Question

Principle Of Discrete Math

In a paragraph (4-6 sentences), reflect on how recurrence relations are/can be used in your discipline.

Answer 1

A recurrence relation is an equation that uses recursion to define a sequence, that is, each term is defined as a function of the previous terms. Recurrence relations are used when it is too tedious or impractical to use an exhaustive approach to solve a problem. Even if a recurrence relation cannot be reduced to a closed form expression, it can still be used and implemented in computer programs. Recurrence relations are used in number theory, for example, in defining the Fibonacci sequence, Harmonic Numbers, Pell Numbers, Pell's Equation and partition of an integer. They are used in combinatorics, for example, in the problem of distribution of distinct objects into identical bins, distributions of identical objects into identical bins, Pascal's Triangle, binomial coefficients and derangements. They are used in calculus, for example, in Euler's method, arithmetic progressions and geometric progressions.