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