## MATH:4050:0002 Introduction to Discrete Mathematics Fall 2015 Section 0002: 12:30P - 1:20P MWF 105 MLH

Instructor:  Dr. Isabel K. Darcy
Department of Mathematics and AMCS
University of Iowa
Office:B1H MLH
Phone: 335- 0778
Email: idarcybiomath+150 AT gmail.com or isabel-darcy AT uiowa.edu
Office hours: MWF 9:45am - 10:15am, MW 11:35am - 12:20pm, and by appointment.

HW will be posted on this web page, but you can check grades via ICON

HW 1 (due 9/4)
1.8: 4 or 7;
2.7: 1, 4, 6, 9, 11, 16, 17, 19, 20, 21, 27, 29, 39a
Extra credit for HW 1: 38 (0.3 points), 39 bc (0.4 points)

HW 2 (due 9/11)
2.7: 38, 39, and 50, 51, 52

HW 3 (due 9/18)
1-1,
onto,
bijection
2.7: 61, 63
3.4: 1

Answers for Ch 3: 4 - 18 are also available on ICON. I particularly recommend 3.4: 4-7, 9, 11, 12, 14, 15, 18, and for a challenge, 9.

HW 4 (due 10/2)
3.4: 20, 23
4.6: 1

HW 5 (due 10/9)
4.6: 7, 8, 10, 11, 12, 15, 17, AND 36.

HW 6 (due 10/16)
4.6: 5, 37, 44, 46, 48, 49, 51 AND ...

HW 7 (due 10/23)
Ch 5: 3, 6, 7, 10, 11, 25 AND ...

recommended problems: Ch 5: 38, 39, 46, 47

HW 8 (due 11/6)
Ch 6: 2, 6, 9

HW 9 (due 11/13)
Ch 6: 11, 12, 14, 15, 16, 20, and
Determine |B_n| for n > 5 where B_n = the number of permutations of {1, 2, ..., n} where none of the patterns 1(n), 2(n-1), 3(n-2) occurs.
For example if n = 8, the permutation 41862573 is not allowed due to the pattern 18. Similarly 13685274 is not allowed due to the patterns 36 and 27. However, 81726345 is in B_8.

HW hints for HW 9 will be provided in class this Monday 11/9.

HW 10 (due 11/20)
Ch 6: 3, 24, 26
Ch 7: 1a AND 13

HW 11 (due 12/4)
Ch 7: 4, 9, 16, 17, 18, 31, 40

HW 12 (due 12/11)
CH 14: 1, 4, 5, 10, 13, 18, 22, (note 24 is extra credit) 25 and

A.) Suppose the sequences $r_n$, $s_n$, and $t_n$ satisfy the homogeneous linear recurrence relation, $h_n = a_1(n)h_{n-1} + a_2(n)h_{n-2} + a_3(n)h_{n-3}$ (**). Show that the sequence, $c_1 r_n + c_2s_n + c_3 t_n$ also satisfies this homogeneous linear recurrence relation (**).
B.) Suppose the sequence $\psi_n$ satisfies the linear recurrence reln, $h_n = a_1(n)h_{n-1} + a_2(n)h_{n-2} + a_3(n)h_{n-3} + b(n)$ (*). Show that the sequence, $c_1 r_n + c_2s_n + c_3 t_n + \psi_n$ also satisfies this linear recurrence relation.
C.) How many terms of the sequence are needed to find a unique sequence with these terms satisfying (*). What linear system of equations can be used to determine $c_1, c_2, c_3$.

HW 12 extra credit (10 pts, due 12/11): Ch 14: 24

Answers for HW are available on ICON or back of your book.

## Final Exam this Wednesay 8:00 PM - 10:00 PM in our classroom, 105 MLH. You may bring the equivalent of a 3 x 5 notecard. You may write on both sides. Study hall in B11 MLH Monday 1 - 3pm, Tuesday 12noon - 2pm, Wednesday 4 - 7:30pm. Review session Tuesday 2 - 3pm in B13 MLH. To study for the exam: Review HW problems. Part of your exam will be written by using a random number generator to select some HW problems -- note the problems will be modified (at least changing the numbers), so make sure you understand how to do the problem. Answers to HW problems are posted under content on ICON (or in the back of your textbook)Do the following review problems and read over the answers: Review problems, answersTake previous years final exams as practice2006 final exam , 2006 final exam answersFor 2006 final exam: Hint for problem 6: To determine a non-homogeneous solutions, plug in h_n = a3^n to determine a. Skip problem 8bc (not covered this semester)2009 final exam -- we have covered all these problems.

Tentative Schedule

 Monday Wednesday Friday Week 1 8/24: 1.1, 2.1, notes 8/26: 2.2, 2.3, notes 8/28:2.4 notes Week 2 8/31: 2.3, 2.4, 2.5, notes 9/2: 2.4, 2.5, notes 9/4: 2.5, notes Week 3 9/7: Holiday 9/9: 2.6, quiz 1 SG, notes 9/11: , notes Week 4 9/14: notes 9/16: , notes 9/18: 3.2 Week 5 9/21: 3.3, Ramsey game, quiz 2 SG, notes 9/23: , Review, notes 9/25: Exam 1, Answers Week 6 9/28: 3.3 notes 9/30: 4.1 notes 10/2: 4.2, 4.3, Det ex., notes Week 7 10/5: 4.3, 4.5, notes 10/7: 4.5 quiz 3 SG 10/9: 4.5, ch 5 Week 8 10/12: 4.5 equiv reln, notes 5.2 10/14: 4.5, notes 10/16: 4.5, 5.1, 5.2, notes Week 9 10/19: 5.2 quiz 4 SG 10/21: 5.2, 5.5 10/23: 5.4, 5.5 Week 10 10/26: Review 4.5, 10/28: Exam 2, Answers 10/30: 6.1 Week 11 11/2: 6.2, notes 11/4:6.3, notes 11/6: 6.3, notes Week 12 11/9: 6.3, :6.4, notes 11/11: 6.4, notes 11/13: 7.1, DE, notes Week 13 11/16: 7.1, 7.2, notes 11/18: 7.2 quiz 5 SG, notes 11/20: 7.1 - 7.4, notes *****Nov 23 - 27: Thanksgiving Break**** Week 14 11/30: linear, 7.4, 7.5, notes 12/2: 14.1 , quiz 6 SG, notes 12/4: 14.1, 14.2 Week 15 12/7: 14.1, 2, notes 12/9: 14.2 examples notes 7.5, 6.5, 5.3, axiom of choice, 12/11: quiz 7 SG REVIEW PROBLEMS, permutation review Final Exam 12/16: 8:00 PM - 10:00 PM