The Statistics and Calculus with Python Workshop by Farrell, Peter -- Read -- Imperial Library of Trantor

Index

The Statistics and Calculus with Python Workshop Preface

About the Book

Audience About the Chapters Conventions Code Presentation Setting up Your Environment Software Requirements Installation and Setup Installing Python Project Jupyter Installing Libraries Accessing the Code Files

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

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

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

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

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

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

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

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

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

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

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

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

1. Fundamentals of Python

Activity 1.01: Building a Sudoku Solver

2. Python's Main Tools for Statistics

Activity 2.01: Analyzing the Communities and Crime Dataset

3. Python's Statistical Toolbox

Activity 3.01: Revisiting the Communities and Crimes Dataset

4. Functions and Algebra with Python

Activity 4.01: Multi-Variable Break-Even Analysis

5. More Mathematics with Python

Activity 5.01: Calculating Your Retirement Plan Using Series

6. Matrices and Markov Chains with Python

Activity 6.01: Building a Text Predictor Using a Markov Chain

7. Doing Basic Statistics with Python

Activity 7.01: Finding Out Highly Rated Strategy Games

8. Foundational Probability Concepts and Their Applications

Activity 8.01: Using the Normal Distribution in Finance

9. Intermediate Statistics with Python

Activity 9.01: Standardized Test Performance

10. Foundational Calculus with Python

Activity 10.01: Maximum Circle-to-Cone Volume

11. More Calculus with Python

Activity 11.01: Finding the Minimum of a Surface

12. Intermediate Calculus with Python

Activity 12.01: Finding the Velocity and Location of a Particle

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