1 / 20

MATH 310, FALL 2003 (Combinatorial Problem Solving) Lecture 3 4, Friday, November 21

MATH 310, FALL 2003 (Combinatorial Problem Solving) Lecture 3 4, Friday, November 21. 7.1 . Recurrence Relation Models. Homework (MATH 310# 10W ): Read 7.1 Do 6. 5 : all odd numbere d problems Turn in 6. 5 : 2,4,6,8 Turn in 7.1: 2,4,6 ,12,16,18,26,48. Test 1 & 2 - Statistics.

pbarrett
Download Presentation

MATH 310, FALL 2003 (Combinatorial Problem Solving) Lecture 3 4, Friday, November 21

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MATH 310, FALL 2003(Combinatorial Problem Solving)Lecture 34, Friday, November 21

  2. 7.1. Recurrence Relation Models • Homework (MATH 310#10W): • Read 7.1 • Do 6.5: all odd numbered problems • Turn in 6.5: 2,4,6,8 • Turn in 7.1: 2,4,6,12,16,18,26,48

  3. Test 1 & 2 - Statistics • Here is a stem-and-leaf report on the total. • Median: 187 • (Bonus points are not counted.)

  4. Test 2 - Statistics • Here is a stem-and-leaf report on the test. • Median: 94 • There are is only one mark.

  5. Test 2 – Problem #1 Median 0

  6. Test 2 – Problem #2 Median -1

  7. Test 2 – Problem #3 Median -3

  8. Test 2 – Problem #4 Median -2

  9. Test 2 – Problem #4 Median -2

  10. Test 2 – Problem #4 Median -2

  11. Test 2 – Problem #5 Median -5

  12. Test 2 – Problem #6 Median -3

  13. Test 2 – Problem #7 Median 0

  14. Test 2 – Problem #8 Median -2

  15. Test 2 – Problem #9 Median -4

  16. Test 2 – Problem #10 Median -1

  17. Test 2 – Problem #11 Median -7

  18. Recurrence Relation • an = c1an-1 + c2an-2 + ... cran-r. • an = can-1 + f(n). • an = a0an-1 + a1an-2 + ... + an-2a1 + an-1a0. • an,m = an-1,m + an,m-1. • Initial Conditions. • an = an-1 + an-2, a0 = 2, a1 = 3.

  19. Example 1: Arrangements • Find a recurrence relation for the number of ways to arrange n objects in a row. • an = nan-1. • a0 = 1.

  20. Example 2: Climbing Stairs • n – stairs to climb • each step can cover either 1 step or 2 steps. • Find a recurrence relation for an, the number of ways to climb the stairs. • an = an-1+an-2. • a0 = a1 = 1.

More Related