Applied math with Python: Solve real-world problems with Python-based solutions

COVER....1

HALF TITLE PAGE....3

TITLE PAGE....5

COPYRIGHT....6

ACKNOWLEDGMENTS....9

ABOUT THE AUTHOR....11

ABOUT THE TECHNICAL EDITOR....13

CONTENTS....15

INTRODUCTION....21

PART 1: GETTING STARTED....25

CHAPTER 1: INTRODUCTION TO PYTHON FOR BUSINESS APPLICATIONS....27

Introducing Python for Business....27

Why Python, Not a Spreadsheet?....28

Setting Up Your Tools....29

Install Python with the Anaconda Distribution (Running Python on Your Machine)....29

Launch Jupyter Notebook....30

Cloud-friendly Alternatives....30

The Python Ecosystem....31

What Is a (Jupyter) Notebook?....32

Installing Libraries Locally or in a Notebook....32

Writing Your First Python Script....33

Summary....34

Continue Your Learning....34

CHAPTER 2: BASIC MATHEMATICAL OPERATIONS IN PYTHON....35

Numbers, Variables, and Functions: The Foundations of Business Logic....35

Understanding Variables....36

Arithmetic in Python....37

Working with the math Module....38

Data Types in Python....38

Core Data Types....38

Why Data Types Matter....40

Converting Between Types....41

Business Data Structures: Arrays and Matrices....42

One-dimensional Arrays....42

Matrices: Two-dimensional Arrays....43

Data Manipulation Basics with Pandas....47

Constructing a DataFrame....47

First Looks: head(), info(), describe()....48

Working with Columns and Rows....48

Filtering with Booleans....49

Creating New Columns....49

Grouping and Aggregation....50

Joins and Merges....51

Reshaping: Pivot, Melt, Stack....52

Summary....52

Continue Your Learning....52

CHAPTER 3: VISUALIZATION FOR BUSINESS DECISION-MAKING....53

The Landscape of Visualization Tools in Python....53

Visualization Applications: Dashboarding Frameworks....54

Choosing the Right Visualization Tool for Your Work....55

Graphing Basics with Matplotlib....56

Understanding the Structure of a Plot....56

Creating and Working with Plots....57

Customizing Visualizations to Enhance Understanding....59

Plotting Options....60

Creating Effective Visuals to Communicate Business Data....61

Time-series Data and Line Charts....62

Cross-sectional Data and Bar or Pie Charts....62

Relational Data and Scatterplots....63

Other Charts You Can Create....65

Visualizing Trends and Patterns for Business Insights....66

Highlighting Seasonality and Long-term Growth....66

Comparing Categories and Segments....68

Visualizing Cumulative Effects....70

Smoothing Trends with Rolling Averages....71

Line Charts with Confidence Intervals Using Seaborn....73

Analyzing Relationships and Distributions with jointplot....76

Summary....79

Continue Your Learning....79

PART 2: APPLYING THE MATH....81

CHAPTER 4: LINEAR ALGEBRA FOR BUSINESS AND FINANCE....83

Working with Vectors and Matrices....83

Understanding Vectors....84

Understanding Matrix....85

Operations with Vectors and Matrices....86

Scalar Multiplication....87

The Dot Product....87

Norms (Vector Lengths)....88

Combining Matrices....88

Slicing Matrices....89

Matrix Multiplication....90

Transpose....91

Creating and Manipulating Vectors (and Matrices) with NumPy....91

Step 1: Compute Asset Returns from Prices....93

Step 2: Portfolio with Constant Weights....94

Step 3: Portfolio with Time-varying Weights....96

Comparing Strategies (Same Math, Different Inputs....99

Eigenvalues and Eigenvectors: Business Applications....100

What Eigenvalues and Eigenvectors Represent....100

Why Eigenvalues Matter for Long-term Stability....101

Summary....104

Continue Your Learning....104

CHAPTER 5: CALCULUS FOR BUSINESS PROBLEM SOLVING....107

Numerical Differentiation and Integration in Business Analytics....108

The Derivative: Finding the Rate of Change....108

The Second Derivative: Pinpointing the Point of Diminishing Returns....110

The Integral: Accumulating the Totals....111

The Calculus Ecosystem in Python....114

Numerical Calculus with NumPy....114

Symbolic Calculus with SymPy....115

Advanced Numerical Methods with SciPy....116

Choosing the Right Tool....117

Solving Business Growth and Pricing Models with Differential Equations....117

Sensitivity Analysis with Partial Derivatives....120

Case Study: Revenue, Cost, and Profit Analysis....122

Step 1: Understanding Marginal Cost (the Derivative of Cost)....123

Step 2: Understanding Marginal Revenue (the Derivative of Revenue)....124

Step 3: Finding the Sweet Spot with Marginal Profit....126

Summary....128

Continue Your Learning....128

CHAPTER 6: OPTIMIZATION TECHNIQUES FOR BUSINESS STRATEGY....131

The Python Optimization Ecosystem....132

A Framework for Solving Most Optimization Problems....133

The Four-step Formulation Process....133

Understanding the Local vs. Global Optima Issue....134

Applying the Framework: Profit Maximization....134

Linear Programming....136

Constrained Optimization....140

The Geometry of Optimization....140

Visualizing the Difference Between Constrained and Unconstrained Optimization....143

