Welcome to MAT110/MAT110E! You should be enrolled in MAT110 if you have a 22 or higher on the ACT or passed the math placement exam (MPE) with a 70 or higher. Otherwise, you should be enrolled in MAT110E and MAT099. Keep in mind that if you fail MAT099, you will fail MAT110E as well, regardless of your exam and homework scores in MAT110E. Hence, it is imperative that you attend and actively participate in your MAT099 section.
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 fifth 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 2.5 year old daughter and a 9-month 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 Monday, 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?
Hello, Dr.McCune I am having a little trouble with Graph Theory set 1 question 8. I have drawn many graphs to get the correct answer but in mot sure if I'm putting the information in right or is it I'm just not getting how to do the materials as a whole.
ReplyDeleteA "disjoint part" is a component, so if your questions asks for "3 disjoint parts" it is asking for 3 components. Make sure you click on the view preview button to see that the computer is drawing the graph the way you expected. Without knowing who this is or what you've tried so far, I would suggest that you start with the advice I've given, and if you're still having trouble, please see me in office hours or send me an email.
ReplyDeleteThis is an interesting question! There are many variations of the TSP. One variation is to try to solve the problem on a directed graph. (So maybe you can only travel from A to B, but not from B to A or maybe the cost to travel from A to B differs from the cost to travel from B to A.) Other variations put restrictions, like the triangle inequality, (or a metric) on the "distances" between vertices. The "vehicle routing problem" and the "bottleneck traveling salesman problem" are two other interesting variations. The wikipedia pages for both of these give a nice introduction.
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