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Essential Math for Data Science by Thomas Nield Preface

1. Basic Math And Calculus Review (EsMthDS 2022)

• 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
• Partial Derivatives
• The Chain Rule
• Integrals
• Conclusion
• Exercises

2. Probability (EsMthDS 2022)

• 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 (EsMthDS 2022)

• Descriptive Statistics 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 (EsMthDS 2022)

• 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 (EsMthDS 2022)

• 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 (EsMthDS 2022)

• 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 (EsMthDS 2022)

• When to Use Neural Networks and Deep Learning
• A Simple Neural Network
• Activation Functions
• Forward Propogation
• Backpropogation
• Calculating the Weight and Bias Derivatives
• Stochastic Gradient Descent
• Using Scikit-learn
• Limitations of Neural Networks and Deep Learning
• Conclusions
• Exercise

8. Career Advice And The Path Forward (EsMthDS 2022)

• Data Science and Machine Learning 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 Adviser
• 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. Appendix (EsMthDS 2022)

• 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

Thomas Nield

Fair Use Source:

• 1098102932 (EsMthDS 2022)