Real-world Applications....146

Portfolio Allocation....146

Supply Chain and Operations....152

Integer Programming for Workforce Scheduling....155

Summary....158

Continue Your Learning....158

CHAPTER 7: PROBABILITY AND STATISTICS FOR BUSINESS ANALYTICS....161

The Python Statistics Ecosystems....161

Understanding Random Variables and Distributions in Business Contexts....162

Discrete vs. Continuous Distributions....163

The Most Common Business Distributions....164

Hypothesis Testing....168

Test Statistics....169

The p-value....170

The AB Test....171

Confidence Intervals: The Other Side of the Coin....172

Linear Regression....173

Analyzing Marketing Effectiveness....175

Explaining Financial Risk Factors....177

Other Considerations....179

Logistic Regression....180

Predicting Customer Churn....180

Forecasting....185

Summary....188

Continue Your Learning....188

CHAPTER 8: APPLIED BUSINESS PROBLEMS WITH MATH AND PYTHON....191

Building a Dynamic Loan Amortization Engine....192

Building a Simple Recommender System....195

Maximizing Yield with Constrained Optimization....197

Quality Control with Hypothesis Testing....201

Predicting Employee Attrition with Logistic Regression....203

Summary....209

Continue Your Learning....209

PART 3: VISUALIZING THE NUMBERS ....211

CHAPTER 9: ILLUSTRATING TIME-SERIES AND LINEAR DATA....213

Understanding Your Data Structure....213

Cross-sectional Data....214

Time-series Data....216

Panel Data....217

Visualizing Change Over Time (Time-series)....218

Time-series Diagnostics....219

Seasonality and Autocorrelation....225

Panel Data....230

Summary....232

Continue Your Learning....233

CHAPTER 10: ILLUSTRATING CROSS-SECTIONAL DATA....235

Data Categories....235

The Pie Chart....235

Donut Charts....237

Stacked Bar Charts....240

Correlations and Distributions....241

Bar Charts....242

Boxplots....244

Correlations in the Cross Section....246

Scatterplots....246

Correlation Heatmaps....249

The Pair Plot....251

Summary....253

Continue Your Learning....254

Essential Cross-sectional Functions....254

CHAPTER 11: ILLUSTRATING ALTERNATIVE DATA TYPES....257

Textual Analysis....257

The Word Cloud....258

N-grams....260

Visualizing Customer Sentiment....263

Geospatial Data....266

The Choropleth Map....267

The Marker Map....268

The Heatmap....270

Visualizing Networks....272

Visualizing Structure....273

Weighted Graphs....276

Summary....278

Continue Your Learning....278

INDEX....281

EULA....286

A step-by-step guide for using Python to transform abstract mathematical concepts into effective, on-the-ground scripts that solve real-world business problems

Applied Math with Python: Solve Real-World Problems with Python-Based Solutions is a detailed, step-by-step guide for business professionals, analysts, and data scientists interested in using Python to perform crucial organizational tasks: optimizing inefficient supply chains, calculating probabilities, forecasting financial performance, mining customer data for new insights, and more.

Author, researcher, and Assistant Professor of Finance at the University of North Florida, Blake Rayfield uses practical examples and hands-on exercises to explain how to combine concepts from optimization, probability, statistics, and other branches of mathematics with the Python language to solve difficult, common business problems. You’ll discover how marketing managers can use Python to create useful customer segments, how to model revenue growth, and how to allocate limited resources in a product launch or expansion.

Inside the book:

• Modular, plug-and-play strategies for solving hard problems in Python in situations where a spreadsheet is inadequate
• Instructions for building effective, scalable Python scripts incorporating many of the most powerful Python libraries, including pandas, NumPy, matplotlib, seaborn, scikit-learn, and Plotly
• Start-to-finish coverage for business professionals – from building a Python scripting environment on your local computer or in a cloud environment to designing, writing, testing, and running a functional script

Perfect for entrepreneurs, analysts, managers, and professionals working in AI, data science, and finance, Applied Math with Python is an expert guide for transforming abstract mathematical concepts into useful, repeatable, scalable solutions you can put to work immediately in your team and in your organization.