Foundations of Classical Mechanics and Markov Chains

Understanding the physical world requires a firm grasp of both deterministic systems and probabilistic models. This course bridges the gap between classical mechanics and Markov chains, giving you the mathematical tools to analyze both predictable and random processes. You will develop a strong conceptual foundation in Newtonian mechanics, Lagrangian formulations, and stochastic processes. By reading through clear explanations and working through guided mathematical exercises, you will learn how to model physical systems and transition states with confidence. What you'll learn: * Understand the fundamental laws of classical mechanics, including motion, force, and energy conservation. * Explore Lagrangian and Hamiltonian mechanics to analyze complex physical systems. * Master the mathematics of Markov chains, transition matrices, and state spaces. * Apply stochastic modeling techniques to predict long-term probabilities and steady states. * Analyze the intersection of classical physics and probabilistic models in statistical mechanics. * Practice solving analytical problems through structured step-by-step written derivations. The course begins with essential definitions of classical dynamics before moving into probability theory and Markovian processes. You will progress from single-particle motion to multi-state stochastic systems, building a comprehensive toolkit for advanced scientific analysis. This course is designed for beginners in physics, mathematics, or data science, and requires no prior advanced mechanics or probability experience. Start reading today to unlock the mathematical frameworks that govern both deterministic and random systems.