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.
The Sociology, Pedagogy, and Theology of Huey P. Newton: Toward a Radical Democratic Utopia *
What is happening ... to the theories of revolutionary thinkers and leaders of oppressed classes fighting for emancipation.... After their death attempts are made to convert them into harmless icons, to canonize them, so to say and to hallow their names, to a certain extent, for the "consolation" of the oppressed classes and with the object of duping the latter, while at the same time robbing the revolutionary theory of its substance, blunting its revolutionary edge and vulgarizing it. --V. I. Lenin, The State and Revolution, 1917 It was as if the Huey Newton they mourned had been dead for years. A small ftorist's card, resting with bouquets of red gladiolus and white dahlias on a chain-link fence near the [Newton] shooting scene, summed it up: "Huey: for the early years." --B. Turque and L. Wright, Newsweek, 4 September 1989 The Context of Newton's Pedagogy, Theology, and Sociology On 17 February 1942, Huey Percy Newton was born to Armelia and Walter Newton of Monroe, Louisiana. The "deep south" was in the clutches of de jure Jim Crow--entrenched and naturalized laws and social conditions that reproduced intertwining racism and poverty. Huey P. Newton's upbringing in this milieu was supplemented by a blend of traditional black southern family relations and the newly blossoming social consciousness of the time. From the famous 1955 Montgomery, Alabama bus boycott, to the sit-ins of all-white public facilities led by SNCC (Student Nonviolent Coordinating Committee) activists, the civil rights movement challenged the racial status quo of the U.S. Under the nonviolent philosophy of Dr. Martin Luther King, Jr. blacks and whites protested and marched for social and legal freedom. At the dawn of the 1960s, the major goals of egalitarian societal progress were attacked as contradictory; with "private affluence" on one side of the coin that was backed by "public poverty" on the other. The latter side began to demand increased attention and prominence in political discussions. In 1964, just two years prior to the formation of the Black Panther Party (hereafter BPP), the U.S. Congress passed a civil rights act that outlawed racial segregation in public facilities, but failed to enforce such legislation throughout the country. That same year, U.S. President Lyndon B. Johnson stated, "...the great society [my emphasis] is concerned not with how much, but with how good--not with the quantity of goods but with the quality of their lives." It was the push toward a "great society" that forced many to take a critical look at the contradictions of the state, the subject, and the supposed congealing ideology of the "American Dream" which--just one month prior to Johnson's statements--Malcolm X called "an American nightmare" (3 April 1964). These social contradictions were manifested publicly in the televised images of civil rights demonstrators being beaten and water hosed by police, spat on by detractors, and jailed without cause. Young urban blacks began to reject King's form of non violence. Just one year after Johnson's "Great Society" plan was announced the full expression of this "American Dilemma" (Myrdal 1944) came in the form of the 1965 Watts rebellion in Los Angeles, California. By 1967 there were over one hundred major urban race-related riots and rebellions in cities across the country. At the same time the Vietnam War was escalating and many of the nation's youth, regardless of race, questioned the war and became openly hostile to the established social and governing order. It was this social order in which Huey P. Newton gained his adolescent maturity and which set the stage for the formation of his pedagogical, theological and sociological imagination. In the years after the turmoil of the 1960s, posters of Newton were plastered on walls of college dormitory quarters athwart the nation. "Many of those who followed or were frightened by Newton knew him from that famous poster (beret, black leather jacket, spear in one hand, rifle in the other, seated in a wicker chair) that decorated people's walls, especially those of students all over the world" (Jeffries 2002, p. …