Math 156 – Fall 2011
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Problem Sets Between Test 1 and Test 2
Only turn in problems that are not bracketed. Bracketed problems are additional problems you can look
at. Round brackets indicate problems that may help you with problems that are assigned; square brackets are
additional problems on material that you should know, but you are not required to write up solutions; curly
brackets are truly optional and may contain extra nuggets that you will not be required to know but may be
interested in.
Additional assignments will be filled in over time.
notation
meaning
unbracketed
assigned problem – turn these in for grading
()
helper/warm-up problem
[]
additional problems (you are responsible for content, but don’t turn them in)
{}
covers optional material
PS
Due
Source
Problems
10
Tue 10/11
Rosen 3.1
52
11
Fri 10/14
Rosen 3.2
1ace 2 (5) 6 (7) 8 [9] [11] 12 19
(21) order 22 order (25) 26 (27) 28 30
greedy algorithms
54
greedy algorithms
56
greedy algorithms
exponential
20
logarithms
Note directions (especially for 1–14).
12
Tue 10/18
Rosen 9.1
(1) (3,5,7)
10
30
13
14
15
Fri 10/21
Fri 10/28
Tue 11/1
properties
anti-symmetric
4
properties
(11,13)
irreflexive
6dfh properties
12 irreflexive
32
composition
33
Rosen 3.3
(1) 2 13–14
polynomials
[15]
Rosen 9.3
(1) 2
Rosen 2.6
(1,3) 2a addition 4ac mutliplication 10abc sizes of products 26 [27] 28 29
Rosen 9.4
(1) (5,7)
Rosen 9.5
(1)
eq relation?
24
matrices
operations
composition
largest size
(35,37) 47a
16a–f
counting
50ab
largest size
matrix rep [3] matrix rep 4ac matrix rep (5–7) properties 8 properties
14a–d operations 18 digraphs [19] digraphs 20 digraphs [21] digraphs
26 set from graph 32 properties from digraphs
reflexive closure 6 reflexive closure 16 paths 18acegi paths
19 Rk 20 Rk (25) trans closure 26ac trans closure (27) Warshall’s algorithm
28ac Warshall’s algorithm 32 path lengths
Rosen 8.1
3
Rosen 8.2
(1)
stamps
2–3 eq relation? 7 logical equivalence 16 products 21–22
40 eq classes 60a bit Theta 63–64 closures
12
identify
2
stairs
identify
(3)
solve
4
solve
Created October 31, 2011 — See web site for most current version.
graphs
Math 156 – Fall 2011
2/2
PS
Due
Source
Problems
*
*
Rosen 2.RQ
[13] [14] [17]
Rosen 2.SE
[37] [41]
Rosen 3.RQ
[1–5] [7–10]
Rosen 3.SE
[3–4] [11–19] [21–22] [29–30] {31–34}
Rosen 8.RQ
[1–2] [6–7]
Rosen 8.SE
[2] [4] [6]
Rosen 9.RQ
[1–4] [6–10] [12a] [13]
Rosen 9.SE
[1–5] [7–10] [20]
Created October 31, 2011 — See web site for most current version.