Lesson 1:
Chapter 5 The Mathematics of Getting Around
Now we really switch gears, to look at routing problems. Postal deliverers and sanitation trucks need to plan routes that will cover all the buildings in a fixed area. Airlines and buses need to plan routes that can be combined to get the passengers from various locations to various other locations. Utility companies need to maintain networks so that outages will affect as few customers as possible for as short a time as possible. How can these be done effectively and reliably?
In this chapter you will learn how these problems are modeled with graphs--not the graphs of functions you know from algebra, but simple collections of vertices and edges that represent routes and connections. You will learn how to determine if it is possible to move through a graph crossing each edge exactly once, and, if possible, how you would find such a route. You will also learn what to do if you cannot find such a route, that is, how you would need to adjust the graph to achieve the goal.
How to study the chapter:
Go to MyLabsPlus.
Open Chapter 5.
Start with the chapter introduction video.
Proceed through the chapter opener and the individual sections.
As you read the text, be sure to click on "You Try It", where you will work out small examples, and on the Videos accompanying some of the examples.
When you finish Section 5.2, do the online homework assignment #1.
When you finish Section 5.4, do the online homework assignment #2.
Then do the Chapter 5 written homework in Blackboard.
Deadlines:Online Homework #1: 1/23
Online Homework #2: 1/30
Written Homework 1: 1/30 Quiz 1: 1/30
Lesson 2:
We continue with routing problems. While it turned out easy to decide if a graph has an Euler circuit, it is much harder to decide if a graph has a route that visits each vertex exactly once. Well, it is easy enough if the graph has 6 or 8 vertices. But the graphs in typical real applications have thousands of vertices.
In this chapter you will learn about Hamilton paths and circuits in graphs--routes that visit each vertex exactly once. You will learn how to find Hamilton circuits in small graphs. You will consider graphs with different edge lengths and learn how to search for Hamilton circuits which minimize the total length of edges crossed. You will learn an algorithm that takes too long in practice, but gives the accurate answer, and other algorithms that are faster to use, but don't always give the most accurate answer.
How to study the chapter:
Go to MyLabsPlus.
Open Chapter 6.
Start with the chapter introduction video.
Proceed through the chapter opener and the individual sections.
As you read the text, be sure to click on "You Try It", where you will work out small examples, and on the Videos accompanying some of the examples.
When you finish Section 6.2, do the online homework assignment #3.
When you finish Section 6.5, do the online homework assignment #4.
Then do the Chapter 6 written homework in Blackboard. After you complete the Chapter 6 homework assignments, do the Chapter 6 online quiz in MyLabsPlus.
Deadlines:
Online Homework #3: 2/6
Online Homework #4: 2/13
Written Homework 2: 2/13
Quiz #2: 2/13
Lesson 3:
Did you ever hear the phrase, "six degrees of separation"? Imagine a huge graph (about seven billion vertices) with one vertex for each person on earth, and an edge connecting two people if they know each other. Some think that in this graph, every pair of vertices is connected by a path of at most six edges. That is, you can always find a chain of acquaintances between yourself and anyone else in the world. No one could actually draw such a graph, of course. But transportation and communication networks (the internet) are modeled by graphs in a similar way. Here are some natural questions to ask about such graphs: Is there a path from each vertex to every other vertex? How long are the paths from one vertex to another? How many different paths connect one vertex with another? If I remove some edges (some communication link stops working, say), will the graph still be connected? How should I design a network to keep everything connected in the cheapest possible way?
In this chapter you will learn to identify and construct minimally connected graphs ("trees"), to find spanning trees within graphs and spanning trees of minimal length in weighted graphs, and to recognize shortest networks to connect a given set of points.
How to study the chapter:
Go to MyLabsPlus.
Open Chapter 7.
Start with the chapter introduction video.
Proceed through the chapter opener and the individual sections.
As you read the text, be sure to click on "You Try It", where you will work out small examples, and on the Videos accompanying some of the examples.
When you finish Section 7.2, do the online homework assignment #5.
When you finish Section 7.3, do the online homework assignment #6.
Then do the Chapter 7 written homework in Blackboard.
After you complete the Chapter 7 homework assignments, do the Chapter 7 online quiz in MyLabsPlus.
Deadlines:
Online Homework #5: 2/20
Online Homework #6: 2/27
Written Homework 3: 2/27
Quiz 3: 2/27
Lesson 4:
In this country, state and national elections are usually dominated by two parties. When just two candidates are on a ballot, there is almost no question about how the winner is determined. If one candidate gets more votes than the other, he or she is declared the winner. The only question arises when there is an exact tie in the number of votes for the two candidates. But third party or independent candidates are sometimes on the ballot, and can influence the outcome of an election. And other voting situations occur more often in local government elections and in elections in other organizations. Sometimes several positions are to be filled, and each voter can vote for more than one candidate. Sometimes many candidates are on the same ballot for a single position, and no one is likely to get a majority (or near majority) of the votes. What is a fair way to determine the winner(s) in these situations? What do we mean by fair?
