A GRAPH FROM THE VIEWPOINT OF ALGEBRAIC TOPOLOGY
The conventional method of describing a graph as a pair (V,E), where V and E repectively denote the sets of vertices and edges, is simple to understand and adopted in many applications. It, however, does not provide a very rich foundation for mathematical endeavor. An alternative approach is to construct a graph in algebraic topological way. In this paper, we explore how this different perspective can help us better understand group theory and topology as well as the theory of graph.
In Wikipedia the Free Encyclopedia
The Cold War was the period of protracted conflict and competition between the United States and the Soviet Union and their allies from the late 1940s until the late 1980s. The main U.S. allies were Western Europe, Turkey, Japan and Canada. The main Soviet allies were Eastern Europe and (until the Sino-Soviet Split) China. Throughout the period, the rivalry between the two superpowers was played out in multiple arenas: military coalitions, ideology, a massive conventional and nuclear arms race, and proxy wars.
On Hilbert's thirteenth problem and related questions
Hilbert's thirteenth problem involves the study of solutions of algebraic equations. The object is to obtain a complexity estimate for an algebraic function. As of now, the problem remains open. There are only a few partial algebraic results in this connection, but at the same time the problem has stimulated a series of studies in the theory of functions with their subsequent applications. The most brilliant result in this cycle is Kolmogorov's theorem on superpositions of continuous functions.