Our semester will be broken into three major units: Graph Theory, Financial Math, and Probability and Statistics. We will have a fourth shorter unit over Voting Theory at the end of the semester. I hope that you will enjoy learning a little bit about each of these topics and how they are used in your everyday life and the world around you. I'm looking forward to a great semester!
We will be kicking off the semester this week with an introduction to graph theory. A graph is a collection of vertices (think dots) and edges (think lines) between the vertices. We can use graphs to study many things in the world around us. For example, a graph can represent streets and intersections from a map (see The Traveling Salesperson Problem), computer networks, social networks, or even be used to study DNA (see A Graph Theoretical Approach to DNA Fragment Assembly). By the end of this week, you should know what a graph is and be able to describe several properties of a graph.
A little bit about me: I am in my sixth year as an Assistant Professor of mathematics here at Missouri Western State University. Before coming to MWSU, I spent a year as a visiting assistant professor at Ashland University. I received my PhD from the University of Nebraska-Lincoln in 2011. (Go Big Red!) My husband is also a mathematician at William Jewell College. We have a 3.5 year old daughter and a 1.5 year old son who are both a bundle of energy.
Please ask for help as soon as you are having trouble with this class. You can visit me in my office (Agenstein 135K). Peer tutoring is also available (for free) through the Center for Academic Support.
Challenge Problem #1: (Due at the start of class on Tuesday, January 23) Sketch several examples of graphs. Determine the degree of the vertices in each graph. When you add the degrees of all the vertices, you will always get an even number. Why is that?
The Traveling Salesperson Problem is interesting because it shows us how we can use this math concept in real life situation. Getting to multiple different places quickly and efficiently is very important to many businesses. The amount of money that a business can save based off of this concept is astounding and is very important. Delivery businesses probably use this concept very commonly because of the cities and areas that they have to travel to.
ReplyDeleteNoah Rasmussen MAT110 Section 8
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ReplyDeleteThe travelling salesperson problem is intriguing because there are different methods to solve it such a nearest neighbors and sorted edges in a Hamiltonian or Euler curcuit. Knowing how to solve the travelling salesperson problem can come in handy when you have to travel to multiple places and want to do it in the cheapest way possible. This problem shows you how to use graph theory in real life situations.
ReplyDeleteI really liked the traveling salesperson problem. I liked this problem so much because it can relate to real life problems. I also liked how there was several ways to solve the problem. I prefer using nearest neighbor just because it is easier for me. I really wasn't to crazy about sorted edges just because I get really confused when it comes to drawling the graph out. Other than that I really love it.
ReplyDeleteTuesday Thompson
In the traveling sales person problem, you have to figure out how to get from one place to another by finding the shortest route. This can relate to everyday life by trying to figure out how to get from lets say walmart, to your job in so many minutes. i like to use the side sorted method.
ReplyDeleteTaylor Cockriel