Topology

Topology(Q42989) is a field of mathematics that initially studies geometrical objects deformed under continuous transformations. Many of its analytical techniques can be applied to other kinds of mathematical analysis, including algebra and language interpretation, and compilation. It is also the starting point of Category Theory and can be thought of as the origin of meta mathematics. The following video is presented by Dr. Tadashi Tokieda |https://www.youtube.com/watch?v=SXHHvoaSctc&l%7C%7C%7C%7C%7C}} Mobius strip is a strip twist by one or more times . One twist is equal to $180^{o}$. Before the strip becomes a Mobius strip can be divided into to two side we will name it as red and blue, after you twist the strip and make turn it into Mobius strip. If the Mobius strip has a odd twist the blue part will connected to the red Part, If you have a even twist the blue part will connected to the blue red will connected to red. if you start to cut the middle for the blue part and the red part of the Mobius strip you will get to different kinds of out come: 1. The Mobius strip has an odd twist so you will get bigger Mobius strip 2. The Mobius strip has an even twist then you will get two Mobius strip. (that has the same length and same number of twist as the Mobius strip before you cut)

Tokieda's advise in Topological Problem Solving

Prof. Tokieda demonstrated that mathematical thinking, particularly in the world of topology, strategically pave solutions in the following ways:

1. Always draw pictures for you problem
2. Problems may exist in different forms
   1. Try to first convert a problem to simpler forms and solve it there
   2. Some problems have dual forms and can be converted bi-directionally

Application Areas

One of the areas to apply Toplogy is in fact: politics.

James Munkres wrote a well-known textbook on Topology. Another interesting video by Tony Feng is here.