The Statistics and Calculus with Python Workshop: A comprehensive introduction to mathematics in Python for artificial intelligence applications

Cover
FM
Copyright
Table of Contents
Preface
Chapter 1: Fundamentals of Python
	Introduction
	Control Flow Methods
		if Statements
		Exercise 1.01: Divisibility with Conditionals
		Loops
			The while Loop
			The for Loop
		Exercise 1.02: Number Guessing Game
	Data Structures
		Strings
		Lists
		Exercise 1.03: Multi-Dimensional Lists
		Tuples
		Sets
		Dictionaries
		Exercise 1.04: Shopping Cart Calculations
	Functions and Algorithms
		Functions
		Exercise 1.05: Finding the Maximum
		Recursion
		Exercise 1.06: The Tower of Hanoi
		Algorithm Design
		Exercise 1.07: The N-Queens Problem
	Testing, Debugging, and Version Control
		Testing
		Debugging
		Exercise 1.08: Testing for Concurrency
		Version Control
		Exercise 1.09: Version Control with Git and GitHub
		Activity 1.01: Building a Sudoku Solver
	Summary
Chapter 2: Python's Main Tools for Statistics
	Introduction
	Scientific Computing and NumPy Basics
		NumPy Arrays
		Vectorization
		Exercise 2.01: Timing Vectorized Operations in NumPy
		Random Sampling
	Working with Tabular Data in pandas
		Initializing a DataFrame Object
		Accessing Rows and Columns
		Manipulating DataFrames
		Exercise 2.02: Data Table Manipulation
		Advanced Pandas Functionalities
		Exercise 2.03: The Student Dataset
	Data Visualization with Matplotlib and Seaborn
		Scatter Plots
		Line Graphs
		Bar Graphs
		Histograms
		Heatmaps
		Exercise 2.04: Visualization of Probability Distributions
		Visualization Shorthand from Seaborn and Pandas
		Activity 2.01: Analyzing the Communities and Crime Dataset
	Summary
Chapter 3: Python's Statistical Toolbox
	Introduction
	An Overview of Statistics
	Types of Data in Statistics
		Categorical Data
		Exercise 3.01: Visualizing Weather Percentages
		Numerical Data
		Exercise 3.02: Min-Max Scaling
		Ordinal Data
	Descriptive Statistics
		Central Tendency
		Dispersion
		Exercise 3.03: Visualizing Probability Density Functions
		Python-Related Descriptive Statistics
	Inferential Statistics
		T-Tests
		Correlation Matrix
		Exercise 3.04: Identifying and Testing Equality of Means
		Statistical and Machine Learning Models
		Exercise 3.05: Model Selection
	Python's Other Statistics Tools
		Activity 3.01: Revisiting the Communities and Crimes Dataset
	Summary
Chapter 4: Functions and Algebra with Python
	Introduction
	Functions
		Common Functions
		Domain and Range
		Function Roots and Equations
		The Plot of a Function
		Exercise 4.01: Function Identification from Plots
	Function Transformations
		Shifts
		Scaling
		Exercise 4.02: Function Transformation Identification
	Equations
		Algebraic Manipulations
		Factoring
		Using Python
		Exercise 4.03: Introduction to Break-Even Analysis
	Systems of Equations
		Systems of Linear Equations
		Exercise 4.04: Matrix Solution with NumPy
		Systems of Non-Linear Equations
		Activity 4.01: Multi-Variable Break-Even Analysis
	Summary
Chapter 5: More Mathematics with Python
	Introduction
	Sequences and Series
		Arithmetic Sequences
		Generators
		Exercise 5.01: Determining the nth Term of an Arithmetic Sequence and Arithmetic Series
		Geometric Sequences
		Exercise 5.02: Writing a Function to Find the Next Term of the Sequence
		Recursive Sequences
		Exercise 5.03: Creating a Custom Recursive Sequence
	Trigonometry
		Basic Trigonometric Functions
		Exercise 5.04: Plotting a Right-Angled Triangle
		Inverse Trigonometric Functions
		Exercise 5.05: Finding the Shortest Way to the Treasure Using Inverse Trigonometric Functions
		Exercise 5.06: Finding the Optimal Distance from an Object
	Vectors
		Vector Operations
