Essential Math for Data Science

Cover
Copyright
Table of Contents
Preface
	Conventions Used in This Book
	Using Code Examples
	O’Reilly Online Learning
	How to Contact Us
	Acknowledgments
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Appendix 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
Appendix B. Exercise Answers
	Chapter 1
	Chapter 2
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 6
	Chapter 7
Index
About the Author
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