Mathematics
Statistical theory and mathematical foundations for Data Science
Core Topics
Linear Algebra
Matrices, vectors, eigenvalues, and their applications in ML
- • Matrix Operations
- • Vector Spaces
- • Eigendecomposition
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Calculus
Derivatives, integrals, and optimization techniques
- • Differentiation
- • Integration
- • Optimization
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Statistics
Probability theory and statistical inference
- • Probability
- • Hypothesis Testing
- • Distributions
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Probability
Random variables, distributions, and probabilistic modeling
- • Random Variables
- • Distributions
- • Bayes Theorem
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Optimization
Mathematical optimization methods for machine learning
- • Gradient Descent
- • Convex Optimization
- • Lagrange Multipliers
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Numerical Methods
Computational approaches to mathematical problems
- • Numerical Integration
- • Root Finding
- • Interpolation
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Interactive Examples
Linear Regression Mathematics
Explore the mathematical foundations of linear regression
Intermediate30 minutes
Principal Component Analysis
Understanding the mathematics behind PCA
Advanced45 minutes
Learning Resources
Additional Resources
Key Formulas
Matrix Multiplication
C_{ij} = \sum_{k=1}^n A_{ik}B_{kj}The fundamental operation in linear algebra
Gradient Descent
\theta_{t+1} = \theta_t - \alpha \nabla J(\theta_t)Optimization algorithm for finding local minima