{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# lec0221 - CS 173 Discrete Mathematical Structures Cinda...

This preview shows pages 1–10. Sign up to view the full content.

CS 173: Discrete Mathematical Structures Cinda Heeren [email protected] Siebel Center, rm 2213 Office Hours: W 9:30-11:30a

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

View Full Document
Cs173 - Spring 2004 CS 173 Announcements Homework 6 available. Due02/26, 8a. Midterm 1: 2/23/06, 7-9p, SC 1404. Conflict: 2/24/06, 7-9p, SC 3405 (email me!) Sections this week will beexam review. Three additional reviews: Tues, 2/21, 6-7p, SC 1129 Thur, 2/23, 9:30-10:45a, SC 1404 Thur, 2/23, 11:00a-12:15, SC 1214
Cs173 - Spring 2004 CS 173 Mathematical Induction, an example Prove that for all n, k 2 k =1 ν = ν ( ν + 1 29 (2 ν + 1 29 6

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

View Full Document
Cs173 - Spring 2004 CS 173 Strong Mathematical Induction If P(0) and 2200 n 0 (P(0) P(1) P(n)) P(n+1) Then 2200 n 0 P(n) In our proofs, to show P(k+1), our inductive hypothesis assures that ALL of P(0), P(1), … P(k) are true, so we can use ANY of them to make the inference.
Cs173 - Spring 2004 CS 173 Strong Mathematical Induction An example. Given n bluepoints and n orange points in a plane with no 3 collinear, provethereis a way to match them, blueto orange, so that none of thesegments between thepairs intersect.

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

View Full Document
Cs173 - Spring 2004 CS 173 Strong Mathematical Induction Basecase (n=1): Assumeany matching problem of size less than (k+1) can be solved. Show that we can match (k+1) pairs.
Cs173 - Spring 2004 CS 173 Strong Mathematical Induction Show that we can match (k+1) pairs. Supposethere is a linepartitioning the group into a smaller oneof j blues and j oranges, and another smaller oneof (k+1)-j blues and (k+1)-j oranges. OK!! (by IH) OK!! (by IH)

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

View Full Document
Cs173 - Spring 2004 CS 173 Strong Mathematical Induction How do weknow such a linealways exists? Consider the convex hull of the points: If thereis an alternating pair of colors on the hull, we’re done! OK!! (by IH) OK!! (by IH)
Cs173 - Spring 2004 CS 173 Strong Mathematical Induction If thereis no alternating pair, all points on hull arethesame color.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ 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