Name:
Math 411.1 Exam 2 Solutions
November 24, 2015
1. Give precise and complete mathematical definitions of the following terms:
(a) (5 points) If H is a subgroup of a group G, a left coset of H in G is . . .
Solution:
a subset of G of the form gH = cfw_

Math 411 Exam 1
Solutions
1. (10 points) The function '(x, y) = xy is a binary operation on the set of positive integers. Is it associative? Is it commutative? Why or why not?
Solution:
Saying that ' is associative means that for all positive integers x,

Algebra 411 Homework 1: hints and solutions
Stephen Coughlan
Below are solutions to the first homework assignment. I give a little explanation where necessary, but these are only hints and not intended to be a
substitute for full solutions. Also, please c

Math 400.1Fall 2014
Review Sheet for Exam 2
Thursday, November 20
The exam questions may include definitions, calculations in a particular
group (like Zn , D8 or Sn ), and proofs. (In fact, you should assume it will
include definitions!) While the main em

Name:
Math 411.1 Quiz 2
November 4, 2014
Give precise and complete definitions.
1. (10 points) The alternating group An is . . .
Solution:
the subgroup consisting of the even permutations in Sn .
2. (10 points) Let G be a group and x 2 G. The conjugacy cl

Math 411.1 Solutions for Quiz 1
October 28, 2014
1. (10 points) Let
2 Sn . Say precisely what it means for
Solution:
The permutation
number of transpositions in Sn .
is odd if and only if
to be odd.
can be written as the product of an odd
2. (10 points) L

Math 400.1Fall 2014
Review Sheet for Exam 1
Thursday, October 16
The exam questions may include definitions, calculations in a particular
group (like Zn , D8 or Sn ), and proofs. Youre responsible for all the material
from class, covering Sections 110 fro

Name:
Math 411.1 Quiz 3
November 13, 2014
Give precise and complete definitions.
1. (10 points) Let G1 and G2 be groups. A homomorphism from G1 to G2 is . . .
Solution: a function f : G1 ! G2 satisfying the condition that, for all x, y 2 G1 , f (x 1 y) =

Stat 515, Section 2, Spring 2014
Midterm Exam 1 Information and Practice Problems.
Location and Time:
Midterm Exam 1 is an Evening Exam on Wednesday, March 5, from 7:00 9:00 pm, in
LGRT 121. There is no regular class that day, and there is no homework due

Stat 515, Section 2, Spring 2014
Midterm Exam 1 Information and Practice Problems.
Location and Time:
Midterm Exam 1 is an Evening Exam on Wednesday, March 5, from 7:00 9:00 pm, in
LGRT 121. There is no regular class that day, and there is no homework due

Name:
Stat 515
Midterm Examination II
November 10, 2008
(11:15 a.m. - 12:05 a.m.)
Instructions:
The total score is 100 points.
There are six questions. Each one is worth 20 points.
TA will grade the best five questions that you solved.
Show ALL your wo

Probability
1
Sample Space and Events
Definition 1 A sample space, denoted S, is the collection of all outcomes when an
experiment is performed.
Example 1 Toss a coin two times, the sample space is S = cfw_HH, HT, T H, T T
4
Example 2 Toss a coin until a