Mathematics
These are my personal study notes taken while working through the Mathematics for Machine Learning and Data Science Specialization offered by DeepLearning.AI on Coursera. All theoretical content, definitions, and examples are derived from that course. My own contributions are limited to additional annotations, connections to telecommunications and network engineering, and Python implementations.
Source: Coursera. Mathematics for Machine Learning and Data Science Specialization. DeepLearning.AI. Retrieved from https://www.coursera.org/specializations/mathematics-for-machine-learning-and-data-science
Areas of Study
Linear Algebra
Linear algebra is about manipulating vectors and matrices to do powerful calculations.
Reference: https://www.coursera.org/learn/machine-learning-linear-algebra
- Systems of Equations
- Solving Systems of Linear Equations: Elimination
- Solving Systems of Linear Equations: Row Echelon Form and Rank
- Gaussian Elimination Algorithm
- Vector Algebra
- Linear Transformations
- Lab: Linear Transformations and Neural Networks
- Determinants In-depth
- Eigenvalues and Eigenvectors
- Lab: Interpreting Eigenvalues and Eigenvectors
- Dimensionality Reduction and PCA
- Lab: Eigenvalues in Action (Webpage Navigation and PCA)
Calculus
Differential and integral calculus, optimization methods.
Reference: https://www.coursera.org/learn/machine-learning-calculus
- Derivatives and Their Intuition
- Derivatives of Basic Functions
- Derivative Rules
- Optimization
- Log Loss
- Gradients
- Partial Derivatives
- Gradient Descent
- Gradient Descent in Multiple Variables
- Optimization Using Gradient Descent
- Lab: Linear Regression with Gradient Descent
- Optimization in Neural Networks
- Lab: Regression with a Perceptron
- Classification with a Perceptron
- Lab: Classification with a Perceptron
- Classification with a Neural Network
- Newton's Method
- Second Derivative
- Hessian Matrix
- Newton's Method for Multiple Variables
- Lab: Neural Network with Two Layers
Probability
Probability theory, random variables, distributions, and their properties.
Reference: https://www.coursera.org/learn/machine-learning-probability-and-statistics
- Introduction to Probability
- Conditional Probability
- Bayes Theorem
- Random Variables
- Probability Distributions (Discrete)
- Probability Distributions (Continuous)
- Uniform Distribution
- Normal Distribution
- Chi-Squared Distribution
- Lab: Intro to Pandas
- Lab: Rideshare Exploratory Data Analysis 1
- Expected Value, Median, and Mode
- Variance
- Skewness and Kurtosis
- Quantiles and Box Plots
- Joint Distributions
- Marginal and Conditional Distributions
- Covariance and Correlation
- Lab: Rideshare Exploratory Data Analysis 2
Statistics
Statistical inference, hypothesis testing, and regression.
Reference: https://www.coursera.org/learn/machine-learning-probability-and-statistics
- Populations and Samples
- Sample Variance
- Central Limit Theorem
- Point Estimation and Maximum Likelihood
- MLE and Linear Regression
- Bayesian Statistics
- Lab: Linear Regression and World Happiness
- Confidence Intervals
- Hypothesis Testing
- t-Distribution and t-Tests
- Comparing Two Populations
- Lab: Confidence Intervals and Hypothesis Testing
Notes for graduate research and professional development.