MATH 381: Discrete Mathematics
| Course Home Page | Blackboard | Instructor’s E-mail |
|---|---|---|
| Welcome | Your Instructor | Materials |
| How to Take This Course | Guidelines for Success | Netiquette |
| Course Mechanics | Honor Code | Schedule |
Welcome to Discrete Mathematics!
Since your first algebra course, you have been studying continuous mathematics, the mathematics based on the properties of the real number system. In this course, you return to the study of discrete mathematics, the mathematics based on the properties of the integers (the whole numbers). A large part of the mathematics you studied in grades K–8 was discrete mathematics, so in a way this is a return to familiar territory. However, if you think you know everything there is to know about the integers, you will soon be convinced otherwise!
In addition, this is a course in the machinery of mathematics, in particular the machinery of sets, mathematical logic, and proof. These matters were touched on, from time to time, in your calculus courses. Here, they will play an important role in everything we do.
You should expect to learn many things about familiar mathematical objects, and some not-so-familiar structures as well. You will learn some good techniques for problem solving. And I think you will find that discrete mathematics is, at its foundation, common-sense mathematics—something to be understood and enjoyed.
An introductory discrete mathematics course is designed to acquaint students with a number of topics. At first, this may look like a grab bag of unrelated material, but there are many interconnections and parallels among the topics, and one of our goals is to illuminate these connections. Here are the topics we will consider:
- Sets and functions. No doubt you have studied sets and functions before, but in this course, we will review the properties of these fundamental structures in a thorough and careful way.
- Propositional logic. Mathematicians have developed some clear rules and useful notations for dealing with questions of logic. These rules will be essential to you in all subsequent mathematics courses.
- Counting. You know how to count, but we will study techniques for counting the number of objects in a given set, such as the number of ways to rearrange the letters of Mississippi, or the number of different ways to select a dozen doughnuts if the shop has fourteen varieties. These techniques are important in many applications, and counting sets builds your problem-solving skills.
- Probability. These days the basic ideas of probability are taught as early as the sixth grade, but with our counting techniques we will be able to compute the probabilities of intricate events.
- The integers. We will explore several key properties of the integers related to prime numbers, divisibility, and factorization, and learn the techniques and uses of modular arithmetic, a subject in many advanced mathematics courses.
- Operations and relations. Throughout the course, we will deal with a variety of operations and relations involving different mathematical objects. You will learn how to classify and describe these operations and relations so that you can recognize and analyze similar structures in other courses.
Your Instructor
Dr. Russ Rowlett
I am director of the UNC-Chapel Hill Center for Mathematics and Science Education, a unit of the School of Education. The Center offers continuing education courses in mathematics and science for teachers of grades K–12. Although I work for the School of Education, my PhD degree is in mathematics. Before coming to UNC in 1987, I was a math professor at the University of Tennessee, Knoxville, for thirteen years. My research interest was in topology, the branch of modern geometry sometimes described as “rubber-sheet geometry.” At UNC-Chapel Hill, I have taught classes in geometry, topology, discrete mathematics, and combinatorics.
Materials
Calculator
You will need a calculator with the combinatorial functions (permutations and combinations). Any graphing calculator has these functions, so you probably already have what you need. If you need to buy a calculator, the Texas Instruments TI-84 is used by many students.
Writing Mathematical Notation: Scanner or Equation Editor
To submit your work (by e-mail), you will need either a scanner to scan handwritten pages or an equation editor to use with your word processor. Your copy of Microsoft Word may already have Microsoft Equation Editor. To find out, choose Object from the Insert menu—if Equation is one of the options available, then you have Microsoft Equation Editor.
A good choice for an equation editor is MathType by Design Science, which is a more powerful tool than Equation Editor. (You can pay by credit card and download the program to install on your computer.) MathType works within Microsoft Word the same way Equation Editor does, by creating and inserting equations in your Word document.
Browser Requirements
You will need to use a specific browser and extra free software (if you are a PC user) in order to view the mathematical notation on the Web pages of this course.
PC Users: Use Internet Explorer 6 or Internet Explorer 7 and download the free software MathPlayer by Design Science. With MathPlayer, if you mouse over equations and click, they will appear very clearly in a small pop-up window; if you right click over an equation and select Speak Expression, MathPlayer will speak the math expression.
Mac Users: Use Mozilla Firefox 3.0, which you can download for free.
If you have problems viewing the mathematical notation in the lessons, contact the instructional designer at the Friday Center.
Optional Textbooks
This is a self-contained course, and you are not required to purchase a textbook. However, there are many excellent discrete mathematics texts available, and you may wish to have one as a reference. I recommend:
- Susanna S. Epp, Discrete Mathematics with Applications, Brooks Cole. A student favorite.
- Kenneth R. Rosen, Discrete Mathematics and Its Applications, McGraw Hill. The leading university text.
- Seymour Lipschutz, Discrete Mathematics, Schaum’s Outline. A bargain at less than $20; like all Schaum’s Outlines, it is strong on worked-out problems but weak on text and explanation.
How to Take This Course
The course is divided into twelve lessons (see Schedule). Each lesson lasts from one to two weeks and contains the following components:
- readings
- reading comprehension questions (ungraded)
- problems (graded)
- class discussion (graded).
The readings are are the equivalent of a classroom lecture. In each reading there are one or two reading comprehension questions. When you reach a question, stop and answer the question. If you can’t answer it, go to the discussion forum (more information on this below) and see if the discussion there helps. If not, post a question there for the class.
When you finish each reading, send me an e-mail with your answers to the reading comprehension questions. You won’t be graded on these answers. I want to know whether you have understood the reading. If you do not understand the reading and are not able to get help from the discussion forum, send me your questions and I will respond as quickly as possible.
Each lesson also includes a set of problems to work and submit for grading. If you need help with the problems, post your questions on our discussion forum. You cannot ask for the answer to a problem, but you can ask how to begin, or what technique you should use. Everyone in the class, including me, is responsible for coming up with answers to posted questions. If you don’t have any trouble with the problems, you must participate in the discussion forum anyway. Help your classmates. If you can answer any of the posted questions, please do so. Or if you see a technique suggested for a problem and you can think of a better way to do the problem, please make your suggestion. You will be graded on your participation in the discussions, and you must post three times per lesson, either asking or answering questions, or sharing your comments and observations.
Submit the solutions to the problems on or before the last day of the lesson. Instructions for submitting your assignments are in the first lesson.
Guidelines for Success in Discrete Mathematics
Set a Routine and Stay on Course
- Assume everything will take twice the time you originally thought—here as with all things.
- Print documents if that helps you stay more organized.
- Do not get behind. Begin reading and working on the first day of each lesson so you can get and give timely help.
- Do not—ever!—leave the problems until the last day of the lesson. Start early in the week.
- Set time aside each day—even just a few minutes if that is all you have—to log in to the course and check the discussion forums. Remember, you are responsible for helping your classmates with their questions if you can.
- If you don’t understand something, ask for help right away.
Participate in the Discussion Forums
One of the most important aspects of any course is good and regular communication. Communication makes online courses real; lack of communication undermines them. Participating in an online course means making thoughtful contributions in the discussion forum—this is the only place where we are a class, a community of scholars. Frequent participation will help us all learn as much as possible from each other. You will be graded on your participation in the discussion forums. You are required to post three times on three separate days per lesson, but the general rule is: Let us hear from you often. Our discussions are held on Blackboard, and I will provide instructions for posting in the first lesson.
Follow these rules:
- Do not ask for the answer to an assigned problem. If you have difficulty with a problem, describe the difficulty and ask for a suggestion as to how you might proceed.
- Do not give a classmate the answer to an assigned problem. To help, suggest a course of action—perhaps a theorem to consider or a way to structure the problem differently.
- Keep the discussion cordial and make only helpful remarks (see Netiquette). In our forums there is no cause for debate or criticism. Our purpose in communicating is to get help or give help, not to criticize.
If I don’t routinely hear from you or “see” your presence on the discussion forums at least three times per lesson, I will be in touch to find out why you are not meeting your participation requirements. If you anticipate not being able to participate because of some personal or family emergency, let me know as far in advance as possible.
Ask Questions, Early and Often
The world’s most talented instructors can still leave you uncertain and confused. Not only can confusion happen, it will happen. Mathematical text is not easy reading (you have probably noticed this before). In an online course there is no lecturer standing in front of you to stop and explain as the class proceeds through the material. So ask—whenever you need to, as often as you need to.
Who should you ask? First, check our discussion forums and see if others are having the same questions. Participate—ask and answer questions. Make it a general practice to post some question, answer, tip, or observation every time you get on your computer to work on the course. If you are not able to get help on the discussion forum, send me an e-mail and I will respond as soon as possible.
Also, if at any time you feel lost or fall behind in the course, do not panic or keep silent—ask questions on the discussion forum so we can help, or send me an e-mail. If you suffer silently, I may not know you’re having difficulties until you have become discouraged—and I don’t want that to happen!
Netiquette
I am sure you know this, but I'll say it again for the record: It is important to be polite, respectful, and kind to your virtual classmates. Here are some general tips:
- Keep your voice down. USING ALL CAPITAL LETTERS is the equivalent of yelling. Ouch! Instead, use bold, italics, or *asterisks* around text to be emphasized.
- Avoid sarcasm and subtleties. Tone of voice and body language convey a substantial amount of information that is not available in written communications. It is easy to sound insensitive and hurt someone’s feelings, or have them miss the point, when communicating through text only. To counter this, be clear and straightforward, and very careful with humor and joking.
- Use Emoticons. Some folks hate them, but these little icons can be quite effective in supplying primitive facial expressions to supplement your words. ;-) If you don’t like emoticons, use other ways of conveying your intentions such as the phrases “no offense meant,” or “this is just my opinion.”
- Think before replying. Assume any comment that sounds abrasive wasn’t proofed for tone and wasn’t meant to offend. If you are upset with a classmate, wait a little before posting a too-hasty reply that you may regret. Ask for clarification of the author’s intent.
And last but not least, remember that your posts are recorded and saved in this course.
Course Mechanics
Blackboard
Some of your class components (discussion forums, announcements, the class listserv) are accessed through a software package called Blackboard, and you will need to log in to Blackboard using a unique identifier known as your UNC Onyen (Only Name You'll Ever Need) and Onyen password.
There is a link to the Blackboard site in the gray navigation bar at the top of every page in this course. Click on that link, and then use your Onyen to log in to Blackboard. Click on the MATH 381 link, and you will see navigation buttons on the left side of the screen labeled Announcements, Discussion Forums, and so on.
If you experience problems accessing Blackboard, this is what you should do:
- If you do not already have a UNC Onyen, go to the Onyen Web site and follow the instructions for creating an Onyen.
- If you have an Onyen but have forgotten it (or the password), go to the Onyen Web site.
- If you have your Onyen but can’'t log in to Blackboard, contact Janice Durham at the Friday Center.
- If you can log in to Blackboard but can’t find this course listed, contact Janice Durham at the Friday Center.
- If you can’t locate a forum in Blackboard, contact the instructional designer at the Friday Center.
If you have technical problems while using Blackboard, contact UNC-Chapel Hill Help & Support (use the Help button in Blackboard, or call 919-962-HELP).
Using E-mail
All communication from your instructor will go to your UNC Onyen e-mail address (the one that appears when you post to the discussion forum). Off-campus users can access their UNC e-mail using Webmail. You can have your e-mail forwarded to a different e-mail address by clicking “Forward e-mail” at the Onyen Web site. We recommend that you use your UNC Onyen e-mail account for this course.
We strongly recommend that you use your UNC e-mail account for all e-mails regarding your course. Hotmail users should be aware that Hotmail will block messages sent from within Blackboard because Blackboard uses “blind carbon copy” to protect privacy. If you forward your mail to a commercial e-mail service provider (yahoo.com or msn.com, for example), messages from your instructor, Friday Center staff, or other students may be delayed because these service providers sometimes place temporary blocks on messages originating from universities. If you are using a commercial e-mail service provider, the e-mail links in this course may not work for you.
It is extremely important for you to save copies of any messages you send to your instructor via e-mail. If your instructor doesn't receive your message, you must have a copy of the e-mail (with any attached file), indicating the date sent, to prove that you sent the message. It is your responsibility to maintain copies of your sent e-mails, as there is no way to guarantee that any e-mail message will be delivered. Please check your e-mail software to see how it manages sent and saved messages. Some software automatically deletes messages one month after they have been sent; others only save messages if they are filed in folders; others save messages received but not those sent. You may need to send yourself a copy of your e-mailed assignment at the same time you send it to your instructor, or you may need to print a copy of the e-mail message and any attachments to keep in your paper files. No matter how your system works, make sure you know how to save copies of all messages that you send to your instructor and that you save the copies for several months beyond the end of the course.
Library Services
Students enrolled in Carolina Courses Online have access to the UNC Library System. Visit Distance Education Library Services to access a wide array of online services and resources including online databases, online journals, online books, and live help with research and library access. Most online resources require you to log in with your Onyen and password. If you have any trouble finding the resource that you need or logging in to a resource, you can contact the library through the contact information at Distance Education Library Services. You can chat live about your problem, or send an e-mail to request assistance.
Other Questions
Contact your instructor with questions regarding the content of the course and your progress. (There is an e-mail link at the top of every lesson page.) Please include “CCO MATH 381” in the subject line of your e-mail.
Contact the instructional designer at the Friday Center about problems with this Web site, including viewing the mathematical notation on the lesson pages and bad links.
Contact the UNC Help desk (not your instructor) for any problem you have with technology—your Internet connection, downloads, Blackboard, and so on. Help is available twenty-four hours a day, seven days a week.
If you have any logistical questions as you work through the course (enrollment, Onyen, credits, withdrawal, and so on), contact the Student Services staff at the Friday Center for Continuing Education (phone 919-962-1134 or 800-862-5669).
Honor Code
Remember that as a student of UNC-Chapel Hill, you are bound by the University’s Honor Code: “It shall be the responsibility of every student at The University of North Carolina at Chapel Hill to obey and support the enforcement of the Honor Code, which prohibits lying, cheating, or stealing when these actions involve academic processes or University students or academic personnel acting in an official capacity.”
Schedule
Click on the link for each lesson to read my lecture and see your assignments. Pay close attention to the schedule—not all lessons are the same length, depending on content to be covered. Mark due dates (the last day of each lesson) on your personal calendar.