This course was developed in conjunction with Dr. David
Dennis (UTEP) with support from the
Institutions for Excellence (MIE) initiative,
funded at UTEP
by the National Science Foundation
Please feel free to come by 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 sending
The course may be roughly divided into two halves, combinatorics and
graph theory, with a few topics on the edges of these. Combinatorics
will include induction, permutations, combinations, recurrences and
more difficult counting problems. Graph theory will include basic
graph definitions, trees, and graph algorithms. We will also see
modular arithmetic and ``big-O'' notation (order of magnitude). There
is no textbook.
The course grade will be based entirely on projects. Each project
will have an initial due date (approximately weekly), by which time
some work (however partial) must be turned in. These
will be returned as soon as possible with questions and comments,
after which you may respond, revise, amend, and then resubmit the
project. Resubmitted solutions will again be returned with comments
and may again be revised and resubmitted. No more than five projects
will be accepted during the last two weeks of the course, so please
pace yourself in a reasonable way. Your final grade will depend on a
portfolio of all your submissions for the semester;
therefore, keep all your submissions (even after
turning in subsequent resubmissions for the same project).
Each project will be returned with one of three marks:
For a D, you must eventually get at least a "check" on 50% of
the projects. For a C, you must eventually get at least a
"check" on 80% of the projects. For a B, you must eventually
get at least a "check" on 80% of the projects, and a "check plus" on 50%
of the projects. For an A, you must eventually get at a "check plus"
on 90% of the projects. Some projects will have an asterisked (*)
part that can count for an extra "plus" (i.e., it will turn
another "check" into a "check plus").
- "check minus"
Some engagement with the project, but substantial questions remain.
A well reasoned explanation, but some questions remain.
- "check plus"
A complete and thorough explanation, no further questions.
Because of the experimental nature of this class, attendance is
mandatory at all times. Missing more than three classes over the
semester, without prior approval, will result in your being dropped
from the class with a grade of F.
The deadline for student initiated drops with an
automatic W is Fri. Oct. 4. From then until Fri. Nov. 22,
you can drop the course by consulting me; in that case I will drop you
with a W, as long as I feel you have been making a reasonable
effort in the course.
The purpose of this course is for you to become involved with a wide
variety of situations and contexts which give rise to mathematical
concepts essential for computer science. You will be expected to
engage in a dialogue between grounded activity and systematic inquiry.
Grounded activities will include situations arising from physical
activity with games, puzzles, coins, dominoes, paper, rubber bands,
and other physical objects. Systematic inquiry will involve the
fullest possible use of linguistic tools (such as words, numbers,
symbols, drawings, diagrams, tables, graphs, and computer software),
usually using measurements made with the positive integers
Usually working in small groups with your classmates, you will
engage each problem or situation presented in class and will attempt
to describe and explain the results of that engagement in a written
report. You must write your report yourself (a
private oral exam is always possible, in case of irregularities). A
description, experiment, explanation or proof is anything which is
both meaningful to you and convinces other people of
the validity of your thoughts, words and activities. Reports may
incorporate any available media including written words, symbols,
pictures, diagrams, models, tables, graphs, videos, computer discs,
etc. I will be evaluating the written parts of your reports for
grammar and other elements of writing.
After the initial reports are returned, selected students will be
chosen to present their work in class. After such presentations
others may still continue to resubmit those same projects in their own
personal way making full or partial use of what has been presented.
Originality and diversity of expression will always be encouraged.
We hope to use the results of this course as a model for the reform of
this and similar math courses here at UTEP. For this reason some of
our classes may be videotaped. Such videotapes will be used for
research purposes only, and will not be shown in any public forum
without the prior written consent of those who appear in those tapes.
Mathematics is not a march down any particular road, but
rather a walk in a garden with many branching paths that circle and
wind back onto themselves. Visitors stroll in many different ways,
pausing to look down at a single small flower, or gaze out over an
enchanting vista, or perhaps even to water, weed or plant (for a
garden is a human creation constructed within the constraints of
life). Each new return brings its own special set of views and
experiences. - David Dennis