Mathematics for Machine Learning
Unlock the mathematical foundations of machine learning and gain the skills to build, analyze, and optimize intelligent systems.
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Linear Algebra Fundamentals
Unit 1: Vectors and Matrices
Intro to Vectors
Vector Operations
Intro to Matrices
Matrix Operations
Matrix Multiplication
Unit 2: Linear Independence and Span
Linear Combinations
Linear Independence
Span of Vectors
Basis and Dimension
Rank of a Matrix
Unit 3: Eigenvalues and Eigenvectors
Intro to Eigenvalues
Characteristic Equation
Finding Eigenvectors
Diagonalization
Applications
Unit 4: Singular Value Decomposition
Intro to SVD
Singular Values
Calculating SVD
Dimensionality Reduction
Applications of SVD
Calculus Essentials for Machine Learning
Unit 1: Introduction to Calculus
What is Calculus?
Functions & Their Graphs
Limits: The Foundation
Continuity Explained
Recap and Key Concepts
Unit 2: Single-Variable Differentiation
The Derivative Defined
Differentiation Rules
Product & Quotient Rules
The Chain Rule
Derivatives in ML
Unit 3: Multi-Variable Calculus
Partial Derivatives Intro
Second-Order Derivatives
Gradients Defined
Gradient Descent Basics
Multivariable Optimization
Probability and Statistics for Machine Learning
Unit 1: Introduction to Probability
What is Probability?
Sample Spaces & Events
Axioms of Probability
Conditional Probability
Bayes' Theorem
Unit 2: Random Variables and Distributions
Random Variables
Discrete Distributions
Continuous Distributions
Expected Value & Variance
Joint Distributions
Unit 3: Descriptive Statistics
Measures of Centrality
Measures of Spread
Percentiles and Quartiles
Covariance & Correlation
Data Visualization
Unit 4: Hypothesis Testing
Null Hypothesis
Test Statistics
P-Values
Significance Level
Errors in Hypothesis
Optimization Techniques in Machine Learning
Unit 1: Introduction to Optimization
What is Optimization?
Loss Functions Overview
Gradient Descent Intro
Learning Rate Explained
Local vs Global Minima
Unit 2: Gradient Descent Variants
Batch Gradient Descent
Stochastic GD (SGD)
Mini-Batch GD
Comparing GD Variants
Momentum Explained
Unit 3: Regularization Techniques
Overfitting Explained
L1 Regularization (Lasso)
L2 Regularization (Ridge)
Elastic Net
Dropout Regularization
Unit 4: Advanced Optimization Algorithms
RMSprop Explained
Adam Optimizer
Adam vs. RMSprop
Learning Rate Scheduling
When to Use Which?
Applying Math to Machine Learning Algorithms
Unit 1: Linear Regression with Linear Algebra
Intro to Linear Regression
Matrices and Vectors
Matrix Multiplication
Solving Linear Equations
Linear Regression in Code
Unit 2: Gradient Descent in Linear Regression
Intro to Gradient Descent
Partial Derivatives
Gradient Descent Algorithm
Linear Regression
Stochastic Gradient Descent
Advanced Topics and Current Trends
Unit 1: Mathematics of Convolutional Neural Networks (CNNs)
Convolution Operation
Pooling Layers
CNN Architecture
Backpropagation in CNNs
CNN Regularization
Unit 2: Mathematics of Recurrent Neural Networks (RNNs)
RNN Fundamentals
Backpropagation Through Time
LSTM Networks
GRU Networks
RNN Applications
Unit 3: Mathematics of Transformers
Self-Attention
Multi-Head Attention
Transformer Architecture
Encoder-Decoder Math
Transformer Applications
Unit 4: Mathematics of Generative Models: VAEs
Autoencoders
Variational Inference
VAE Architecture
VAE Loss Function
VAE Applications
Unit 5: Mathematics of Generative Models: GANs
GAN Fundamentals
Minimax Game
GAN Loss Functions
DCGANs
GAN Challenges
Unit 6: Mathematical Approaches to Explainable AI (XAI)
XAI: Introduction
Feature Importance
LIME
SHAP
Counterfactuals