Introduction to Combinatorics

Math 28 is a course in combinatorial mathematics. This year the course is being taught as a "guided discovery" course. This means that the primary text for the course is a set of problems with just enough prose so that the problems will make sense. It is available at the course web page www.math.dartmouth.edu/~m28w03/book.html in the form of course notes. By working these problems, students will discover for themselves the main theorems of combinatorial mathematics (and their proofs) and examples of how these theorems are used. Students are encouraged to work together on the problems. Students are expected to work as many of the problems as they can and submit them. Certain problems will be designated each week in advance as "mandatory" problems. These problems will be graded and returned to the student.

Class time will be devoted largely to a discussion of the problems and the broad themes in combinatorial mathematics that the problems illustrate. This discussion will be split between whole class discussion, including possible student presentations of their ideas, and small group discussions. Students will be graded on class participation. Unfortunately, coming late to class may disrupt small group discussions, and so this will have to be reflected in the class participation grades of students who habitually come late to class. Of course it is difficult to participate if one does not come to class at all, and so habitual absence will also be reflected in the class participation grade.

I hope the following quote will inspire you to participate in this course.

"Mathematics is not for spectators; in order to gain in understanding, confidence, and enthusiasm one has to participate." M.A. Armstrong

Required

• Combinatorics Through Guided Discovery by Ken Bogart

• MWF 11:15-12:20, Bradley 103
• (xhour) Tuesday, 12-12:50 Bradley 103

Note: X-hours will be used when the instructor has to be out of town and miss a class, when the class needs additional time working together, for review and for other purposes. However the use of an X-period will be announced in advance. Since the advance notice may be short, students are expected to keep the X-period open.

 Please, do not make plans to leave Hanover before the exam.

• Written homework will be assigned daily and will be collected two lectures later  (ex: homework assigned on Wed. will be collected on Monday) at the beginning of class.
• The mandatory homework will be graded on a 10/9/5/0 rule. Perfect papers (correct and well written) will be assigned a 10, paper that are almost perfect except for a minor problems with writing or correctedness will be assigned a 9, problems where the student has made significant progress towards a correct solution will be assigned a 5, and if the solution is completely incorrect the student will receive a 0.  Problems done during class will count 1 point for the write-ups.
• If a student receives a 5 or 0 on a problem, he or she will be allowed to hand-in the problem a second time within a week from the time the paper is returned to the student.
• All homework assignments will be posted on the course assignment's web page.
• Unexcused late and missing papers count zero.
• Homework is to be written neatly using both sides of 8 1/2 x 11 inch paper. Do not use paper from a spiral notebook unless you can tear off the ragged edge. All papers are to be stapled.
• Use English. If you can't read your solutions aloud as fluently as if you were reading a textbook, try using nouns and verbs in your write ups!

The course grade will be based upon the scores on the homework, two exams, participation (this means attending class as well as asking and responding to questions), and the final exam.
 

Exams (2)	15% (each)
Homework	40%
Participation	10%
Final Exam	20%

On Exams: No help given or received from anyone. You may not use books or notes during in-class exams. For take-home exams you can use your class notes only.

On Homework: Collaboration is permitted and encouraged, but NO COPYING . In other words, you should feel free to talk to other students while you are in the process of thinking about a problem. However, when it comes time to write up your solutions, you should do this by yourself without outside assistance.

Any student with a documented disability needing academic adjustments or accommodations is requested to speak with the instructor by January 17. All discussions will remain confidential, although the Academic Skills Center may be consulted to verify the documentation of the disability. Students who think they may have a disability but are not sure are encouraged to consult with the Academic Skills Center in Collis Center to register for support services.

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