		Exercise 5.07: Visualizing Vectors
	Complex Numbers
		Basic Definitions of Complex Numbers
		Polar Representation and Euler's Formula
		Exercise 5.08: Conditional Multiplication of Complex Numbers
		Activity 5.01: Calculating Your Retirement Plan Using Series
	Summary
Chapter 6: Matrices and Markov Chains with Python
	Introduction
	Matrix Operations on a Single Matrix
		Basic Operations on a Matrix
		Inspecting a Matrix
		Exercise 6.01: Calculating the Time Taken for Sunlight to Reach Earth Each Day
		Operations and Multiplication in Matrices
		Axes in a Matrix
		Exercise 6.02: Matrix Search
		Multiple Matrices
			Broadcasting
	Operations on Multiple Matrices
		Identity Matrix
		The eye Function
		Inverse of a Matrix
		Logical Operators
		Outer Function or Vector Product
	Solving Linear Equations Using Matrices
		Exercise 6.03: Use of Matrices in Performing Linear Equations
	Transition Matrix and Markov Chains
		Fundamentals of Markov Chains
			Stochastic versus Deterministic Models
			Transition State Diagrams
			Transition Matrices
		Exercise 6.04: Finding the Probability of State Transitions
			Markov Chains and Markov Property
		Activity 6.01: Building a Text Predictor Using a Markov Chain
	Summary
Chapter 7: Doing Basic Statistics with Python
	Introduction
	Data Preparation
		Introducing the Dataset
		Introducing the Business Problem
		Preparing the Dataset
		Exercise 7.01: Using a String Column to Produce a Numerical Column
	Calculating and Using Descriptive Statistics
		The Need for Descriptive Statistics
		A Brief Refresher of Statistical Concepts
		Using Descriptive Statistics
		Exercise 7.02: Calculating Descriptive Statistics
	Exploratory Data Analysis
		What Is EDA?
		Univariate EDA
		Bi-variate EDA: Exploring Relationships Between Variables
		Exercise 7.03: Practicing EDA
		Activity 7.01: Finding Out Highly Rated Strategy Games
	Summary
Chapter 8: Foundational Probability Concepts and Their Applications
	Introduction
	Randomness, Probability, and Random Variables
		Randomness and Probability
		Foundational Probability Concepts
		Introduction to Simulations with NumPy
		Exercise 8.01: Sampling with and without Replacement
		Probability as a Relative Frequency
		Defining Random Variables
		Exercise 8.02: Calculating the Average Wins in Roulette
	Discrete Random Variables
		Defining Discrete Random Variables
		The Binomial Distribution
		Exercise 8.03: Checking If a Random Variable Follows a Binomial Distribution
	Continuous Random Variables
		Defining Continuous Random Variables
		The Normal Distribution
		Some Properties of the Normal Distribution
		Exercise 8.04: Using the Normal Distribution in Education
		Activity 8.01: Using the Normal Distribution in Finance
	Summary
Chapter 9: Intermediate Statistics with Python
	Introduction
	Law of Large Numbers
		Python and Random Numbers
		Exercise 9.01: The Law of Large Numbers in Action
		Exercise 9.02: Coin Flipping Average over Time
		A Practical Application of the Law of Large Numbers Seen in the Real World
		Exercise 9.03: Calculating the Average Winnings for a Game of Roulette If We Constantly Bet on Red
	Central Limit Theorem
		Normal Distribution and the CLT
		Random Sampling from a Uniform Distribution
		Exercise 9.04: Showing the Sample Mean for a Uniform Distribution
		Random Sampling from an Exponential Distribution
		Exercise 9.05: Taking a Sample from an Exponential Distribution
	Confidence Intervals
		Calculating the Confidence Interval of a Sample Mean
		Exercise 9.06: Finding the Confidence Interval of Polling Figures
		Small Sample Confidence Interval
		Confidence Interval for a Proportion
	Hypothesis Testing
		Parts of a Hypothesis Test
		The Z-Test
		Exercise 9.07: The Z-Test in Action
