A scientific theory is an ability to predict the outcome of experiments. All the steps are important in number theory and in mathematics. Devise an argument that conjectures are correct. Test the conjectures by collecting additional data and check whether the new information fits or notĥ. Formulate conjectures that explain the patterns and relationships.Ĥ. Examine the data and find the patterns and relationships.ģ. The theoretical part tries to devise an argument which gives a conclusive answer to the questions.Ģ. Experimental part leads to questions and suggests ways to answer them. Number Theory is partly experimental and partly theoretical. As it holds the foundational place in the discipline, Number theory is also called "The Queen of Mathematics".ĭescription: The number theory helps discover interesting relationships between different sorts of numbers and to prove that these are true. It is the study of the set of positive whole numbers which are usually called the set of natural numbers. This suggests that all transport networks can be represented by graph theory in some way.ĭefinition: Number theory is a branch of pure mathematics devoted to the study of the natural numbers and the integers. The core of the internet or servers can also be represented as nodes while the physical infrastructure between them, like fiber optic cables, can act as links. However, cell phones and antennas can be represented as nodes whereas links could be individual phone calls. Mobile telephone networks or the internet is the considered the most complex graph. A telecommunication system can also be represented as a network. For instance, air networks are defined more by their nodes than by their links since links are mostly not clearly defined. But it is not true for all transportation networks. Most networks, namely road, transit, and rail networks, are defined more by their links than by nodes. Transport geography can be defined by a graph. This chapter introduces set theory, mathematical in- duction, and formalizes the notion of mathematical functions. If an arrow is not used, it means the link is bi-directional. It has a direction that is generally represented as an arrow. It denotes a location such as a city, a road intersection, or a transport terminal (stations, harbours, and airports).Įdge (Link): An edge e is a link between two nodes.
Vertex (Node): A node v is an intersection point of a graph. Each object in a graph is called a node.ĭescription: A graph ‘G’ is a set of vertex, called nodes ‘v’ which are connected by edges, called links ‘e'. If you leave the start index empty, the interpreter assumes the first item, so.
Here is an example of the usage: You can use the colon to access array ranges. The length of the lines and position of the points do not matter. Negative numbers start from the end to the beginning, and -1 is the last item. A graph consists of some points and lines between them. We say that adivides bif and only if there exists an integer q such that aq b. We could also consider multiples of 3, 4, 5, or any particular number. First we will discuss the Euclidean algorithm, which also provides us with a useful property of the greatest common divisor, which is denoted as \gcd'. Divisibility Even numbers are multiples of 2. Definition: Graph is a mathematical representation of a network and it describes the relationship between lines and points. Some Number Theory Before we start studying cryptography, we need a few basic concepts in elemen-tary number theory to explain the algorithms involved.
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