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.
Table of Contents:
Introduction xix
Part 1: Getting Started
Chapter 1: Introduction to Python for Business Applications 3
Introducing Python for Business 3
Why Python, Not a Spreadsheet? 4
Setting Up Your Tools 5
Install Python with the Anaconda Distribution (Running Python on Your Machine) 5
Launch Jupyter Notebook 6
Cloud-friendly Alternatives 6
The Python Ecosystem 7
What Is a (Jupyter) Notebook? 8
Installing Libraries Locally or in a Notebook 8
Writing Your First Python Script 9
Summary 10
Continue Your Learning 10
Chapter 2: Basic Mathematical Operations in Python 11
Numbers, Variables, and Functions: The Foundations of Business Logic 11
Understanding Variables 12
Arithmetic in Python 13
Working with the math Module 14
Data Types in Python 14
Core Data Types 14
Why Data Types Matter 16
Converting Between Types 17
Business Data Structures: Arrays and Matrices 18
One-dimensional Arrays 18
Matrices: Two-dimensional Arrays 19
Data Manipulation Basics with Pandas 23
Constructing a DataFrame 23
First Looks: head(), info(), describe() 24
Working with Columns and Rows 24
Filtering with Booleans 25
Creating New Columns 25
Grouping and Aggregation 26
Joins and Merges 27
Reshaping: Pivot, Melt, Stack 28
Summary 28
Continue Your Learning 28
Chapter 3: Visualization for Business Decision-making 29
The Landscape of Visualization Tools in Python 29
Visualization Applications: Dashboarding Frameworks 30
Choosing the Right Visualization Tool for Your Work 31
Graphing Basics with Matplotlib 32
Understanding the Structure of a Plot 32
Creating and Working with Plots 33
Customizing Visualizations to Enhance Understanding 35
Plotting Options 36
Creating Effective Visuals to Communicate Business Data 37
Time-series Data and Line Charts 38
Cross-sectional Data and Bar or Pie Charts 38
Relational Data and Scatterplots 39
Other Charts You Can Create 41
Visualizing Trends and Patterns for Business Insights 42
Highlighting Seasonality and Long-term Growth 42
Comparing Categories and Segments 44
Visualizing Cumulative Effects 46
Smoothing Trends with Rolling Averages 47
Line Charts with Confidence Intervals Using Seaborn 49
Analyzing Relationships and Distributions with jointplot 52
Summary 55
Continue Your Learning 55
Part 2: Applying the Math
Chapter 4: Linear Algebra for Business and Finance 59
Working with Vectors and Matrices 59
Understanding Vectors 60
Understanding Matrix 61
Operations with Vectors and Matrices 62
Scalar Multiplication 63
The Dot Product 63
Norms (Vector Lengths) 64
Combining Matrices 64
Slicing Matrices 65
Matrix Multiplication 66
Transpose 67
Creating and Manipulating Vectors (and Matrices) with NumPy 67
Step 1: Compute Asset Returns from Prices 69
Step 2: Portfolio with Constant Weights 70
Step 3: Portfolio with Time-varying Weights 72
Comparing Strategies (Same Math, Different Inputs) 75
Eigenvalues and Eigenvectors: Business Applications 76
What Eigenvalues and Eigenvectors Represent 76
Why Eigenvalues Matter for Long-term Stability 77
Summary 80
Continue Your Learning 80
Chapter 5: Calculus for Business Problem Solving 83
Numerical Differentiation and Integration in Business Analytics 84
The Derivative: Finding the Rate of Change 84
The Second Derivative: Pinpointing the Point of Diminishing Returns 86
The Integral: Accumulating the Totals 87
The Calculus Ecosystem in Python 90
Numerical Calculus with NumPy 90
Symbolic Calculus with SymPy 91
Advanced Numerical Methods with SciPy 92
Choosing the Right Tool 93
Solving Business Growth and Pricing Models with Differential Equations 93
Sensitivity Analysis with Partial Derivatives 96
Case Study: Revenue, Cost, and Profit Analysis 98
Step 1: Understanding Marginal Cost (the Derivative of Cost) 99
Step 2: Understanding Marginal Revenue (the Derivative of Revenue) 100
Step 3: Finding the Sweet Spot with Marginal Profit 102
Summary 104
Continue Your Learning 104
Chapter 6: Optimization Techniques for Business Strategy 107
The Python Optimization Ecosystem 108
A Framework for Solving Most Optimization Problems 109
The Four-step Formulation Process 109
Understanding the Local vs. Global Optima Issue 110
Applying the Framework: Profit Maximization 110
Linear Programming 112
Constrained Optimization 116
The Geometry of Optimization 116
Visualizing the Difference Between Constrained and Unconstrained Optimization 119
Real-world Applications 122
Portfolio Allocation 122
Supply Chain and Operations 128
Integer Programming for Workforce Scheduling 131
Summary 134
Continue Your Learning 134
Chapter 7: Probability and Statistics for Business Analytics 137
The Python Statistics Ecosystems 137
Understanding Random Variables and Distributions in Business Contexts 138
Discrete vs. Continuous Distributions 139
The Most Common Business Distributions 140
Hypothesis Testing 144
Test Statistics 145
The p-value 146
The A/B Test 147
Confidence Intervals: The Other Side of the Coin 148
Linear Regression 149
Analyzing Marketing Effectiveness 151
Explaining Financial Risk Factors 153
Other Considerations 155
Logistic Regression 156
Predicting Customer Churn 156
Forecasting 161
Summary 164
Continue Your Learning 164
Chapter 8: Applied Business Problems with Math and Python 167
Building a Dynamic Loan Amortization Engine 168
Building a Simple Recommender System 171
Maximizing Yield with Constrained Optimization 173
Quality Control with Hypothesis Testing 177
Predicting Employee Attrition with Logistic Regression 179
Summary 185
Continue Your Learning 185
Part 3: Visualizing the Numbers
Chapter 9: Illustrating Time-series and Linear Data 189
Understanding Your Data Structure 189
Cross-sectional Data 190
Time-series Data 192
Panel Data 193
Visualizing Change Over Time (Time-series) 194
Time-series Diagnostics 195
Seasonality and Autocorrelation 201
Panel Data 206
Summary 208
Continue Your Learning 209
Chapter 10: Illustrating Cross-sectional Data 211
Data Categories 211
The Pie Chart 211
Donut Charts 213
Stacked Bar Charts 216
Correlations and Distributions 217
Bar Charts 218
Boxplots 220
Correlations in the Cross Section 222
Scatterplots 222
Correlation Heatmaps 225
The Pair Plot 227
Summary 229
Continue Your Learning 230
Essential Cross-sectional Functions 230
Chapter 11: Illustrating Alternative Data Types 233
Textual Analysis 233
The Word Cloud 234
N-grams 236
Visualizing Customer Sentiment 239
Geospatial Data 242
The Choropleth Map 243
The Marker Map 244
The Heatmap 246
Visualizing Networks 248
Visualizing Structure 249
Weighted Graphs 252
Summary 254
Continue Your Learning 254
Index 257
About the Author :
BLAKE RAYFIELD, PhD, is an Assistant Professor of Finance at the University of North Florida. He's a Fulbright Specialist with expertise in applying mathematical solutions to common, difficult business problems. His research has appeared in the Journal of Financial Research, the Quarterly Review of Economics and Finance, and the Review of Behavioral Finance.
