# The Mathematical Garden

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 Mathematical methods HMMs Mathematical Induction Pigeonhole principle Random Walk Solving Linear Systems

#### Topics in the Mathematical Methods Section

Hidden Markov Models (HMMs) are widely used in science, engineering and many other areas. In a HMM, there are two types of states: the hidden states and the observable states. Here we present a HMM via the framework of a classical Markov chain model. A simple estimation method for the transition probabilities among the hidden states is also discussed.

Mathematical Induction is an well-known and useful method in Mathematics.

Pigeonhole Principle - "If we put n balls in m boxes, and m < n, then at least one box must have more than n/m balls."

Random Walks, Gambler's Ruin and Queueing Systems - A losing drunk gambler queuing for loosing money ?

Solving linear systems is a problem arises in many practical applications and it is a key issue in modern scientific computing.