Markov Chains
Markov Chains are a mathematical concept in probability theory that model systems transitioning between states over time, where the probability of moving to the next state depends only on the current state and not on the sequence of events that preceded it (the Markov property). They are used to analyze and predict the behavior of stochastic processes in fields like computer science, economics, and natural language processing. In practice, Markov Chains can be represented as graphs or matrices to simulate random sequences, such as text generation or user behavior modeling.
Developers should learn Markov Chains when building applications that involve probabilistic modeling, such as predictive text algorithms, recommendation systems, or simulations of random processes like game AI or financial forecasting. They are particularly useful in natural language processing for tasks like auto-completion and chatbots, where the next word or action depends on the current context. Understanding Markov Chains also provides a foundation for more advanced topics like Hidden Markov Models, which are used in speech recognition and bioinformatics.