Math 546
Homework 10
1
546 Problems.
11.2 Show that the subgroup
a b
H=
: ad 6= 0 GL(2, R)
0 d
is not normal.
0 1
0
1
Proof: We observe that S =
GL(2, R), that S
=
1
0
1
1 1
T =
H. We compute
0 1
0 1
1 1
0 1
0 1
0 1
1
1
ST S =
=
=
1 0
0 1
1 0
1 1
1
Math 546
Homework 3
1
546 Problems.
4.16. Suppose that G = hxi is a cyclic group. Prove that G = hx1 i.
Proof: We observe that G = hxi = cfw_. . . , x2 , x1 , e, x, x2 , . . . , and that
hx1 i = cfw_. . . , (x1 )2 , (x1 )1 , e, x1 , x2 , . . . = cfw_. .
Math 546
Homework 4
1
546 Problems.
5.1 g) Determine whether or not H = cfw_I, J, K is a subgroup of Q8 .
Claim: H is not a subgroup of Q8 .
Proof: H is not a subgroup since it is not closed. For example, J 2 = I 6 H.
5.4 c)
(a) How many subgroups does (Z
Math 546
Homework 1
1.3 and 1.6. For each of the following sets S and functions on SS, determine whether is
a binary operation on S. If is a binary operation on S, determine whether it is commutative
and whether it is associative.
a) S = Z, a b = a + b2 .
Math 546
Homework 2
546 Problems.
3.4. Let g be an element of a group (G, ) such that there exists x G with x g = x.
Show that g = e.
Proof: We have x g = x implies that x1 (x g) = x1 x = e, where multiplied on the
left by x1 on both sides. Associativity
Maple Lab for Calculus I
Lab 13
Definite Integrals, Riemann Sums, and FTC
Douglas Meade, Ronda Sanders, and Xian Wu
Department of Mathematics
Overview
This lab will develop your understanding of the definite integral as defined and computed via Riemann
su
Maple Lab for Calculus I
Lab 10
Mathematical Models: Designing a Roller Coaster
Douglas Meade, Ronda Sanders, and Xian Wu
Department of Mathematics
Overview
There are three objectives in this lab:
understand the mathematical reasoning associated with a r
Maple Lab for Calculus I
Lab 9
Differentiation Drill
Douglas Meade, Ronda Sanders, and Xian Wu
Department of Mathematics
Overview
This lab uses Maple to help you practice your differentiation skills. Three different user interfaces are
introduced.
The De
Maple Lab for Calculus I
Lab 8
Implicit Differentiation
Douglas Meade, Ronda Sanders, and Xian Wu
Department of Mathematics
Overview
This lab provides experience working with functions defined implicitly.
Maple Essentials
Important Maple commands introdu
Maple Lab for Calculus I
Lab 7
Differentiation and Tangent Lines
Douglas Meade, Ronda Sanders, and Xian Wu
Department of Mathematics
Overview
We will learn in this lab how to use Maple to find derivatives and the equation of the tangent line to
a curve at
Maple Lab for Calculus I
Lab 5
A More Rigorous Approach to Limits
Douglas Meade, Ronda Sanders, and Xian Wu
Department of Mathematics
Overview
The rigorous definition of limits can be difficult for students to grasp. This lab is designed
to provide visual
Maple Lab for Calculus I
Lab 3
Functions and Plots
Douglas Meade, Ronda Sanders, and Xian Wu
Department of Mathematics
Overview
You will likely have to deal with graphs on a daily basis in your study of Calculus and beyond.
The main objective of this lab
Maple Lab for Calculus I
Lab 4
Limits, Infinity, and Asymptotes
Douglas Meade, Ronda Sanders, and Xian Wu
Department of Mathematics
Overview
The concept of a limit is an idea that all other calculus concepts are based on. Limits involving infinity
are clo
Maple Lab for Calculus I
Lab 2
New Functions from Old
Douglas Meade, Ronda Sanders, and Xian Wu
Department of Mathematics
Overview
In this lab, we will use Maple to help us to calculate and simplify combinations of functions.
A maplet (Shift) will also be
Maple Lab for Calculus I
Lab 1
The Maple Lab for Math-141: An Introduction
Douglas Meade, Ronda Sanders, and Xian Wu
Department of Mathematics
Note
If you took Math-141 last semester, this will serve as a review for you.
Welcome
Welcome to the computer la
Project Report Guideline
Douglas B. Meade, Ronda Sanders, and Xian Wu
Department of Mathematics, University of South Carolina
The purpose of a project report is to present your answer to the project problem(s) and to
communicate the mathematical ideas and
Maple Lab for Calculus I
Lab 10
Project: Designing a Roller Coaster
Douglas Meade, Ronda Sanders, and Xian Wu
Department of Mathematics
Preparation
Be sure to read Project Report/Grading Guideline before beginning your project. Remember, you are to turn i
Math 242, Section E01 Name [Sgy
Short Quiz No. 8 March 22, 2017
Show all work, and if your solution involves several steps, place a around your nal
answer. Answer ve of the questions I.VI. Questions V. and VI. are on the back of this
page.
I. (2) Find a f
Math 242, Section E01 Name
Test No. 2 March 15, 2017
Show all work, and if your solution involves several steps, place a around your nal answer.
Omit one of the entire questions I.V.
I.
A. (1) Complete the following denition that we studied. Let I be an i
In the above example we first checked that the result was true for
the result was true for
for
n k 1
nk
n 1
. Then we assumed
. Finally using this assumption we proved the result was true
. By mathematical induction we have proven
12 22 32 . n 2
n n 1 2n
Example: Given f ( x) 3x 4 11x3 10 x 4 :
a) Find the rational zeros and then the other
zeros; that is, solve f ( x ) 0.
b) Factor f ( x ) into linear factors.
Solution:
a) Because the degree of f ( x) is 4, there
are at most 4 distinct zeros. The
p
possib
February/19/1415
Dear Journal,
Im going to start off by saying that Caesar is one of my closest friends but I
need to do what I and the people of Rome think. Thats to kill caesar so
today Im going alone with the plan. I know I have no right to take someon
March /15/1415
Dear journal,
The pain i feel inside is so hard to explain because i killed one of my best
friends. There's so much going to my head about what happened now that i
think about i know we all was wrong for what we did and we shouldn't have
do
February/11/1415
Dear journal,
Today was a very difficult day because Cassius is trying to convince to kill
Caesar. He say that i would make a better king then Caesar but would i
really? But i really don't want to have take the role of being king. At the
Do the playspent first. It's a game about budgeting.
Be ready to discuss this with me Friday.
1. Last month, I used atm five times. I also used another banks ATM twice. How much
will the Bank charge me for using my atm card last month? $21.00
2. Last week
To For Starch, Protein, and Reduced of
Sugar, and Fats
Indeyah
Jackson
2/20/17
3rd
block
Materials:
beaker, burner, test tube,hot plate test tube holder.
Please note the following :
Purple color change means protein is present in food sample
Color change
1. Banking - business of depositing and withdrawing money from an account.
2. Budget - a statement of estimated income and expenses.
3. Checking - an account in a bank from which the depositor can draw money by writing
checks.
4. Taxes - to require to pay