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Math Adventures with Python: An Illustrated Guide to Exploring Math with Code [Pehme köide]

4.12/5 (67 hinnangut Goodreads-ist)

Peter Farrell

Formaat: Paperback / softback, 304 pages, kõrgus x laius: 236x178 mm, 304 Illustrations
Ilmumisaeg: 08-Jan-2019
Kirjastus: No Starch Press,US
ISBN-10: 1593278675
ISBN-13: 9781593278670

Teised raamatud teemal:

Mathematics - (Hetkel poes: 12 nimetust)

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Formaat: Paperback / softback, 304 pages, kõrgus x laius: 236x178 mm, 304 Illustrations
Ilmumisaeg: 08-Jan-2019
Kirjastus: No Starch Press,US
ISBN-10: 1593278675
ISBN-13: 9781593278670

Teised raamatud teemal:

Mathematics - (Hetkel poes: 12 nimetust)

Püsilink: https://www.kriso.ee/db/9781593278670.html

Märksõnad:

"Teaches math concepts through programming. Begins with a crash course in basic programming concepts and how to use Python's built-in Turtle module, and then explores topics like writing programs to solve equations and matrices, drawing polygons and fractals, and using the Processing graphics library to create interactive 2D and 3D models"--

Learn math by getting creative with code! Use the Python programming language to transform learning high school-level math topics like algebra, geometry, trigonometry, and calculus!

Math Adventures with Python will show you how to harness the power of programming to keep math relevant and fun. With the aid of the Python programming language, you'll learn how to visualize solutions to a range of math problems as you use code to explore key mathematical concepts like algebra, trigonometry, matrices, and cellular automata.

Once you've learned the programming basics like loops and variables, you'll write your own programs to solve equations quickly, make cool things like an interactive rainbow grid, and automate tedious tasks like factoring numbers and finding square roots. You'll learn how to write functions to draw and manipulate shapes, create oscillating sine waves, and solve equations graphically.

You'll also learn how to:
- Draw and transform 2D and 3D graphics with matrices
- Make colorful designs like the Mandelbrot and Julia sets with complex numbers
- Use recursion to create fractals like the Koch snowflake and the Sierpinski triangle
- Generate virtual sheep that graze on grass and multiply autonomously
- Crack secret codes using genetic algorithms

As you work through the book's numerous examples and increasingly challenging exercises, you'll code your own solutions, create beautiful visualizations, and see just how much more fun math can be!

Arvustused

"We have entered an era where learning Python is as essential as knowing the analytical skills of mathematics, and so from students to teachers, Math Adventures with Python is an indispensable book for all." Gabrielle Birkman, Mathematician and Writer

"Peter Farrell subverts the structure of a traditional math textbook and adopts an approach centered on student creation and discovery. Rather than treating mathematical facts as symbolic formalism to be mindlessly imitated by students, Math Adventures with Python seeks to teach mathematics through guided discovery. " Dr. Tien Chih, Professor of Mathematics, Montana State University-Billings

"If youre a mathy type and want to get into some computer programming, or if youre a computer person but want to learn what kinds of math you can do with code, Math Adventures with Python will help you achieve those goals." Jenny Bristol, GeekDad

Muu info

Learn math by getting creative with code. Use the Python programming language to transform learning high school-level math topics like algebra, geometry, trigonometry, and calculus.

About the Author

About the Technical Reviewer

Acknowledgments

Introduction

xvii

The Problem with School Math

xviii

About This Book

Who Should Use This Book

xxi

What's in This Book?

xxi

Downloading and Installing Python

xxii

Starting IDLE

xxiii

Installing Processing

xxiv

PART I HITCHIN' UP YOUR PYTHON WAGON

1 Drawing Polygons With The Turtle Module

(16)

Python's turtle Module

(3)

Importing the turtle Module

(1)

Moving Your Turtle

(1)

Changing Directions

(1)

Repeating Code with Loops

(2)

Using the for Loop

(2)

Using a for Loop to Draw a Square

(1)

Creating Shortcuts with Functions

(2)

Using Variables to Draw Shapes

(2)

Using Variables in Functions

(1)

Variable Errors

(1)

Equilateral Triangles

(4)

Writing the triangle() Function

(1)

Making Variables Vary

(3)

Summary

(2)

2 Making Tedious Arithmetic Fun With Lists And Loops

(18)

Basic Operators

(2)

Operating on Variables

(1)

Using Operators to Write the average)) Function

(1)

Mind the Order of Operations!

