![]() ![]() Topics covered: Sets (Ch 1), Logic (Ch 2), Counting (Ch 3 + extra materials), Direct Proofs (Ch 4). ![]() 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.Although it is one of the most powerful tools of combinatorics. It is one of the strategies which is often used for problem-solving. This is known as a pigeon-hole principle (or Dirichlet’s). : Second part of logic slides is posted. If n objects are placed in k boxes, where n qk + r, q and r are positive integers, and 0 : 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). : Quiz #5 will be held next week on Friday, March 27, in the class.: Solutions to the even numbered questions of Chapter 10 (Induction) can be found.: Solutions to the even numbered questions of Chapter 11 can be found.: More practice problems on relations can be found.: Lecture slides on Probability Theory are posted.: Lecture slides on Functions are posted.: Lecture slides on Functions are updated.: Lecture slides on Pigeonhole Principle are posted.The information on the classrooms can be found here. Typically in these cases someone has exhibited a \(K_m\) and a coloring of the edges without the existence of a monochromatic \(K_i\) or \(K_j\) of the desired color, showing that \(R(i,j)>m\) and someone has shown that whenever the edges of \(K_n\) have been colored, there is a \(K_i\) or \(K_j\) of the correct color, showing that \(R(i,j)\le n\).MACM 101-D2: Discrete Mathematics (Spring 2015) Generalizations of this problem have led to the subject called Ramsey Theory.Ĭomputing any particular value \(R(i,j)\) turns out to be quite difficult Ramsey numbers are known only for a few small values of \(i\) and \(j\), and in some other cases the Ramsey number is bounded by known numbers. Ramsey proved that in all of these cases, there actually is such a number \(n\). ![]() \) contained in \(K_n\) all of whose edges are color \(C_j\).
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