Together we will work through countless problems and see how the pigeonhole principle is such a simple but powerful tool in our study of combinatorics. Topics covered: Sets (Ch 1), Logic (Ch 2), Counting (Ch 3 + extra materials), Direct Proofs (Ch 4).Consequently, using the extended pigeonhole principle, the minimum number of students in the class so that at least six students receive the same letter grade is 26. In this issue, we revisit an idea, the pigeonhole principle, that I used to. Generalized permutations and combinations continued Click here to submit solutions, comments and generalizations to any. Generalized permutations and combinations Generalized Permutations and Combinations (Chapter 6.5 of Rosen book)Ĭhapter 3 Study Guide (includes extra topics) Principle of inclusion-exclusion (section 3.5) Logical Connectives, Conditional, Biconditional Operations on sets, Venn diagram, Indexed sets Set Theory - definitions, representations, power set, Cartesian product : First part of set theory slides posted.Ĭourse outline Course Information Handout.: The remaining set of set-theory-slides is posted. The solution to Problem 1.2 implies a stronger version of the Pigeonhole.: Quiz 1 will be held next week in the tutorial.: Solution to the even numbered questions of Set Theory is. : First part of logic slides and Chapter 2 (Part I) study guide are updated with new materials.: Second part of logic slides is posted.: Second part of logic slides is updated.: First part of counting slides is added.: Solutions to the even numbered questions of Logic chapter.Prove that among 13 people, there are two born in the same month. : Quiz #3 will be held during the week of Feb. Here the sexes are the boxes, and the people are the.: Solutions to the even numbered questions of Counting chapter.: Practice problems discussed in the tutorials of week 8.: Extra Lecture slides on Proofs are added.The syllabus is Chapters 4 through 9 of the text. : Quiz #4 will be held next week (Week of March 9).: Solutions to the even numbered questions of chapters 5 and 6.If no two teams play each other more than once, prove that two teams have to play the same number of games. : Lecture slides on Inductions are added. Problem 1: Suppose n 2 baseball teams play in a tournament.: Solutions to the even numbered practice questions of chapters 7,8 and 9.: Lecture slides on Relations are posted. The syllabus is the contents of Chapter 11, partial orders (Section 9.6 of Rosen's text).
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