(1)

Using Parentheses with Operators

(1)

Data Types in Python

(3)

Integers and Floats

(1)

Strings

(1)

Booleans

(1)

Checking Data Types

(1)

Using Lists to Store Values

(2)

Adding Items to a List

(1)

Operating on Lists

(1)

Removing Items from a List

(1)

Using Lists in Loops

(5)

Accessing Individual Items with List Indices

(1)

Accessing Index and Value with enumerated

(1)

Indices Start at Zero

(1)

Accessing a Range of List Items

(1)

Finding Out the Index of an Item

(1)

Strings Use Indices, Too

(1)

Summation

(2)

Creating the running_sum Variable

(1)

Writing the mySum() Function

(1)

Finding the Average of a List of Numbers

(1)

Summary 35

(3)

3 Guessing And Checking With Conditionals

(16)

Comparison Operators

(1)

Making Decisions with if and else Statements

(1)

Using Conditionals to Find Factors

(4)

Writing the factors.py Program

(1)

The Wandering Turtle

(2)

Creating a Number-Guessing Game

(5)

Making a Random Number Generator

(1)

Taking User Input

(1)

Converting User Input to Integers

(1)

Using Conditionals to Check for a Correct Guess

(1)

Using a Loop to Guess Again!

(1)

Tips for Guessing

(1)

Finding Square Roots

(2)

Applying the Number-Guessing Game Logic

(1)

Writing the squareRoot() Function

(1)

Summary

(3)

PART 2 RIDING INTO MATH TERRITORY

4 Transforming And Storing Numbers With Algebra

(24)

Solving First-Degree Equations

(4)

Finding the Formula for First-Degree Equations

(1)

Writing the equation() Function

(1)

Using print() Instead of return

(1)

Solving Higher-Degree Equations

(3)

Using quad() to Solve Quadratic Equations

(1)

Using plug() to Solve a Cubic Equation

(1)

Solving Equations Graphically

(1)

Getting Started with Processing

(2)

Creating Your Own Graphing Tool

(6)

Graphing an Equation

(4)

Using Guess and Check to Find the Roots

(1)

Writing the guess() Function

(2)

Summary 75

(2)

5 Transforming Shapes With Geometry

(1)

Drawing a Circle

(1)

Specifying Location Using Coordinates

(1)

Transformation Functions

(6)

Translating Objects with translate()

(3)

Rotating Objects with rotate()

(1)

Drawing a Circle of Circles

(1)

Drawing a Circle of Squares

(1)

Animating Objects

(3)

Creating the t Variable

(1)

Rotating the Individual Squares

(1)

Saving Orientation with pushMatrix() and popMatrix()

(1)

Rotating Around the Center

(1)

Creating an Interactive Rainbow Grid

(4)

Drawing a Grid of Objects

(1)

Adding the Rainbow Color to Objects

(2)

Drawing Complex Patterns Using Triangles

(9)

A 30-60-90 Triangle

(2)

Drawing an Equilateral Triangle

(2)

Drawing Multiple Rotating Triangles

(1)

Phase-Shifting the Rotation

(1)

Finalizing the Design

100

(2)

Summary

102

(1)

6 Creating Oscillations With Trigonometry

103

(24)

Using Trigonometry for Rotations and Oscillations

105

(1)

Writing Functions to Draw Polygons

106

(4)

Drawing a Hexagon with Loops

107

(2)

Drawing an Equilateral Triangle

109

(1)

Making Sine Waves

110

(6)

Leaving a Trail

113

(1)

Using Python's Built-in enumerated Function

114

(2)

Creating a Spirograph Program

116

(4)

Drawing the Smaller Circle

117

(1)

Rotating the Smaller Circle

117

(3)

Making Harmonographs

120

(6)

