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Unformatted text preview: Combinatorial Structures Freely using the textbook by LovászPelikánVesztergombi Péter Gács Computer Science Department Boston University Fall 2009 Péter Gács (Boston University) CS 131 Fall 09 1 / 176 Introduction Introduction For details on the course structure (syllabus, policies, lecture schedule, homework), see the course homepage www.cs.bu.edu/ ∼ gacs/courses/cs131 . The course introduces some general techniques of mathematical reasoning used in computer science. You will get most benefit from it as a freshman, but I hope it is not completely useless for those taking it later just to satisfy the requirement. The material is sets, functions, relations, counting, graphs. Much emphasis will be on methods of sound reasoning and proof. (We will practice rigorous reasoning, but not learn any rigid formats for doing proofs!) Péter Gács (Boston University) CS 131 Fall 09 2 / 176 Introduction On our books We use: LPV (LovászPelikánVesztergombi) Péter Gács (Boston University) CS 131 Fall 09 3 / 176 Introduction Homework Start early, so that you have time to ask questions. Do not skimp on time: many of the problems will be deliberately such that they cannot be solved in a snap. In my experience, this is necessary for real learning. Work neatly. First, your grader is not obliged to spend extra time trying to decipher what you were trying to do. Second, sorting out things on paper helps sorting out your own ideas. Do not skimp on paper: start new line, new paragraph, new sheet of paper frequently. Péter Gács (Boston University) CS 131 Fall 09 4 / 176 Introduction Grading Homework: The purpose of homework grade is to give you some incentive to work and to provide feedback. But the percentage contribution of homework to your final grade is low, so you do not gain much by plagiarizing the work of others. Also it is not worth wasting your and my time coming to office hours and haggling on homework partial credit: come only if you think there is real misunderstanding or mistake by the grader. Exams: I do not give partial credit easily, and give it only if I see some real understanding. Even a lot of writing will not get credit if the reasoning is wrong. Be careful about how you argue over a grade. I am frequently amused over students who do it even before they tried to understand what they did wrong. Péter Gács (Boston University) CS 131 Fall 09 5 / 176 Counting Some examples Counting Some examples Names: Alice, Bob, Carl, Diane, Eve, Frank, George. How many handshakes among these 7 people? 6 + 5 +···+ 2 + 1 = 6 · 7 2 (arithmetic series). 7 · 6 2 since everybody shakes with everybody else, and here we counted each shake twice, from both sides....
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 Spring '11
 FredPhelps
 Math

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