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Applied Math with Python
Solve Real-World Problems with Python-Based Solutions
Blake Rayfield (Author)
9781394370757, Wiley
Paperback / softback, published 1 June 2026
288 pages
22.9 x 18.3 x 1.5 cm, 0.59 kg
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: 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.
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
Subject Areas: Mathematics [PB]
