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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.

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

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  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.

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