Part one of term paper
Topological ideas are present in almost all areas of today's mathematics. The subject of itself consists of several different branches, such as point set , algebraic and differential , which have relatively little in common. We shall trace the rise of topological concepts in a number of different situations. Perhaps the first work which de ...

Part two of term paper
... Euler was aware that he was dealing with a different type of geometry where distance was not relevant. The next step in freeing mathematics from being a subject about measurement was also due to Euler. In 1750 he wrote a letter to Christian Goldbach which gives Euler's famous formula for a polyhedron, v - e + f = 2, where v is the number of vertices of the polyhedron, e is the number of edges and f is the number of faces. It is interesting to realize that this, really rather simple, formula see ...