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

by Thomas Nield

Overview

Master the math needed to excel in data science, machine learning, and statistics. In this book author Thomas Nield guides you through areas like calculus, probability, linear algebra, and statistics and how they apply to techniques like linear regression, logistic regression, and neural networks. Along the way you'll also gain practical insights into the state of data science and how to use those insights to maximize your career.

Learn how to:

• Use Python code and libraries like SymPy, NumPy, and scikit-learn to explore essential mathematical concepts like calculus, linear algebra, statistics, and machine learning
• Understand techniques like linear regression, logistic regression, and neural networks in plain English, with minimal mathematical notation and jargon
• Perform descriptive statistics and hypothesis testing on a dataset to interpret p-values and statistical significance
• Manipulate vectors and matrices and perform matrix decomposition
• Integrate and build upon incremental knowledge of calculus, probability, statistics, and linear algebra, and apply it to regression models including neural networks
• Navigate practically through a data science career and avoid common pitfalls, assumptions, and biases while tuning your skill set to stand out in the job market

Product Details

ISBN-13:	9781098102937
Publisher:	O'Reilly Media, Incorporated
Publication date:	07/05/2022
Pages:	349
Sales rank:	225,654
Product dimensions:	7.00(w) x 9.19(h) x 0.73(d)

About the Author

Thomas Nield is the founder of Nield Consulting Group as well as an instructor at O'Reilly Media and University of Southern California. He enjoys making technical content relatable and relevant to those unfamiliar or intimidated by it. Thomas regularly teaches classes on data analysis, machine learning, mathematical optimization, and practical artificial intelligence. At USC he teaches AI System Safety, developing systematic approaches for identifying AI-related hazards in aviation and ground vehicles. He's authored two books, including Getting Started with SQL (O'Reilly) and Learning RxJava (Packt).



He is also the founder and inventor of Yawman Flight, a company developing universal handheld flight controls for flight simulation and unmanned aerial vehicles.

Table of Contents

Preface ix

1 Basic Math and Calculus Review 1

Number Theory 2

Order of Operations 3

Variables 5

Functions 6

Summations 11

Exponents 13

Logarithms 16

Euler's Number and Natural Logarithms 18

Euler's Number 18

Natural Logarithms 21

Limits 22

Derivatives 24

Partial Derivatives 28

The Chain Rule 31

Integrals 33

Conclusion 39

Exercises 39

2 Probability 41

Understanding Probability 42

Probability Versus Statistics 43

Probability Math 44

Joint Probabilities 44

Union Probabilities 45

Conditional Probability and Bayes' Theorem 47

Joint and Union Conditional Probabilities 49

Binomial Distribution 51

Beta Distribution 53

Conclusion 60

Exercises 61

3 Descriptive and Inferential Statistics 63

What Is Data? 63

Descriptive Versus Inferential Statistics 65

Populations, Samples, and Bias 66

Descriptive Statistics 69

Mean and Weighted Mean 70

Median 71

Mode 73

Variance and Standard Deviation 73

The Normal Distribution 78

The Inverse CDF 85

Z-Scores 87

Inferential Statistics 89

The Central Limit Theorem 89

Confidence Intervals 92

Understanding P-Values 95

Hypothesis Testing 96

The T-Distribution: Dealing with Small Samples 104

Big Data Considerations and the Texas Sharpshooter Fallacy 105

Conclusion 107

Exercises 107

4 Linear Algebra 109

What Is a Vector? 110

Adding and Combining Vectors 114

Scaling Vectors 116

Span and Linear Dependence 119

Linear Transformations 121

Basis Vectors 121

Matrix Vector Multiplication 124

Matrix Multiplication 129

Determinants 131

Special Types of Matrices 136

Square Matrix 136

Identity Matrix 136

Inverse Matrix 136

Diagonal Matrix 137

Triangular Matrix 137

Sparse Matrix 138

Systems of Equations and Inverse Matrices 138

Eigenvectors and Eigenvalues 142

Conclusion 145

Exercises 146

5 Linear Regression 147

A Basic Linear Regression 149

Residuals and Squared Errors 153

Finding the Best Fit Line 157

Closed Form Equation 157

Inverse Matrix Techniques 158

Gradient Descent 161

Overfitting and Variance 167

Stochastic Gradient Descent 169

The Correlation Coefficient 171

Statistical Significance 174

Coefficient of Determination 179

Standard Error of the Estimate 180

Prediction Intervals 181

Train/Test Splits 185

Multiple Linear Regression 191

Conclusion 191

Exercises 192

6 Logistic Regression and Classification 193

Understanding Logistic Regression 193

Performing a Logistic Regression 196

Logistic Function 196

Fitting the Logistic Curve 198

Multivariable Logistic Regression 204

Understanding the Log-Odds 208

R-Squared 211

P-Values 216

Train/Test Splits 218

Confusion Matrices 219

Bayes' Theorem and Classification 222

Receiver Operator Characteristics/Area Under Curve 223

Class Imbalance 225

Conclusion 226

Exercises 226

7 Neural Networks 227

When to Use Neural Networks and Deep Learning 228

A Simple Neural Network 229

Activation Functions 231

Forward Propagation 237

Backpropagation 243

Calculating the Weight and Bias Derivatives 243

Stochastic Gradient Descent 248

Using scikit-learn 251

Limitations of Neural Networks and Deep Learning 253

Conclusion 256

Exercise 256

8 Career Advice and the Path Forward 257

Redefining Data Science 258

A Brief History of Data Science 260

Finding Your Edge 263

SQL Proficiency 263

Programming Proficiency 266

Data Visualization 269

Knowing Your Industry 270

Productive Learning 272

Practitioner Versus Advisor 272

What to Watch Out For in Data Science Jobs 275

Role Definition 275

Organizational Focus and Buy-In 276

Adequate Resources 278

Reasonable Objectives 279

Competing with Existing Systems 280

A Role Is Not What You Expected 282

Does Your Dream Job Not Exist? 283

Where Do I Go Now? 284

Conclusion 285

A Supplemental Topics 287

B Exercise Answers 309

Index 323