Math 102 Review SheetFinal
Sections 1.1-1.4
Definitions: Algorithm, n!, subset, empty set
Concepts: Be able to implement PERT and find critical paths. Be familiar with typical
matching and knapsack problems. Be able to apply the counting results from this
Exam 3 Review Key for Practice Problems
1. a. The two sets of vertices are V1 = cfw_ A, C, E, F and V2 = cfw_ B, D, G. The bipartite
matrix is given below.
B D G
A
C
E
F
1
1
1
0
1
0
1
1
0
1
0
1
b. One possible answer: Highlight edges j, o, and q on th
Review Sheet for Exam 3
Section 4.5 + Traveling Salesperson Sheet
Definitions: Ranking (in a tournament directed graph)
Concepts: Be able to represent the results of a round-robin tournament with a directed graph and then to
find a ranking (Hamiltonian pa
Math 102Exam 1
Tuesday, September 22, 2015
Name
INSTRUCTIONS:
1. Read each question carefully.
2. Show your work. Answers without justification may not receive full credit.
Part I. TRUE/FALSE: (15 points) Mark each statement True or False. (No justificati
Chapter 5 Trees
SUPPLEM ENTARY EXERCESES
14- (a) k,e,f,i,j,d,cea; 21 (b) f,e,b,c,j,g,d,k,q,i,o;36
16.
7
18. (a) A,C,F,D,B,E,H,G (b) A,B,C,F,H,D,E
50 Chapter 5 Supplementary Exercises
20. (a) (b)
A D
m E F
B
A
E B D H
24.1213123132
26. 8 28. (q—1)p+1
38.
Chapter 6 Matching
32. (a) 10 (b) 19
6.3 A MATCHING ALGORITHM
2. After applying step 2.2, the matrix is as follows.
A B C D E
1 1* 0 1 0 1 CR/
2 0 1* O 1 1 E\/
3 1 1 0 0 O A
4 O 1 O 1* O B
w w .w w
4. 4C,1C,1E 6. 1D, 20, 3A, 4B
8. 1D,2B,3A,4C 10. 1D,2C',3
Prompt and Assignment Guidelines for the First Artifact
of your Saint Marys ePortfolio:
A Reflection on the Integration of Learning
Write a 500-word essay (about 2-3 well-developed paragraphs) responding to the prompt
below. This is a formal academic assi
A) «2? id
Math 102 Exam3 Name: “id? gj
Thursday, November 1' 9, 2015
Show your work to receive full credit!
1. (18) For each statement below,flll in the blank.
:J@ a) A connected graph with 57 vertices has AT LEAST 3 Q edges.
b) In a tree with 92 edges, t
MATH 102
REVIEW SHEET-EXAM 1
Section 1.1:
Definitions: algorithm
Concepts: Be able to classify problems (existence, counting, or optimization problems). Be able to
implement PERT and find critical paths.
Section 1.2:
Definitions: n! and permutation
Concep
Math 102: Review Sheet for Exam 2
Section 4.1
Definitions: isomorphism
Concepts: Be able to work with the relationship between degree sum and the number of edges in a graph.
Know how to show that a pair of graphs isomorphic or nonisomorphic.
Section 4.2
D
Math 102 Exam 1 Review Key
1. 27=128 since different pizzas correspond to subsets of the set of 7 toppings
2. See back of textbook.
3. 4! = 24 (permutation principle)
4. 15! calculations take 1,307,674 se
Math 102—Exa1n 1 Name Us
Tuesday, September 22, 2015 j
INSTRUCTIONS:
1. Read each question carefully.
2. Show your work. Answers without justiﬁcation may not receive full credit.
Part I. TRUE/FALSE: (15 points) Mark each statement True or False. (No justi
Math 102 Exam 2 Review Key
1. a) AmB«F~C-A of length 4
b) No.
c) chromatic number m 3
(One possible coloring: A, D, F, E—red; Bw—blue; Cm green.)
d) A-C-D (2); A—B-C-D (3); A—B-F—C—D (4)
2. 121
3. Yes, each vertex has even degree (namely, 120].
. Euler
1
Lab 1: Introduction to Geology Labs
Objectives
A. Describe the various subdisciplines of geologic study.
B. Practice the basic measurement, math, and graphing skills used by geoscientists.
A. Subdisciplines of Geology
In this course, we will study the geo
Math 102 Exam 3
Thursday, November 19, 2015
Name:_
Show your work to receive full credit!
1. (18) For each statement below, fill in the blank.
a) A connected graph with 57 vertices has AT LEAST _ edges.
b) In a tree with 92 edges, there are exactly _ vert
Chapter 4 Graphs
4.5 DIRECTED GRAPHS AND MULTIGRAPHS
2. v = {AB}; 5 : {A,B}, {B,A}
4. v : {A,B,0, D,E}; 5 = {B,A}, {0,3}, {13,0}, {D,E}
5. 8.
A D
A o .B
C
C' 'D c B
10'. 12.
V1
0
v20 0 v3
14. none; none; 0; 0.
16. C'; B,E; 1; 2
0 O 0 A: none
20. 0 O 1 B
MATH 102 EXAM 2 Name: K€%
Thursday, October 15, 2015
Consider the graph below and answer the questions (1—6) that follow. (20)
9 @ 1. Is the graph connected? [1 E19 What is the chromatic number of the graph? 3)
I} 2. Determine each: deg (B): Li dist (A,
MATH 102 EXAM 2
Name:_
Thursday, October 15, 2015
Consider the graph below and answer the questions (1-6) that follow. (20)
B
C
m
D
n
o
j
l
p
q
A
k
E
s
r
F
H
t
u
G
1. Is the graph connected? _
2. Determine each:
What is the chromatic number of the graph?
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