Essential Math for Data Science

Description

Preface 1. Basic Math and Calculus Review Number Theory Order of Operations Variables Functions Summations Exponents Logarithms Euler’s Number and Natural Logarithms Natural Logarithms Limits Derivatives 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 Cumulative Density Function (CDF) Inferential Statistics The Central Limit Theorem Confidence Intervals Understanding P-Values Hypothesis Testing The T-Distribution: Dealing with Small Samples Big Data Considerations and Texas Sharpshooter Fallacy Conclusions 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 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 Conclusions 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 the Confusion Matrix Reciever Operator Characteristics (ROC)/Area Under Curve (AUC) Class Imbalance Conclusions Exercises 7. Neural Networks When to Use Neural Networks and Deep Learning A Simple Neural Network Activation Functions Forward Propogation Backpropogation The Chain Rule Calculating the Weight and Bias Derivatives Stochastic Gradient Descent Using Scikit-Learn Limitations of Neural Networks and Deep Learning Conclusions About the Author