Discrete Mathematics

Discrete Mathematics

Introduction

It can be defined as a process that explains itself in terms of something. For example, a dictionary is also recursive as it gives an explanation of every word using different words. A lion is a mammal that roars. In this simple example, a lion is explained by the words mammal and roar, these words would have different meaning in the same dictionary explained by different words. Having this idea in mind, we can straight away begin thinking of things like cycles (for example, when an original word is defined back after following a sequence of definitions) and early conditions (words those are assumed to be understood by definition, and shaped the ground for explaining all the other words).

To give a mathematical explanation of the recursion process, recurrence relations is brought under consideration. We shall start by using given values and produce a series of values by applying the applying the same rule, again and again, in these functions. The terms are denoted as a series,,. Therefore an is the nth number in the series. Following is the simple equation denotes the most common example of a recurrence.

The existing nth number is defined by recurrence relation defines as the sum of the two preceding terms. If initial value is and, then the following sequence of the number is generated:

a-n = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 …

Although the above sequence may look like an ordinary one at first sight, but it one of the most notable sequence ever. Its simplicity contradicts its significance and numerous applications. It is known as the Fibonacci sequence, and it turns up in domains as diverse as flower petals, architecture of Greeks and complicated stock trading algorithms. It provides, for example, numerous ways to climb a staircase moving single or two steps at once. This (Fibonacci) sequence was famous after being used in popular movies like The DaVinci Code and Mr. Magorium’s Wonderful...