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.
Hedy: A Gradual Language for Programming Education
One of the aspects of programming that learners often struggle with is the syntax of programming languages: remembering the right commands to use and combining those into a working program. Prior research demonstrated that students submit source code with syntax errors in 73% of cases and even the best students do so in 50% of cases. An analysis of 37 million compilations by 250.000 students found that the most common error was a syntax error, which occurred in almost 800.000 compilations. It was also found that Java and Perl are not easier to understand than a programming language with randomly generated keywords, stressing the difficulties that novices face in understanding syntax. This paper presents Hedy: a new way of teaching the syntax of a programming language to novices, inspired by educational methods by which punctuation is taught to children. Hedy starts as a simple programming language without any syntactic elements such as brackets, colons or indentation. The rules slowly and gradually change until the novices are programming in Python. Hedy is evaluated on 9714 programs.