Essential Math for Data Science: Take Control of Your Data with Fundamental Linear Algebra, Probability, and Statistics

Preface
    Conventions Used in This Book
    Using Code Examples
    O’Reilly Online Learning
    How to Contact Us
    Acknowledgments
1. Basic Math and Calculus Review
    Number Theory
    Order of Operations
    Variables
    Functions
    Summations
    Exponents
    Logarithms
    Euler’s Number and Natural Logarithms
        Euler’s Number
        Natural Logarithms
    Limits
    Derivatives
        Partial Derivatives
        The Chain Rule
    Integrals
    Conclusion
    Exercises
2. Probability
    Understanding Probability
        Probability Versus Statistics
    Probability Math
        Joint Probabilities
        Union Probabilities
        Conditional Probability and Bayes’ Theorem
        Joint and Union Conditional Probabilities
    Binomial Distribution
    Beta Distribution
    Conclusion
    Exercises
3. Descriptive and Inferential Statistics
    What Is Data?
    Descriptive Versus Inferential Statistics
    Populations, Samples, and Bias
    Descriptive Statistics
        Mean and Weighted Mean
        Median
        Mode
        Variance and Standard Deviation
        The Normal Distribution
        The Inverse CDF
        Z-Scores
    Inferential Statistics
        The Central Limit Theorem
        Confidence Intervals
        Understanding P-Values
        Hypothesis Testing
    The T-Distribution: Dealing with Small Samples
    Big Data Considerations and the Texas Sharpshooter Fallacy
    Conclusion
    Exercises
4. Linear Algebra
    What Is a Vector?
        Adding and Combining Vectors
        Scaling Vectors
        Span and Linear Dependence
    Linear Transformations
        Basis Vectors
        Matrix Vector Multiplication
    Matrix Multiplication
    Determinants
    Special Types of Matrices
        Square Matrix
        Identity Matrix
        Inverse Matrix
        Diagonal Matrix
        Triangular Matrix
        Sparse Matrix
    Systems of Equations and Inverse Matrices
    Eigenvectors and Eigenvalues
    Conclusion
    Exercises
5. Linear Regression
    A Basic Linear Regression
    Residuals and Squared Errors
    Finding the Best Fit Line
        Closed Form Equation
        Inverse Matrix Techniques
        Gradient Descent
    Overfitting and Variance
    Stochastic Gradient Descent
    The Correlation Coefficient
    Statistical Significance
    Coefficient of Determination
    Standard Error of the Estimate
    Prediction Intervals
    Train/Test Splits
    Multiple Linear Regression
    Conclusion
    Exercises
6. Logistic Regression and Classification
    Understanding Logistic Regression
    Performing a Logistic Regression
        Logistic Function
        Fitting the Logistic Curve
    Multivariable Logistic Regression
    Understanding the Log-Odds
    R-Squared
    P-Values
    Train/Test Splits
    Confusion Matrices
    Bayes’ Theorem and Classification
    Receiver Operator Characteristics/Area Under Curve
    Class Imbalance
    Conclusion
    Exercises
7. Neural Networks
    When to Use Neural Networks and Deep Learning
    A Simple Neural Network
        Activation Functions
        Forward Propagation
    Backpropagation
        Calculating the Weight and Bias Derivatives
        Stochastic Gradient Descent
    Using scikit-learn
    Limitations of Neural Networks and Deep Learning
    Conclusion
    Exercise
8. Career Advice and the Path Forward
    Redefining Data Science
    A Brief History of Data Science
    Finding Your Edge
        SQL Proficiency
        Programming Proficiency
        Data Visualization
        Knowing Your Industry
        Productive Learning
        Practitioner Versus Advisor
    What to Watch Out For in Data Science Jobs
        Role Definition
        Organizational Focus and Buy-In
        Adequate Resources
        Reasonable Objectives
        Competing with Existing Systems
        A Role Is Not What You Expected
    Does Your Dream Job Not Exist?
    Where Do I Go Now?
    Conclusion
A. Supplemental Topics
    Using LaTeX Rendering with SymPy
    Binomial Distribution from Scratch
    Beta Distribution from Scratch
    Deriving Bayes’ Theorem
    CDF and Inverse CDF from Scratch
    Use e to Predict Event Probability Over Time
    Hill Climbing and Linear Regression
    Hill Climbing and Logistic Regression
    A Brief Intro to Linear Programming
    MNIST Classifier Using scikit-learn
B. Exercise Answers
    Chapter 1
    Chapter 2
    Chapter 3
    Chapter 4
    Chapter 5
    Chapter 6
    Chapter 7
Index
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