The Mathematical Garden

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Mathematical methods
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.

Department of Mathematics, HKU, 2010