Office hours: 11-12 and 1-3 on Thursday and Friday
These are my official office hours, but my door is normally open. If
you have questions or if your want to explore an idea, come by. You may
leave a short note on my office door or leave a message on the phone or
e-mail. ("I can't make your hours" is no excuse!)
Americans with Disabilities Act Notice: If you have a disability
and need an accommodation or assistance in this course, please come in
or make an appointment to talk with me to discuss how I can help you succeed
in this course. If you prefer, you may contact Myrna McGaffin Director
of Student Support Services, South Hall.
Catalog Description: Mat 253 Discrete Mathematics Enumeration,
mathematical induction, binomial and multinomial theorems, equivalence
relations and partitions, Stirling numbers, principle of inclusion and
exclusion, generating functions, recursion, graph theory and applications,
elementary algorithm analysis. Prerequisites: Cos 105 and Mat 131 or equivalent.
Credits: 3.
Extended Course Description: This course plays a key role among
our mathematics course offerings. It meets the need for a course in discrete
mathematics in the preparation of secondary mathematics teachers as specified
by the State Department of Education and lays groundwork for further study
in computer science. Discrete math appears in numerous places within other
mathematical developments such as geometry, abstract algebra, probability
and statistics, and operations research. In addition, it is an opportunity
to sharpen ones basic reasoning and counting skills and gain confidence
in communication mathematical ideas. The prerequisites of calculus and
computer programming are mainly to ensure the "mathematical maturity" necessary
to enjoy combinatorial problem solving.
Goals: The course has two primary aims:
1) For you to develop a deeper understanding of the natural numbers, and
2) For you to use and demonstrate that understanding by devising your own mathematical arguments and proofs.
Also, the aim is to have fun, and make logical
reasoning come alive! The course provides a stimulating review/discovery
of elementary counting principles. We predict a rather different experience
from the average mathematics course.
Teaching Methods: This course will be taught featuring a mixture of a highly interactive lecture format and cooperative learning experiences, with a great deal of emphasis on the latter. Students will be required to do a great deal of writing (e.g., answering questions like ), indeed this is the way most of the credit for the course will be earned. There will be few "mathematical computation" assignments.
We will use Excel, a spreadsheet program available on both Macintosh and Windows platforms.
The course will be organized around a series of problems from the text Combinatorics: A Problem Oriented Approach. Several of these problems will be assigned each week. You should explore each question and write out your thinking in a way that can be shared with others. Focus on your own ideas and understandings. Turn in whatever your thinking is on a question, even if only to say, "I do not understand such and such" or "I am stuck here." Be as specific as possible. Conjecture. Use pictures. I will return your papers with comments, questions and suggestions. Respond to my comments. Use them as invitations to clarify your understanding of the problem or our understanding of your solution.
Your responses to the problems will be due weekly (drop off options discussed below), so that I can offer you comments and feedback. In class, students will share and explain their solutions, ask questions, etc. The cycle of writing, comments, and discussion will continue on each problem until both you and I are satisfied that you have reached a resolution or time constraints intervene.
There will be many times when we will pose questions
to which we do not know the answer. Such answers will be sought together,
often over a period of time.
Attendance and Tardiness: Participation is an important part
of your learning, therefore class attendance is EXPECTED. Your regular
attendance is necessary and poor attendance may reduce your grade because
of missed information and experiences. I will take attendance from time
to time, especially at first. I will strive to make every class worthy
of your attendance, and helpful in your understanding of the course material.
I plan to start class on time and expect that you
will be there. Class begins at the beginning of the class period. If you
find it necessary to be late for class, I prefer that you come in after
class has started rather than miss the entire class period. However, tardiness
should never develop into a pattern. Remember that you are preparing to
be a professional. Your practice now has bearing on what can be expected
of you in the future.
Required Texts and Materials:
1. The course text: Combinatorics: A Problem Oriented Approach
by Daniel A. Marcus. Published by the Mathematical Association of America,
$22.50 plus $2.95 shipping. http://www.maa.org/pubs/books/cmb.html
Available at the campus bookstore.
