EECS
lec20-review-exam2

# lec20-review-exam2 - EECS 203 Winter 2007 Discrete...

• Notes
• 7
• 100% (1) 1 out of 1 people found this document helpful

This preview shows pages 1–7. Sign up to view the full content.

EECS 203, Winter 2007 Discrete Mathematics Lecture 20 Review for the 2nd Exam March 20 Reading: Covered sections in Rosen March 20 Review for the 2nd Exam, Page 1

This preview has intentionally blurred sections. Sign up to view the full version.

20.1 Matrices and graphs Key concepts: matrix, symmetric, transpose, matrix multiplication, graphs (undirected and directed), path, cycle, walks, connected, connected components, isomorphism, subgraphs, adjacency matrix, incidence matrix. Key results: If A is the adjacency matrix of G , then [ A k ] u,v is the number of different walks from u to v using exactly k steps. Ramsey’s Theorem: for any integers s and t , there exists R ( s, t ) so that any graph with at least R ( s, t ) vertices would have a size s clique, or its complement has a size t clique. March 20 Review for the 2nd Exam, Page 2
20.2 Sum and sequence i a i , i ia i - 1 i i , i i 2 , i i ( i - 1). Approximation by integration: ln( n + 1) = n +1 x =1 1 /xdx n i =1 1 i 1 + n x =1 1 /xdx = 1 + ln n. An approximation of n !: n x =1 ln xdx ln n ! = i ln i n +1 x =2 ln xdx. Since ln xdx = x ln x - x + C , n ln n e ln n ! ( n + 1) ln n + 1 e . March 20 Review for the 2nd Exam, Page 3

This preview has intentionally blurred sections. Sign up to view the full version.

20.2 Sum and sequence A better bound 2 πn ( n e ) n e 1 12 n +1 < n ! < 2 πn ( n e ) n e 1 12 n . Stirling’s formula:

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Winter '07
• YaoyunShi
• Graph Theory, Natural logarithm, ln xdx ln

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern