In order to define and establish what graph theory is, we must first make note of its origin and its basis within the broad subject of mathematics. Graph theory, a smaller branch in a large class of mathematics known as combinatorics, which defined by Jacob Fox as, “is the study of finite or countable discrete structures.” Areas of study in combinatorics include enumerative combinatorics, combinatorial design, extremal combinatorics, and algebraic combinatorics. These subfields consist of the counting of mathematical structures, the constructing and analyzing structures, the discovering “extreme” or “optimal” structures, and the studying of combinatorial structures in the algebraic context. These examples only portray a general sense of combinatorics, just to give a rough idea of what this branch of mathematics covers. After defining the general concept of combinatorics, we can now delve into the distinct subfield of graph theory. Graph theory is defined as the study of graphs, defined as mathematical structures used to portray relationships between mathematical objects. More specifically, graph theory involves ways that finite sets of points, called vertices or nodes, can be connected by lines or arcs, also referred to as edges. The graphs examined through graph theory are not to be confused with the more popularly known graphs, which are functions or relations plotted on the coordinate plane. Graphs can be characterized by multiple properties, the most common of these being complexity. The complexity of a graph depends on various factors such as the number of edges allowed between two vertices, whether or not each edge has an assigned direction to it, and several other elements. This is the most general sense of what graph t... ... middle of paper ... ...would take to get to the other person. Astonishingly it is on average only six. It was actually discovered that the largest amount of edges between two people was a measly twelve. Graph theory really proves the digital age of globalization has connected everyone more than we think. Graph theory has a wide range of applications as we have discovered. These have ranged from the famous Leonhard Euler’s solving of The Seven Bridges of Königsberg problem, to the classic four color theorem, and finally to the current focuses on applications within the realm of computer and data science. With all of these uses, it is certainly clear that graph theory is a subject of modern mathematics that is here to stay. Not only are there enormous applications to a large number of fields, but graph theory does a tremendous job of modeling, explaining, and solving real world problems.
Gender and Race play the most prominent role in the criminal justice system. As seen in the movie Central Park 5, five African American boys were charged with the rape of the a white women. In class decision we’ve discussed how the media explodes when it reports cross-racial crimes. The Central Park 5 were known everywhere and even terms were being made up during the process such as wilding. Also, during one of the class discussions it was brought up that victims of crime are of the same race of the perpetrator. However, the media likes to sensationalize crime of the victim being of a different race, because it makes for a good story. By doing this, the media does create more of a division of race. As seen in the video Donald Trump was trying
“Network topology is the arrangement of the various network elements such as node, link, of computer network. Basically, it is topological structure of a network which ether be physically or logically.”
“Traditionally, scientists have looked for the simplest view of the world around us. Now, mathematics and computer powers have produced a theory that helps
Robert, A. Wayne and Dale E. Varberg. Faces of Mathematics. New York: Harper & Row Publishers, Inc., 1978.
Since hundred years ago, when people started to make maps to show distinct regions, such as states or countries, the four color theorem has been well known among many mapmakers. Because a mapmaker who can plan very well, will only need four colors to color the map that he makes. The basic rule of coloring a map is that if two regions are next to each other, the mapmaker has to use two different colors to color the adjacent regions. The reason is because when two regions share one boundary can never be the same color. Another basic rule of coloring a map is that if two regions share only one point, then they do not necessary have to be colored differently. Many evidence showed that coloring a map required at least four colors but no more than five. Then mathematicians started to asked questions, such as “ Is it true that using only four colors are enough? Is there any exception that one has to color a map that requires more than four colors? Or is it has to do with a special sequence of arrangement that involved with different regions in order to make the theorem true?” However, the first mathmatician who asked these questions is a man named Francis Guthrie. He was the first one who posed the four color problem in1852.
Goldstine, Herman H. "Computers at the University of Pennsylvania's Moore School." The Jayne Lecture. Proceedings of the American Philosophical Society, Vol 136, No.1. January 24, 1991
On first thought, mathematics and art seem to be totally opposite fields of study with absolutely no connections. However, after careful consideration, the great degree of relation between these two subjects is amazing. Mathematics is the central ingredient in many artworks. Through the exploration of many artists and their works, common mathematical themes can be discovered. For instance, the art of tessellations, or tilings, relies on geometry. M.C. Escher used his knowledge of geometry, and mathematics in general, to create his tessellations, some of his most well admired works.
The bridges of the ancient city of Königsberg posed a famous and almost problematic challenge a few centuries ago. But this isn’t just about the math problem; it’s also a story about a famous Swiss mathematician named Leonhard Euler who founded the study of topology and graph theory by solving this problem. The effects of this problem have lasted centuries, and have helped develop several parts of our understanding of mathematics.
Social problem is a broad topic, there is “No conclusive idea of what constitutes a social problem.” To define a social problem, there are generally three different ideas to define a social problem, “Something that impacts a large group; Something that the people in a society collective agree it is problematic; Something that violates a moral code.” (Logan) Healthcare has been on the spot light, because of The American Health Care Act. I’d like to present health care in United States as a social problem, because it qualify the three ideas to define social problem. First of all, it impacts a large group in the society, because of its cost. According to CDC, “28.2 million people who are under age of sixty five are insured” (CDC). Second, people in a society collective
Imagine a world in which all of life’s problems could all just go away at the click of a button. A world where every individual on the face of planet earth is being watched 24/7, therefore eliminating any possibility of a crime being committed. Imagine, if just for a moment, a world where everyone and everything are connected by the same network, which would in essence create a full and complete circle. This is the world that serves as the setting for Dave Eggers novel The Circle. The Circle is a novel about Mae, the young and enthusiastic protagonist, who gets a job at a company known as The Circle. The Circle is a revolutionary company that is creating all sorts of new and exciting technology that appear to benefit the human race as a whole.
If you already know what a binary tree is, but not a general tree, then pay close attention, because binary trees are not just the special case of general trees with degree two. I use the definition of a tree from the textbook, but bear in mind that other definitions are possible.
There is always room in mathematics, however, for imagination, for expansion of previous concepts. In the case of Pascal’s Triangle, a two-dimensional pattern, it can be extended into a third dimension, forming a pyramid. While Pascal himself did not discover nor popularize it when he was collecting information on the Triangle in the 17th century, the new pattern is still commonly called a Pascal’s Pyramid. Meanwhile, its generalization, like the pyramid, to any number of dimensions n is called a Pascal’s Simplex.
Is There a Science of Society, and Does It Affect Scientific Study of Social Phenomena that Effect Norms?
Computers in technological development demand more efficient networking. In a very short period it has changed the way we have looked at things since centuries. It is one industry that is going to shape our future for centuries to come Coming from a background of Electronics and Communication Engineering, I have developed an interest to probe into the area of Networking and Computer Networks. Hence I wish to do Masters in Computer Science (CS) as my major.
The Nature of Mathematics Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its basic interest. The essence of mathematics lies in its beauty and its intellectual challenge. This essay is divided into three sections, which are patterns and relationships, mathematics, science and technology and mathematical inquiry. Firstly, Mathematics is the science of patterns and relationships. As a theoretical order, mathematics explores the possible relationships among abstractions without concern for whether those abstractions have counterparts in the real world.