Computer Science 582/482B
Maple Flavored Concrete Mathematics
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Grad Students: Do you use discrete
mathematics in your research?
Discrete mathematics, in one form or the other, makes its way into
almost every computer science thesis.
Most of our graduate students have taken a discrete math course as part of
their undergraduate training, but quite often they find that they've
forgotten this material and now need some part of it for their
thesis research.
In the past, some grad students have sat through Math 224/324,
but this is not really a satisfactory solution.
This course is designed as a thorough introduction, at the graduate
level, to those areas of discrete mathematics (exclusive of
graph theory), that are most useful to the average
computer science researcher.
There are many software tools available to aid in discrete
mathematical computations, and the best of these is Maple.
We will use Maple as a resource throughout the course, and try
to uncover some of the internal algorithms that it uses.
The only prerequisites for this course are some previous exposure
to discrete mathematics and a beginning programming course.
Concrete Mathematics
The text for this course is
Concrete Mathematics by Graham, Knuth, and Patashnik.
It is the finest Mathematics textbook ever (imho).
The best description of this text is the one given by the
authors themselves, a copy of which has been placed outside
my office door (EOW 321).
The following chapter headings should give you an idea of the
contents of the book and the course: Recurrent Problems,
Sums, Integer Functions, Number Theory, Binomial Coefficients,
Special Numbers, Generating Functions, Discrete Probability,
Asymptotics.
Here
is publisher info about Concrete Mathematics.
Here is a list of errata for the book.
Maple
Maple is a wonderful symbolic computation system.
Many of our graduate students have found it extremely useful
in their research.
On the other hand, I've read several theses that contained page
after page of detailed (and error prone) algebraic manipulation
that could have been handled quite easily by a small Maple
program.
The use of a symbolic manipulation system should be in the
bag of tricks of every graduate student.
There is no text for this portion of the course.
There will be some handouts and some books on reserve.
Here's a picture of those books:
Some Relevant Links:
Grading
Course grading is based on a series of 1/2 hour quizes,
and occassional homework problems.
The problems on these quizes come directly from the text
or are small variants thereof.
There will also be some pass/no-pass Maple programming assignments.
Graduate students will have to undertake a pass/nopass mini-project
based on the course material.
Time
The class will run TW 4:30-6, in Cunningham 146.
Problem List
Click to get them.
