Python编程探索数学：算法与应用

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"《Doing Math with Python》是一本由Amit Saha撰写的实用指南，旨在利用Python编程语言探索和理解数学领域的各个方面，包括代数、统计学和微积分等。本书适合对编程感兴趣且希望将计算技能与数学相结合的读者，无论是初学者还是进阶者，都能从中受益。作者通过这本书展示了如何运用Python的强大功能来解决数学问题，让抽象的概念变得直观且易于操作。读者可以学习到如何编写脚本来执行数值计算、数据可视化、符号计算以及概率和统计分析。书中不仅提供了理论知识，还配以丰富的实例和练习，帮助读者逐步掌握Python在数学中的应用技巧。在版权方面，本书受到严格的保护，未经版权所有者及出版社许可，不得以任何形式复制或传播，包括但不限于打印、录音或通过任何信息存储和检索系统。《Doing Math with Python》是美国印制，首次印刷于2015年，并拥有明确的国际标准书号(ISBN-10和ISBN-13)。出版商是William Pollock，生产编辑为Riley Hoffman，封面插图出自Josh Ellingson之手，内部设计则由Octopod Studios负责。开发编辑包括Seph Kramer和Tyler Ortman，技术评审工作由Jeremy Kun完成，而Julianne Jigour担任校对，确保了内容的专业性和准确性。排版和校对由Riley Hoffman和Paula L. Fleming共同协作完成。本书旨在激发读者对数学的兴趣，同时提升他们在实际问题中使用Python的能力，是一部兼具教育性和实践性的IT学习资源。对于任何希望通过编程增强数学理解的人来说，《Doing Math with Python》无疑是一本不可或缺的参考书籍。"

INTRODUCTION

This book’s goal is to bring together three

topics near to my heart—programming,

math, and science. What does that mean

exactly? Within these pages, we’ll programmati-

cally explore high school–level topics, like manipulating

units of measurement; examining projectile motion;

calculating mean, median, and mode; determining linear correlation;

solving algebraic equations; describing the motion of a simple pendulum;

simulating dice games; creating geometric shapes; and ﬁnding the limits,

derivatives, and integrals of functions. These are familiar topics for many,

but instead of using pen and paper, we’ll use our computer to explore them.

We’ll write programs that will take numbers and formulas as input, do

the tedious calculations needed, and then spit out the solution or draw a

graph. Some of these programs are powerful calculators for solving math

problems. They ﬁnd the solutions to equations, calculate the correlation

between sets of data, and determine the maximum value of a function,

xvi Introduction

among other tasks. In other programs, we’ll simulate real-life events, such

as projectile motion, a coin toss, or a die roll. Using programs to simulate

such events gives us an easy way to analyze and learn more about them.

You’ll also ﬁnd topics that would be extremely difﬁcult to explore with-

out programs. For example, drawing fractals by hand is tedious at best and

close to impossible at worst. With a program, all we need to do is run a for

loop with the relevant operation in the body of the loop.

I think you’ll ﬁnd that this new context for “doing math” makes learn-

ing both programming and math more exciting, fun, and rewarding.

Who Should Read This Book

If you yourself are learning programming, you’ll appreciate how this book

demonstrates ways to solve problems with computers. Likewise, if you teach

such learners, I hope you ﬁnd this book useful to demonstrate the applica-

tion of programming skills beyond the sometimes abstract world of com-

puter science.

This book assumes the reader knows the absolute basics of Python

programming using Python 3—speciﬁcally, what a function is, function

arguments, the concept of a Python class and class objects, and loops.

Appendix B covers some of the other Python topics that are used by the

programs, but this book doesn’t assume knowledge of these additional

topics. If you ﬁnd yourself needing more background, I recommend

reading Python for Kids by Jason Briggs (No Starch Press, 2013).

What’s in This Book?

This book consists of seven chapters and two appendices. Each chapter

ends with challenges for the reader. I recommend giving these a try, as

there’s much to learn from trying to write your own original programs.

Some of these challenges will ask you to explore new topics, which is a

great way to enhance your learning.

• Chapter 1, Working with Numbers, starts off with basic mathematical

operations and gradually moves on to topics requiring a higher level of

math know-how.

• Chapter 2, Visualizing Data with Graphs, discusses creating graphs

from data sets using the matplotlib library.

• Chapter 3, Describing Data with Statistics, continues the theme of

processing data sets, covering basic statistical concepts—mean, median,

mode, and the linear correlation of variables in a data set. You’ll also

learn to handle data from CSV ﬁles, a popular ﬁle format for distribut-

ing data sets.

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