Name:
Solutions
Exam 2
Instructions. Answer each of the questions on your own paper, and be sure to show your
work, including giving reasons, so that partial credit can be adequately assessed. Put your name
on each page of your paper.
1. [20 Points]
(a) S
Name:
Final Exam
Instructions. Answer each of the questions on your own paper. Be sure to show your
work so that partial credit can be adequately assessed. Put your name on each page of your
paper.
1. [20 Points] Solve the congruence 6 27 mod 69.
2. [16 P
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Exam 3
Instructions. Answer each of the questions on your own paper and be sure to show
your work so that partial credit can be adequately assessed. Put your name on each page of
your paper.
1. [20 Points] Let = 4 4 and let = (1, 2) be the cyclic su
Name:
Exam 2
Instructions. Answer each of the questions on your own paper and be sure to show
your work so that partial credit can be adequately assessed. Put your name on each page of
your paper.
Some useful notation: is the group of integers under addit
Name:
Solutions
Exam 3
Instructions. Answer each of the questions on your own paper and be sure to show
your work so that partial credit can be adequately assessed. Put your name on each page of
your paper.
1. [20 Points] Let = 4 4 and let = (1, 2) be the
Name:
Exam 1
Instructions. Answer each of the questions on your own paper, and be sure to show your work
so that partial credit can be adequately assessed. Put your name on each page of your paper.
1. [16 Points] Calculate the greatest common divisor = gc
Name:
Exam 2
Instructions. Answer each of the questions on your own paper, and be sure to show your
work, including giving reasons, so that partial credit can be adequately assessed. Put your name
on each page of your paper.
1. [20 Points]
(a) State Lagra
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Exam 1
Instructions. Answer each of the questions on your own paper, and be sure to show your work
so that partial credit can be adequately assessed. Put your name on each page of your paper.
1. [15 Points] Let = 715 and = 546.
(a) Calculate the gre
Name:
Solutions
Exam 1
Instructions. Answer each of the questions on your own paper, and be sure to show your work
so that partial credit can be adequately assessed. Put your name on each page of your paper.
1. [16 Points] Calculate the greatest common di
Homework #2
Due: September 7, 2012
Do the following exercises from Nicholson:
Section 1.1: 10 (b)
Section 1.2: 7 (a); 9 (h); 31 (d)
Additional Problems:
[
]
]
[
2 1
2 21
for all
1. Let =
. Using mathematical induction, show that =
0 2
0
2
positive intege
Homework #2
Solutions
Due: September 7, 2012
Do the following exercises from Nicholson:
Section 1.1: 10 (b)
10 (b) Show that any postage of 12 cents can be made up of 3 and 7 cent stamps.
Solution. If 3 cent stamps and 7 cent stamps are used, the postage
Exam I Review Sheet
Math 4200
The rst exam will be on Monday, September 19, 2016. The syllabus will be sections 0.3, 0.4, and
1.1 1.4 in Nicholson.
Following are some of the concepts and results you should know:
Know the basic language of mappings: domai
Exam I Review Sheet
Math 4200
The rst exam will be on Monday, September 19, 2016. The syllabus will be sections 0.3, 0.4, and
1.1 1.4 in Nicholson.
Following are some of the concepts and results you should know:
Know the basic language of mappings: domai
Name:
Exam 1
Instructions. Answer each of the questions on your own paper, and be sure to show your work
so that partial credit can be adequately assessed. Put your name on each page of your paper.
1. [15 Points] Let = 715 and = 546.
(a) Calculate the gre
Homework #1
Solutions
Due: August 29, 2016
Do the following exercises from Nicholson:
Page 16: 2 (d); 3 (b), (d), (e), (f); 8, 13
Pages 20-21: 1 (b), (d), (f); 2 (b), (d); 7 (b); 8.
Page 16:
2. In each case, state whether the mapping is onto, one-to-one,