Writing the harmonograph Program

121

(2)

Filling the List Instantly

123

(1)

Two Pendulums Are Better Than One

124

(2)

Summary

126

(1)

7 Complex Numbers

127

(18)

The Complex Coordinate System

128

(1)

Adding Complex Numbers I

129

(1)

Multiplying a Complex Number by i

130

(1)

Multiplying Two Complex Numbers

131

(1)

Writing the magnitude() Function

132

(1)

Creating the Mandelbrot Set

132

(9)

Writing the mandelbrot() Function 1

(104)

Adding Color to the Mandelbrot Set

139

(2)

Creating the Julia Set

141

(2)

Writing the Julia() Function

141

(2)

Summary

143

(2)

8 Using Matrices For Computer Graphics And Systems Of Equations

145

(30)

What Is a Matrix?

146

(1)

Adding Matrices

146

(1)

Multiplying Matrices

147

(4)

Order Matters in Matrix Multiplication

151

(1)

Drawing 2D Shapes

151

(3)

Transforming Matrices

154

(2)

Transposing Matrices

156

(4)

Rotating Matrices in Real Time

160

(1)

Creating 3D Shapes

161

(1)

Creating the Rotation Matrix

162

(4)

Solving Systems of Equations with Matrices

166

(6)

Gaussian Elimination

167

(1)

Writing the gauss() Function

168

(4)

Summary

172

(3)

PART 3 BLAZING YOUR OWN TRAIL

9 Building Objects With Classes

175

(26)

Bouncing Ball Program

177

(9)

Making the Ball Move

178

(1)

Making the Ball Bounce Off the Wall

179

(2)

Making Multiple Balls Without Classes

181

(1)

Creating Objects Using Classes

182

(4)

Grazing Sheep Program

186

(14)

Writing the Class for the Sheep

186

(1)

Programming Sheep to Move Around

187

(2)

Creating the energy Property

189

(1)

Creating Grass Using Classes

189

(3)

Making the Grass Brown when Eaten

192

(2)

Giving Each Sheep a Random Color

194

(2)

Programming Sheep to Reproduce

196

(1)

Letting the Grass Regrow

197

(1)

Providing an Evolutionary Advantage

198

(2)

Summary

200

(1)

10 Creating Fractals Using Recursion

201

(24)

The Length of a Coastline

202

(7)

What Is Recursion?

203

(1)

Writing the factorial() Function

203

(1)

Building a Fractal Tree

204

(5)

Koch Snowflake

209

(5)

Writing the segment() Function

210

(4)

Sierpinski Triangle

214

(2)

Square Fractal

216

(4)

Dragon Curve

220

(4)

Summary

224

(1)

11 Cellular Automata

225

(22)

Creating a Cellular Automaton

226

(8)

Writing a Cell Class

228

(2)

Resizing Each Cell

230

(1)

Making a CA Grow

231

(1)

Putting the Cells into a Matrix

232

(1)

Creating the Cell List

233

(1)

Python Lists Are Strange

234

(4)

List Index Notation

235

(3)

Letting Your CA Grow Automatically

238

(1)

Playing the Game of Life

238

(3)

The Elementary Cellular Automaton

241

(5)

Summary

246

(1)

12 Solving Problems Using Genetic Algorithms

247

(26)

Using a Genetic Algorithm to Guess Phrases

248

(6)

Writing the makeList() Function

248

(1)

Testing the makeList() Function

249

(1)

Writing the score() Function

250

(1)

Writing the mutate() Function

250

(1)

Generating a Random Number

251

(3)

Solving the Traveling Salesperson Problem (TSP)

254

(17)

Using Genetic Algorithms

254

(6)

Writing the calcLength() Method

260

(1)

Testing the calcLength() Method

261

(1)

Random Routes

262

(3)

Applying the Phrase-Guessing Mutation Idea

265

(1)

Mutating Two Numbers in a List

265

(4)

Crossing Over to Improve Routes

269

(2)

Summary

271

(2)

Index

273

Peter Farrell is a math and computer science teacher with a passion for customizing ("hacking") math education and learning with technology. He lives in the San Francisco Bay Area with his wife and children.

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