		Proportional Z-Test
		The T-Test
		Exercise 9.08: The T-Test
		2-Sample T-Test or A/B Testing
		Exercise 9.09: A/B Testing Example
		Introduction to Linear Regression
		Exercise 9.10: Linear Regression
		Activity 9.01: Standardized Test Performance
	Summary
Chapter 10: Foundational Calculus with Python
	Introduction
	Writing the Derivative Function
		Exercise 10.01: Finding the Derivatives of Other Functions
		Finding the Equation of the Tangent Line
	Calculating Integrals
	Using Trapezoids
		Exercise 10.02: Finding the Area Under a Curve
	Using Integrals to Solve Applied Problems
		Exercise 10.03: Finding the Volume of a Solid of Revolution
	Using Derivatives to Solve Optimization Problems
		Exercise 10.04: Find the Quickest Route
		Exercise 10.05: The Box Problem
		Exercise 10.06: The Optimal Can
		Exercise 10.07:  Calculating the Distance between Two Moving Ships
		Activity 10.01: Maximum Circle-to-Cone Volume
	Summary
Chapter 11: More Calculus with Python
	Introduction
	Length of a Curve
		Exercise 11.01: Finding the Length of a Curve
		Exercise 11.02: Finding the Length of a Sine Wave
	Length of a Spiral
		Exercise 11.03: Finding the Length of the Polar Spiral Curve
		Exercise 11.04: Finding the Length of Insulation in a Roll
		Exercise 11.05: Finding the Length of an Archimedean Spiral
	Area of a Surface
		The Formulas
		Exercise 11.06: Finding the Area of a 3D Surface – Part 1
		Exercise 11.07: Finding the Area of a 3D Surface – Part 2
		Exercise 11.08: Finding the Area of a Surface – Part 3
	Infinite Series
		Polynomial Functions
		Series
		Convergence
		Exercise 11.09: Calculating 10 Correct Digits of π
		Exercise 11.10: Calculating the Value of π Using Euler's Expression
		A 20th Century Formula
		Interval of Convergence
		Exercise 11.11: Determining the Interval of Convergence – Part 1
		Exercise 11.12: Determining the Interval of Convergence – Part 2
		Exercise 11.13: Finding the Constant
		Activity 11.01: Finding the Minimum of a Surface
	Summary
Chapter 12: Intermediate Calculus with Python
	Introduction
	Differential Equations
	Interest Calculations
		Exercise 12.01: Calculating Interest
		Exercise 12.02: Calculating Compound Interest – Part 1
		Exercise 12.03: Calculating Compound Interest – Part 2
		Exercise 12.04: Calculating Compound Interest – Part 3
		Exercise 12.05: Becoming a Millionaire
	Population Growth
		Exercise 12.06: Calculating the Population Growth Rate – Part 1
		Exercise 12.07: Calculating the Population Growth Rate – Part 2
	Half-Life of Radioactive Materials
		Exercise 12.08: Measuring Radioactive Decay
		Exercise 12.09: Measuring the Age of a Historical Artifact
	Newton's Law of Cooling
		Exercise 12.10: Calculating the Time of Death
		Exercise 12.11: Calculating the Rate of Change in Temperature
	Mixture Problems
		Exercise 12.12: Solving Mixture Problems – Part 1
		Exercise 12.13: Solving Mixture Problems – Part 2
		Exercise 12.14: Solving Mixture Problems – Part 3
		Exercise 12.15: Solving Mixture Problems – Part 4
	Euler's Method
		Exercise 12.16: Solving Differential Equations with Euler's Method
		Exercise 12.17: Using Euler's Method to Evaluate a Function
		Runge-Kutta Method
		Exercise 12.18: Implementing the Runge-Kutta Method
		Pursuit Curves
		Exercise 12.19: Finding Where the Predator Catches the Prey
		Exercise 12.20: Using Turtles to Visualize Pursuit Curves
		Position, Velocity, and Acceleration
		Exercise 12.21: Calculating the Height of a Projectile above the Ground
		An Example of Calculating the Height of a Projectile with Air Resistance
		Exercise 12.22: Calculating the Terminal Velocity
		Activity 12.01: Finding the Velocity and Location of a Particle
	Summary
Appendix
Index