Instructor: Dr. Isabel
Darcy
Office:B1H MLH
Phone: 335- 0778
Email: idarcy AT math.uiowa.edu
Office Hours:
M 11:45am - 1:15pm, T 4:45pm - 5+,
WF 9:40 - 10:10am, Th 2:30 - 3:15pm, and
by appointment.
HW will be posted on this web page, but you can check grades via ICON
HW 1 (due Friday, Sept 11)
answers
read 1.1; 1.8) 4 or 7;
2.7: 1, 4, 6, 9, 11, 16, 17, 19, 20, 21, 27, 29, 38, 39
HW 2 (due Wednesday 9/16) some answers for
HW2
Ch 2) 48, 49, 50, 51, 52, 61, 63 and
3.4) 1
HW 3 (due Wednesday 9/23)
some answers for HW's 3 and 4
3.4) 8, 12, 18 and (20 or 23);
HW 4 (due Wednesday 10/7)
Ch 4: 1, 5, 7, 8 (exam 1 material)
Ch 4: 15, 19, 20, 35, 36 (exam 2 material)
HW 5 (due 10/14)
Ch 4: 37, 44, 46, 48, 49, 51
HW 6 (due Wednesday 10/21)
Ch 5: 3, 6, 7, 10, 25
Ch 5: 11, 40, 46 (note addition of 46)
Ch 6: 2
HW 7 (due Wednesday 10/28)
Ch 6: 3, 6, 9
HW 8 (due Wednesday 11/11)
Ch 6: 15, 16, 17, 24, 26 [Note the addition of 16]
Note the above HW assignment is the final version. No further changes to
HW 8
will be
made.
HW9 (due Wednesday 11/18)
Ch 6: 27 and
Ch 7: 4, 16, 17, 18
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 $c_1, c_2, c_3$.
HW10 (due Wednesday 12/2)
Ch 7: 8, 38a, 39, 40, 45 and Ch 14: 1
The following is tentative and will change:
HW11 (due Wednesday 12/9)
review HW problems (due 12/6) and ch 7 #4 answer,
review HW answers
Tentative Schedule
| Week 1 | 8/24: 1.1, 2.1 | 8/26: 2.2, 2.3 | 8/28:2.4 |
| Week 2 | 8/31: 2.3, 2.4, 2.5 | 9/2: 2.4, 2.5 | 9/4: 2.5 |
| Week 3 | 9/7: Holiday | 9/9: 2.6 | 9/11: ch 3 |
| Week 4 | 9/14:3.1, 3.2 | 9/16: 3.1, 3.2 | 9/18: 3.2 3.3, Ramsey game |
| Week 5 | 9/21: 3.3 | 9/23: 3.3 , 4.1 | 9/25: 4.2, 4.3 |
| Week 6 | 9/28: Review | 9/30: Exam 1, Answers | 10/2: 4.3, 4.4, |
| Week 7 | 10/5: 4.4, 4.5 | 10/7: 4.5 | 10/9: 4.5, ch 5 |
| Week 8 | 10/12: equiv reln, 5.1, 5.2 | 10/14: 5.2, 5.3 | 10/16: 5.4 |
| Week 9 | 10/19: 5.5, 6.1 | 10/21: 6.1, 6.2 | 10/23: 6.2, 5.5 |
| Week 10 | 10/26: 5.5, 4.5, axiom of choice, | 10/28: Review | 10/30: Exam 2 (4.3 - 6.2), Answers |
| Week 11 | 11/2: 6.3 | 11/4: 6.3, 6.4 | 11/6: 6.4 |
| Week 12 | 11/9: 6.5, 7.1 | 11/11: 7.2, 7.3 | 11/13: 7.2, 7.3 |
| Week 13 | 11/16: 7.4 | 11/18: 7.4, 7.5 | 11/20: 7.7 |
| Thanksgiving Week | Nov 23 -27 | ||
| Week 14 | 11/30: 14.1 | 12/2: 14.1 | 12/4: 14.2 |
| Week 15 | 12/7: 14.3 | 12/9: 14.3 | 12/11: permutation review |
The final is tentatively set for 7:30 A.M. Thursday, December 17, 2009