Doing math with Python : use programming to explore algebra, statistics, calculus, and more!

Brief Contents
Contents in Detail
Acknowledgments
Introduction
Who Should Read This Book
What’s in This Book?
Scripts, Solutions, and Hints
Chapter 1: Working with Numbers
Basic Mathematical Operations
Labels: Attaching Names to Numbers
Different Kinds of Numbers
Working with Fractions
Complex Numbers
Getting User Input
Handling Exceptions and Invalid Input
Fractions and Complex Numbers as Input
Writing Programs That Do the Math for You
Calculating the Factors of an Integer
Generating Multiplication Tables
Converting Units of Measurement
Finding the Roots of a Quadratic Equation
What You Learned
Programming Challenges
Challenge 1: Even-Odd Vending Machine
Challenge 2: Enhanced Multiplication Table Generator
Challenge 3: Enhanced Unit Converter
Challenge 4: Fraction Calculator
Challenge 5: Give Exit Power to the User
Chapter 2: Visualizing Data with Graphs
Understanding the Cartesian Coordinate Plane
Working with Lists and Tuples
Iterating over a List or Tuple
Creating Graphs with Matplotlib
Marking Points on Your Graph
Graphing the Average Annual Temperature in New York City
Comparing the Monthly Temperature Trends of New York City
Customizing Graphs
Saving the Plots
Plotting with Formulas
Newton’s Law of Universal Gravitation
Projectile Motion
What You Learned
Programming Challenges
Challenge 1: How Does the Temperature Vary During the Day?
Challenge 2: Exploring a Quadratic Function Visually
Challenge 3: Enhanced Projectile Trajectory Comparison Program
Challenge 4: Visualizing Your Expenses
Challenge 5: Exploring the Relationship Between the Fibonacci Sequence and the Golden Ratio
Chapter 3: Describing Data with Statistics
Finding the Mean
Finding the Median
Finding the Mode and Creating a Frequency Table
Finding the Most Common Elements
Finding the Mode
Creating a Frequency Table
Measuring the Dispersion
Finding the Range of a Set of Numbers
Finding the Variance and Standard Deviation
Calculating the Correlation Between Two Data Sets
Calculating the Correlation Coefficient
High School Grades and Performance on College Admission Tests
Scatter Plots
Reading Data from Files
Reading Data from a Text File
Reading Data from a CSV File
What You Learned
Programming Challenges
Challenge 1: Better Correlation Coefficient–Finding Program
Challenge 2: Statistics Calculator
Challenge 3: Experiment with Other CSV Data
Challenge 4: Finding the Percentile
Challenge 5: Creating a Grouped Frequency Table
Chapter 4: Algebra and Symbolic Math with SymPy
Defining Symbols and Symbolic Operations
Working with Expressions
Factorizing and Expanding Expressions
Pretty Printing
Substituting in Values
Converting Strings to Mathematical Expressions
Solving Equations
Solving Quadratic Equations
Solving for One Variable in Terms of Others
Solving a System of Linear Equations
Plotting Using SymPy
Plotting Expressions Input by the User
Plotting Multiple Functions
What You Learned
Programming Challenges
Challenge 1: Factor Finder
Challenge 2: Graphical Equation Solver
Challenge 3: Summing a Series
Challenge 4: Solving Single-Variable Inequalities
Chapter 5: Playing with Sets and Probability
What’s a Set?
Set Construction
Subsets, Supersets, and Power Sets
Set Operations
Probability
Probability of Event A or Event B
Probability of Event A and Event B
Generating Random Numbers
Nonuniform Random Numbers
What You Learned
Programming Challenges
Challenge 1: Using Venn Diagrams to Visualize Relationships Between Sets
Challenge 2: Law of Large Numbers
Challenge 3: How Many Tosses Before You Run Out of Money?
Challenge 4: Shuffling a Deck of Cards
Challenge 5: Estimating the Area of a Circle
Chapter 6: Drawing Geometric Shapes and Fractals
Drawing Geometric Shapes with Matplotlib’s Patches
Drawing a Circle
Creating Animated Figures
Animating a Projectile’s Trajectory
Drawing Fractals
Transformations of Points in a Plane
Drawing the Barnsley Fern
What You Learned
Programming Challenges
Challenge 1: Packing Circles into a Square
Challenge 2: Drawing the Sierpinski Triangle
Challenge 3: Exploring Hénon’s Function
Challenge 4: Drawing the Mandelbrot Set
Chapter 7: Solving Calculus Problems
What Is a Function?
Domain and Range of a Function
An Overview of Common Mathematical Functions
Assumptions in SymPy
Finding the Limit of Functions
Continuous Compound Interest
Instantaneous Rate of Change
Finding the Derivative of Functions
A Derivative Calculator
Calculating Partial Derivatives
Higher-Order Derivatives and Finding the Maxima and Minima
Finding the Global Maximum Using Gradient Ascent
A Generic Program for Gradient Ascent
A Word of Warning About the Initial Value
The Role of the Step Size and Epsilon
Finding the Integrals of Functions
Probability Density Functions
What You Learned
Programming Challenges
Challenge 1: Verify the Continuity of a Function at a Point
Challenge 2: Implement the Gradient Descent
Challenge 3: Area Between Two Curves
Challenge 4: Finding the Length of a Curve
Afterword
Things to Explore Next
Project Euler
Python Documentation
Books
Getting Help
Conclusion
Appendix A: Software Installation
Microsoft Windows 7
Installing SymPy
Installing matplotlib-venn
Starting the Python Shell
Linux
Updating SymPy
Installing matplotlib-venn
Starting the Python Shell
Mac OS X
Updating SymPy
Installing matplotlib-venn
Starting the Python Shell
Appendix B: Overview of Python Topics
if __name__ == '__main__'
List Comprehensions
Dictionary Data Structure
Multiple Return Values
Exception Handling
Specifying Multiple Exception Types
The else Block
Reading Files in Python
Reading All the Lines at Once
Specifying the Filename as Input
Handling Errors When Reading Files
Reusing Code
Index
Resources
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About the Author