2. A problem folder or "portfolio". Three ring binder is best.
3. Calculator. One which does tables such as a TI 82 or 83 is nice.
Evaluation, Assessment, and Grading In the cycle of writing, comments, and discussion there is no distinction between learning activities and assessment activities. For each problem, I will indicate your progress by a numerical grade. If you do not submit a response to a problem until after we have begun discussing it in class, your response will be considered late and will be noted as such.
The best approach is to strive for a solid
understanding of the course topics and to accept at the start that this
necessarily entails some struggling with ideas and feelings of frustration.
The problems in the course may take time, especially time to explore and
think about the ideas. Often you will need to walk away for a short while
or for a day and return to a problem for a second or third look before
writing up your response. Expect this. However, do not get behind on the
problems. Stay connected, and see me whenever you are having difficulty
or if extenuating circumstances arise.
Grading principles and defined weight (%) of each component such as exams, quizzes, projects, assignments, papers and criteria for assigning the grade: The grade for the course will be based solely on turned in Homework Assignments (80%) and a Final (20%). There will be no other quizzes or tests.
Your grade in this course will
depend almost exclusively on written work (homework, examination) so that
it is important that you learn how to communicate clearly in writing.
Any work you submit for evaluation calls for an explanation of what you
have done with the aid od of complete, grammatically correct English sentences.
(Symbols abbreviate English words or phrases and may be used as parts of
sentences.) I will read exactly what you have written, and will make
no attempt to deduce what you "really" mean or to supply missing steps
or logical connectives. Any symbols you introduce that are not standard
must also be explained or quantified. Make sure, also, that you supply
an explicit answer to each problem you claim to solve.
In particular, I do not separate
form and content. I I can't understand some part of your work,
I will not struggle to read it, and your grade will suffer accordingly;
even if you got the "right" answer. Your explanations need not be
lengthy to be clear. (From: "You Can and Should Get Your Students
to Write in Sentences" by Melvin Henriksen in Using Writing to Teach
Mathematics, Andrew Sterrett Editor, MAA notes Number 16, The Mathematical
Association of America 1992.)
Each homework will be graded out of 12. Only the best 90% of these scores will go towards your grade, so that for example your lowest 3 scores will be dropped if 30 "homeworks" are assigned.
Up to 3 points may be added to your final course grade based on class participation, including attendance.
More than the equivalent of one week of absence
from the class meetings or excessive late arrivals to class will lower
your final grade.
Collaborative work: You are welcome to discuss
the course problems with others or to look in books or other references.
However, whenever your ideas are shaped by a classmate's solution, a discussion
with a friend, family member, or faculty, or by a written source, be sure
to acknowledge that source in your work. Failure to do so constitutes plagiarism;
it will result in a failing grade for the course and will be reported to
the appropriate authorities.
Some Reminders:
1. Please keep all of your old writings in your
folder so that we can refer back to them. Indicate by a paper clip your
current effort that you would like me to look at.
2. Turn in homework exercises by 10AM on Monday/Wednesday in the plastic gizmo outside my office door. I’ll try to get it back to you at class time. Homework turned in at Monday’s/Wednesday’s class should be back to you by Wednesday’s/Monday’s class.
3. In the event that you are unable to attend
class and need to pick up your folder, I will place it in the plastic gizmo
outside my office door.
Grading policies such as withdrawal, incomplete
work and makeup policy and procedure: Please
refer to the college catalog. I use the UMPI Catalog verbal interpretation
of letter grades: A - High Honors, B - Honors, C - Average, D - Below Average,
F - Failure
Tentative Schedule Course Outline and Content
A brief review(?) of the Natural Number system.
Basics
The Principle of Mathematical Induction
Strings
Combinations
Distributions
Partitions
Special Counting Methods (as time allows)
Inclusion and Exclusion
Recurrence Relations
Generating Functions
The Polya-Redfield Method