Mathematics
Algebra
From the foundations of groups, rings, and fields to Galois theory and homological algebra.
Linear Algebra
Vector spaces, determinants, eigenvalues & diagonalization to function spaces. Step-by-step from introductory to advanced.
Statistics
From descriptive statistics through inferential statistics to Bayesian statistics.
Probability Theory
From the basics of probability to stochastic processes. Step-by-step from high-school level to graduate level.
Matrix Calculus
Differentiation of functions with scalar, vector, and matrix variables. Essential for optimization in machine learning and statistics.
Fourier Analysis
Fourier series and Fourier transforms from basics to applications. Essential techniques for signal processing and physics.
Complex Analysis
From the foundations of complex function theory to conformal mappings and the residue theorem. Applications in physics and engineering.
→ Number theory, geometry, differential equations, optimization and more
Signal Processing
Filter Design
Design methods for analog and digital filters. Chebyshev, Butterworth, elliptic filters, and more.
Wiener Filter
Optimal linear filter in the MMSE sense. Frequency-domain and time-domain derivation with Wirtinger derivative.
Kalman Filter
Recursive optimal estimation based on state-space models. Comparison with Wiener filter, prerequisites and extensions.
Control Theory
State-Space Representation
Foundation of modern control. Link to transfer functions, controllable/observable canonical forms, ZOH discretization.
LQR (Linear Quadratic Regulator)
Optimal state feedback minimizing a quadratic cost. Riccati equation and Bryson's rule.
PID Control
The industrial workhorse. Ziegler-Nichols tuning, anti-windup, and implementation caveats.
→ See all 8 articles: controllability, pole placement, observer, Lyapunov, Riccati, and more
Machine Learning
Introduction
Overview of machine learning. From the three major categories — supervised, unsupervised, and reinforcement learning — to deep learning and generative AI.
Basics
Theory and implementation of classical methods: linear regression, logistic regression, decision trees, k-NN, and more.
Intermediate
Neural networks, CNNs, and RNNs. Gradient descent, regularization, and optimization techniques.
Advanced
Attention, Transformer, ViT, VAE, GAN, diffusion models, and other cutting-edge methods with mathematical rigor.