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Mathematics

- NEXT DEFINITIONGraph TheoryDefinition: Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node. Description: A graph ‘G’ is a set of vertex, called nodes ‘v’ which are connected by edges, called links ‘e'. Thus G= (v , e). Vertex (Node): A node v is an intersection point of a graph. It denotes a location such as a city, a road intersection, or a transport terminal (stations, harbours, and airports). Edge (Link): An edge e is a link between two nodes. A link denotes movements between nodes. It has a direction that is generally represented as an arrow. If an arrow is not used, it means the link is bi-directional. Transport geography can be defined by a graph. Most networks, namely road, transit, and rail networks, are defined more by their links than by nodes. But it is not true for all transportation networks. For instance, air networks are defined more by their nodes than by their links since links are mostly not clearly defined. A telecommunication system can also be represented as a network. Mobile telephone networks or the internet is the considered the most complex graph. However, cell phones and antennas can be represented as nodes whereas links could be individual phone calls. 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. This suggests that all transport networks can be represented by graph theory in some way.Read More

Definition: Analysis is a branch of mathematics which studies continuous changes and includes the theories of integration, differentiation, measure, limits, analytic functions and infinite series. It is the systematic study of real and complex-valued continuous functions. It describes both the discipline of which calculus is a part and one form of the abstract logic theory.

Description: There are two broad subdivisions of analysis named Real analysis and complex analysis, which deal with the real-values and the complex-valued functions respectively. Real Analysis: Real analysis is a branch of analysis that studies concepts of sequences and their limits, continuity, differentiation, integration and sequences of functions. It focuses on the real numbers, including positive and negative infinity to form the extended real line. It deals with functions of real variables and is most commonly used to distinguish that portion of calculus. It is natural to consider differentiable, smooth or harmonic functions in the real analysis, which is more widely applicable but may lack some more powerful properties that holomorphic functions have. Complex analysis: Complex analysis is the study of complex numbers together with their manipulation, derivatives and other properties. It is an extremely powerful tool which helps in providing a way of computing difficult integrals by investigating the singularities of the function near and between the limits of integration.

Description: There are two broad subdivisions of analysis named Real analysis and complex analysis, which deal with the real-values and the complex-valued functions respectively. Real Analysis: Real analysis is a branch of analysis that studies concepts of sequences and their limits, continuity, differentiation, integration and sequences of functions. It focuses on the real numbers, including positive and negative infinity to form the extended real line. It deals with functions of real variables and is most commonly used to distinguish that portion of calculus. It is natural to consider differentiable, smooth or harmonic functions in the real analysis, which is more widely applicable but may lack some more powerful properties that holomorphic functions have. Complex analysis: Complex analysis is the study of complex numbers together with their manipulation, derivatives and other properties. It is an extremely powerful tool which helps in providing a way of computing difficult integrals by investigating the singularities of the function near and between the limits of integration.

- NEXT DEFINITIONGraph TheoryDefinition: Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node. Description: A graph ‘G’ is a set of vertex, called nodes ‘v’ which are connected by edges, called links ‘e'. Thus G= (v , e). Vertex (Node): A node v is an intersection point of a graph. It denotes a location such as a city, a road intersection, or a transport terminal (stations, harbours, and airports). Edge (Link): An edge e is a link between two nodes. A link denotes movements between nodes. It has a direction that is generally represented as an arrow. If an arrow is not used, it means the link is bi-directional. Transport geography can be defined by a graph. Most networks, namely road, transit, and rail networks, are defined more by their links than by nodes. But it is not true for all transportation networks. For instance, air networks are defined more by their nodes than by their links since links are mostly not clearly defined. A telecommunication system can also be represented as a network. Mobile telephone networks or the internet is the considered the most complex graph. However, cell phones and antennas can be represented as nodes whereas links could be individual phone calls. 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. This suggests that all transport networks can be represented by graph theory in some way.Read More

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