and techniques to help you to implement applied mathematical concepts such as probability, calculus, and equations using Pythons numeric and scientific libraries

Key Features
  • Compute complex mathematical problems using programming logic with the help of step-by-step recipes
  • Learn how to utilize Pythons 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

Python, one of the worlds 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. Youll start by developing core skills and learning about packages covered in Pythons scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, youll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, youll discover Pythons 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, youll 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
  • Get familiar with basic packages, tools, and libraries in Python for solving mathematical problems
  • Explore various techniques that will help you to solve computational mathematical problems
  • Understand the core concepts of applied mathematics and how you can apply them in computer science
  • Discover how to choose the most suitable package, tool, or technique to solve a certain problem
  • Implement basic mathematical plotting, change plot styles, and add labels to the 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

This book is for professional programmers and students looking to solve mathematical problems computationally using Python. Advanced mathematics knowledge is not a requirement, but a basic knowledge of mathematics will help you to get the most out of this book. The book assumes familiarity with Python concepts of data structures.

Table of Contents
  1. Basic Packages, Functions, and Concepts
  2. Mathematical Plotting with Matplotlib
  3. Calculus and Differential Equations
  4. Working with Randomness and Probability
  5. Working with Trees and Networks
  6. Working with Data and Statistics
  7. Regression and Forecasting
  8. Geometric Problems
  9. Finding Optimal Solutions
  10. Miscellaneous Topics

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Applying Math with Python
Practical recipes for solving computational math problems using Python programming and its libraries
Sam Morley

BIRMINGHAM - MUM BAI Applying Math with Python Copyright 2020 Packt - photo 2

BIRMINGHAM - MUMBAI
Applying Math with Python

Copyright 2020 Packt Publishing

All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without the prior written permission of the publisher, except in the case of brief quotations embedded in critical articles or reviews.

Every effort has been made in the preparation of this book to ensure the accuracy of the information presented. However, the information contained in this book is sold without warranty, either express or implied. Neither the author, nor Packt Publishing or its dealers and distributors, will be held liable for any damages caused or alleged to have been caused directly or indirectly by this book.

Packt Publishing has endeavored to provide trademark information about all of the companies and products mentioned in this book by the appropriate use of capitals. However, Packt Publishing cannot guarantee the accuracy of this information.

Commissioning Editor: Ravit Jain
Acquisition Editor: Pratik Tandel
Content Development Editor: Divya Vijayan
Senior Editor: Hayden Edwards
Technical Editor:Deepesh Patel
Copy Editor:Safis Editing
Project Coordinator:Kinjal Bari
Proofreader: Safis Editing
Indexer: Rekha Nair
Production Designer: Jyoti Chauhan

First published: July 2020

Production reference: 1300720

Published by Packt Publishing Ltd.
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Birmingham
B3 2PB, UK.

ISBN 978-1-83898-975-0

www.packt.com


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Contributors
About the author

Sam Morley is an experienced lecturer in mathematics and a researcher in pure mathematics. He is currently a research software engineer at the University of Oxford working on the DataSig project. He was previously a lecturer in mathematics at the University of East Anglia and Nottingham Trent University. His research interests lie in functional analysis, especially Banach algebras. Sam has a firm commitment to providing high-quality, inclusive, and enjoyable teaching, with the aim of inspiring his students and spreading his enthusiasm for mathematics.

I would like to thank my friends and colleagues at the University of East Anglia for their support and encouragement while writing this book. I would also like to thank my editorial team and the technical reviewers for their hard work.
About the reviewers

Bryan Johns is an experienced data scientist and mathematician. Since completing his PhD in mathematics, Bryan has been working as a data scientist, where he has been using Python to deliver machine learning solutions to some of today's most intractable business problems. Bryan has worked in the financial services and consulting industries, as well as serving as a data science mentor for the next generation of data scientists. In his free time, Bryan enjoys surfing, skiing, sailing, and other activities that start with "s." Bryan lives in San Diego, California, with his wife, one-year-old son, and two mischievous cats.

Valeriy Babushkin is the senior director of data science at X5 Retail Group, where he leads a team of 80+ people in the fields of machine learning, data analysis, computer vision, natural language processing, R&D, and A/B testing. Valeriy is a Kaggle competition grandmaster and attending lecturer at the National Research Institute Higher School of Economics and the Central Bank of Kazakhstan. He is a technical reviewer of AI Crash Course and Hands-On Reinforcement Learning with Python, Second Edition, published by Packt.

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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 friendly community, and from its ability to communicate seamlessly with compiled extension modules. This means that Python is ideal for solving problems of all kinds, and mathematical problems in particular.

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 logical, 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 provides an introduction to some of the basic concepts from mathematics and how to use Python to work with these concepts and 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 the 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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