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.

** Wiki Site: ** https://wiki.uiowa.edu/display/2396865/Class+List

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

**HW 1 (due 9/4)**

read 1.1;

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.

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, answers

- Take previous years final exams as practice

- 2006 final exam , 2006 final exam
answers

- For 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.

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 |

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 |