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MATH 310, FALL 2003 (Combinatorial Problem Solving) MoWeFr 1:20 McGregory 214

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Instructor Professor Tomaž Pisanski tpisanski@mail.colgate.edu Office: McGregory 208, Phone:7652 Office hours: Tuesday and Wednesday 3-5 and by appointment

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Text Alan Tucker: Applied Combinatorics (4 th edition) We will cover most of Chapters 1,2,5,6 and part of Chapters 3,7,8. If time permits we will cover a bit of Chapters 4 and 9. There will be both theoretical and computer programming challenges. Please bring your text to every class meeting.

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Homework Homework will be assigned after each lecture and will contain mainly exercises from the text and reading from the same source. It will be collected once a week on Mondays in class. The homework will be discussed in detail in class the day it is handed in. There will be answer sheets to selected problems. I will not be correcting the homework, only keeping a record of whether you handed it in on time. I expect everyone to have near- perfect homework records.

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Class participation and homework presentation (50* pts) Class participation is strongly encouraged, in particular during the homework discussion. For each assignment, a pair of students will volunteer for a 5 or 10 minute combined presentation of ONE problem from the assignment. They will also hand in a typewritten version of their presentation. Written version has to be handed in on Monday a week after it was presented in class. All students will make at least one presentation during the semester, and these presentations will be part of your grade for the course. In each assignment you should select at least TWO problems for which you clearly write or print extensive and complete solutions with explanation in English. (*) I reserve the right to assign up to 10 bonus points for outstanding class participation.

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Midterm Evening Exams (100+100 = 200 pts) There will be two open ended Midterm Evening Exams. They begin at 7:30 pm, and you will be allowed as much time as you like. You may aim to finish the exam by 11:00 but you are allowed to stay as long as you need. The exam dates are: Wednesday, October 1 and Monday, November 17.

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Final Exam (150 pts) There will be a traditional 2 hour cumulative final exam.

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Technology The emphasis is on problem solving rather than theory. Some examples in class will involve Mathematica. You may be asked to write an algorithm but not required to turn in a working program. You may choose to write a program for your class presentation. Mastering computer programming in any modern computer language is most useful for clarifying new combinatorial ideas and concepts. In particular, powerful systems such as Maple or Mathematica will save time. Every second Wednesday there will be group office hours in 201E. You may use anything you want on the exams including a two-page “cheat sheet”.

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Grades Your grade will be based on the two midterm exams (200 points), the final (150 points), homework and class participation (50 points). A perfect score is therefore 400 points. Up to 10 bonus points may be obtained for an outstanding class participation. There may be a quiz or two bringing further bonus points (up to 20).

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Guest Lecture There may be a guest lecture in order to show the importance and application of combinatorics to other parts of science.

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Office Hours I expect most office hours to be individual in my office with 10-15 mintes per student. I expect each student to come to my office individually during the first two weeks of classes for a brief mutual introduction. There will be some group office hours intended primarily for Matlab and other computer-related questions. The first one will take place on Wednesday, September 3, 3:00-5:00 in 201E (MATLAB).

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1.1. Graph Models Homework: Read 1.1 and 1.2. Do Exercises1.1: 1,2,5,6,13,14,19,20,27,28. Volunteers: ____________ Problem: 20.

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