Therefore, from the set of integers from 1 to 45, we can choose at most $(3)(2)+(11)(2)=28$ elements where no 2 differ by exactly 14. From the order 3 sets,you can choose a maximum of $\lceil 2/2 \rceil=2$ elements without having any 2 differ by exactly 14. From the order 4 sets, you can choose a maximum of $\lceil 4/2 \rceil=2$ elements without having any 2 differ by exactly 14. The standard solution involves defining the total number of games played by the end of day $i$ (where $i$ ranges from 1 to 30) as $a_$ are sets of order 3. Some number of consecutive days during which the team must play Topics covered: Sets (Ch 1), Logic (Ch 2), Counting (Ch 3 + extra materials), Direct Proofs (Ch 4).This starts with a classic pigeonhole principle question, which has appeared on Mathematics Stack Exchange before, in various forms:ĭuring a month with 30 days, a baseball team plays at least one game aĭay, but no more than 45 games. Generalized permutations and combinations continued 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.: 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.
: Quiz #3 will be held during the week of Feb.: 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.: Lecture slides on Inductions are added.: 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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