In this chapter you will learn about some fairness criteria. You will learn several methods for determining the winner of an election, and will do the calculations to apply these methods. You will see which of the fairness criteria the various methods satisfy. You will learn about Arrow's impossibility theorem, which shows the limitations to achieving all fairness criteria.
How to study the chapter:
Go to MyLabsPlus.
Open Chapter 1. (You can access it through Chapter Contents or Multimedia Library.)
Start with the chapter introduction video.
Proceed through the chapter opener and the individual sections.
As you read the text, be sure to click on "You Try It", where you will work out small examples, and on the videos accompanying some of the examples.
When you finish Section 1.3, do the online homework assignment #7.
When you finish Section 1.6, do the online homework assignment #8.
Then do the Chapter 1 written homework in Blackboard.
After you complete the Chapter 1 homework assignments, do the Chapter 1 online quiz in MyMathLab.
Deadlines:
Homework #7: 3/13
Homework #8: 3/27
Written Homework 4: 3/27
Quiz #4: 3/27
Lesson 5:
In many committees and boards, decisions are made by vote of the members, but individual members representing different constituencies may have different numbers of votes (or different "weights" for their votes). Sometimes this is described explicitly; for example, shareholders of a corporation have votes weighted by the number of shares they own. Sometimes it is hidden; a situation in which a member has veto power could be modeled by assigning weights to the individual members' votes. In general in these situations, some voters have more power than others. How can you quantify that power?
In this chapter you will learn how to find winning coalitions in weighted voting systems. You will learn about two ways of measuring power, the Banzhaf Power Index and the Shapley-Shubik Index. You will compute the indices and see how they are applied to some real examples.
How to study the chapter:
Go to MyLabsPlus.
Open Chapter 2.
Start with the chapter introduction video.
Proceed through the chapter opener and the individual sections.
As you read the text, be sure to click on "You Try It", where you will work out small examples, and on the videos accompanying some of the examples.
When you finish Section 2.2, do the online homework assignment #9.
When you finish Section 2.4, do the online homework assignment #10.
Then do the Chapter 2 written homework in Blackboard.
After you complete the Chapter 2 homework assignments, do the Chapter 2 online quiz in MyLabsPlus.
Deadlines:
Online Homework #9: 4/3
Online Homework #10: 4/10
Written Homework #5: 4/10
Quiz #5: 4/10
Lesson 6:
The number of congressional representatives from the various states is supposed to be proportional to the population of the states. To achieve this, we can divide the total population of the country by the number of seats in the House of Representatives, and produce the "standard divisor"--the number of constituents that each representative should have. This would be great if the population of each state was an exact integer multiple of that standard divisor. But, of course, it is not. We are forced to have representatives in some states with more constituents and representatives in some states with fewer constituents. So how can we determine the number of representatives that should represent each state in a fair way?
In this chapter you will learn how to compute the standard divisor and the fractional number of representatives each state should have. You will learn several methods for assigning an integer number of representatives to each state (called apportionment). You will learn some fairness criteria for this process, and some flaws of the methods, leading to paradoxes. You will learn some American history along the way: how has apportionment for the US House of Representatives actually been carried out?
How to study the chapter:
Go to MyLabsPlus.
Open Chapter 4.
Start with the chapter introduction video.
Proceed through the chapter opener and the individual sections.
As you read the text, be sure to click on "You Try It", where you will work out small examples, and on the Videos accompanying some of the examples.
When you finish Section 4.3, do the online homework assignment #11.
When you finish Section 4.6, do the online homework assignment #12.
Then do the Chapter 4 written homework in Blackboard
After you complete the Chapter 4 homework assignments, do the Chapter 4 online quiz in MyLabsPlus.
Deadlines:
Online Homework #11: 4/17
Online Homework #12: 4/24
Written Homework 6: 4/24
Quiz #6: 4/24
Lesson 7:
We see percentage in our regular life. Tax, sale, share and interestare some examples. It is important to understand percentages. For example if at the department store, a pair of shoes goes on sale for 30% off and you have a coupon for 15% off. What would the total discount percentage be? Often, people incorrectly add the percentages. We learn in this chapter why that is not correct.
In section 10.2, we start on simple interest and how it works. Concepts such as principal, APR, term, face value and payday loan are discussed.
Then in the following sections, we learn about compounded interest and continuous compounding. Finally, we learn about consumer debt and calculating payments for a loan.
How to study the chapter:
Go to MyLabsPlus.
Open Chapter 10.
Start with the chapter introduction video.
Proceed through the chapter opener and the individual sections.
As you read the text, be sure to click on "You Try It", where you will work out small examples, and on the Videos accompanying some of the examples.
After you finished working on Section 10.2, do the online homework assignment #13.
After you finished working on Section 10.4, do the online homework assignment #14.
Then do the Chapter 10 written homework in Blackboard
After you complete the Chapter 10 homework assignments, do the Chapter 10 online quiz in MyLabsPlus.
Deadlines:
Online Homework #13: 5/1
Online Homework #14: 5/8
Written Homework 7: 5/8
Quiz #7: 5/8
Due Dates: