Discrete Mathematics
Spring 2006
Other resources
Syllabus
Please feel free to come by my office any time during scheduled
office hours.
You are welcome to
come at other times, but in that case you might want to make
an appointment, just to make sure that I will be there then. You can
make an appointment simply by talking to me before or after class, by
calling me at
my office
or at home, or by sending
email.
You may also ask any questions directly via phone or email. If I'm
not in when you call, please leave a message on the voicemail or
answering machine with your name, number, and a good time for me to
call you back. I will try to respond to your phone or email message
as soon as possible.
Course Objectives:
Upon successful completion of the course, you will know and be able
to use the basic algebra of sets and of logic. You will be able to
identify and use common classes of relations. You will know basic
properties of arbitrary functions. You will be able to solve counting
problems involving combinations and permutations, including counting
problems with restrictions. You will know the basic definitions and
theorems of graph theory, and be able to apply them to specific
graphs. You will know the basic algorithms for traversing trees, and
be able to apply them to specific trees.
Note that this class will probably be quite different from other math
classes you have taken, in at least two important ways. First, in
contrast to calculus and related courses, the objects under
consideration are (as the course title suggests) discrete, not
continuous. This has the advantage that you can often explicitly list
all the pieces (try listing all the function values of a continuous
function!), but the disadvantage of not having continuity to "tie"
things together nicely. Second, although there is still a lot of
problemsolving, the problems and their answers have a very different
flavor: the problems are not equations to be solved, and the answers
often aren't even numbers. We also may spend more time explaining why
a particular solution works than in finding the solution.
Textbook:
Discrete Mathematics, 5th ed., Dossey,
et. al., Chs. 2, 4, 5, 8, Appendix A.
We will skip some sections, as announced in class.
The textbook is required at all class meetings.
Required Reading:
Read each section that we cover in class, both before and after class.
Skim the section before class, even if you don't understand it fully,
to have some idea of what we'll be doing in class. Read it more
carefully after class to clarify and fill in details you missed in
class.
Warning:
Sometimes, I will not "cover" all the material from a section, but
instead focus on a particular aspect of the section. In such cases, I
will point out in class (and at this
website) which other
parts of the section I expect you to read on your own.
Grades:
 Homework (15%):

Individual homework will be assigned
regularly, and due approximately weekly. You are allowed to work
together on homework (in fact, I encourage you to do so), but the
paper you turn in you must write yourself. Homework is due at the
beginning of class (10:30 sharp); if you cannot make it to
class, arrange to either deliver the homework to me early, or have
someone else bring it to class for you. Your lowest homework score
will be dropped.
 Exams (15% each):

There will be three inclass tests on the following days:
 Ch. 2: Fri. 17 Feb.
 Ch. 8: Fri. 10 Mar.
 Chs. 4,5: Fri. 28 Apr.
Makeup exams can be given only in extraordinary and unavoidable
circumstances, and with advance notice. (See also "Exception"
below.)
 Final (40%)
 comprehensive (including Appendix A)
Fri. 12 May, 10:00 a.m.12:45 p.m.
 Exception
 Your final exam score will be used in place of your lowest
inclass test score, if this increases your overall class average. In
particular, if you miss a test, your final exam score will replace it.
Attendance Policy:
I strongly encourage you to attend every class, though there is no
particular grade penalty for absences. My goal is for class meetings and
activities to complement, rather than echo, the textbook, and thus for
every class to be worth attending.
Drop date:
The deadline for studentinitiated drops with a W is Fri., 24 Mar. After
this date, you can only drop with the Dean's approval, which is granted
only under extenuating circumstances.
I hope everyone will complete the course successfully, but if you are
having doubts about your progress, I will be happy to discuss your
standing in the course to help you decide whether or not to drop.
You are only allowed three enrollments in this
course, so please exercise the drop option judiciously.