Algebra for Teachers
Homework 3
Due 2/26
Name
Score
Present a complete solution for each problem. Answers alone will give no credit.
1. In which positional system the following is true: 216 3 = 654?
2. Let G be a group. Prove that for all a, b, c G, ac =
310g2(x + 4) . Include a sketch of the basic
function and each intermediate graph with iabels.
7.) Sketch the graph of the function )2
IVA 12.)
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Algebra for Teachers
Homework 4
Due 3/5
Name
Score
Present a complete solution for each problem. Answers alone will give no credit.
1. Show all points x on the complex plane such that
(1)
(2)
(3)
(4)
(5)
(6)
z 1 = z;
| arg z| < ;
6
1 |z 2i| < 2;
1 < |Im z
Algebra for Teachers
Homework 2
Due 2/17
Name
Score
Present a complete solution for each problem. Answers alone will give no credit.
1. Let G be a multiplicative group. Prove that (ab)1 = b1 a1 for all a, b G.
2. Let G be a multiplicative group. Prove tha
Algebra for Teachers
Homework 1
Due 2/3
Name
Score
Present a complete solution for each problem. Answers alone will give no credit.
1. Using digit 3 exactly ve times, signs of four arithmetical operations (addition,
subtraction, multiplication, division)
Pogulation Growth [Decay P :P;(1+ i)
:71
P =-.p0p,uiarion 'aerT years rug u {6 0 m 0 U 1 G 1 '30 9
PG: Eniriai papulaon DC) 9 . 310 H w i '{h
r: rare of-increase or decrease r01 +6
n: number of Timesspopularion increases/decreases:perryear (1) h: l
r