Essential Math for Data Science: Take Control of Your Data with Fundamental Linear Algebra, Probability, and Statistics, ISBN-13: 978-1098102937

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Essential Math for Data Science: Take Control of Your Data with Fundamental Linear Algebra, Probability, and Statistics, ISBN-13: 978-1098102937

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• Publisher: ‎ O’Reilly Media; 1st edition (July 5, 2022)
• Language: ‎ English
• 349 pages
• ISBN-10: ‎ 1098102932
• ISBN-13: ‎ 978-1098102937

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

Table of Contents:

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

Matrix Decomposition

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

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.

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