MATH 4023 Applied Algebra

Final Exam     Review

Exam 2     Review     Answers

Exam 1     Review     Answers

Homework Assignments

Assigned from Lax Modern Algebra and Discrete Structures, and from Supplements.
Assigned Problems Turn In Reading
1/16 Lax page 6, exercises 1, 4, 6 - 9, 13 - 15, 17 Lax page 6, exercises 1, 8, 17 on Thursday 1/23 read Section 1.1 in Lax
1/21 Lax page 16, exercises 1, 2, 3, 5 read Section 1.2 in Lax
1/23 Lax page 16, exercises 6 - 10 Lax page 16, exercises 2, 6, 10 on Thursday 1/30
these will be collected on Tuesday 2/4
2/4 Lax page 16, exercise 12
Supplement 1 page 13, exercises 3, 5, 7, 8
Lax page 16, exercise 5
Supplement 1 page 13, exercises 3(c), 5(c)
on Tuesday 2/11
read Section 1.1 in Supplement 1
2/6 Supplement 1 page 14, exercises 8, 9, 12
Supplement 1 page 22, exercises 1, 7, 11
Find all integers that can be expressed as 12m+30n, where m and n are integers
all of these except p. 14 #9 and p. 22 #1
on Tuesday 2/18
read Section 1.2 in Supplement 1
2/11 Supplement 1 page 32, exercises 1, 3, 5, 6 read Section 1.3 in Supplement 1
2/13 Supplement 1 page 33, exercises 7, 8, 10, 12, 15
2/15 Supplement 1 page 33, exercises 18, 19, 20, 24
Supplement 1 page 43, exercises 1, 2, 4, 5
read Section 1.4 in Supplement 1
2/18 Supplement 1 page 43, exercises 3, 8, 9
Find all units and zero divisors in Z18
Compute 676(mod 13), 91001(mod 11), 225(mod 21), 766(mod 120)
Compute φ(32), φ(33), φ(120), φ(384)
Supplement 1 pages 32-34 #3(d), 10, 18
Supplement 1 page 43 #2(a), 4
and possible others will be collected later
(probably Thursday 2/27)
Note: Exam 1 will take place Thursday 2/27
covering sections 1.1 and 1.2 in Lax and Supplement 1
2/24 Turn in on Thursday 2/27:
Supplement 1 pages 32-34 #3(d), 10, 18
Supplement 1 page 43 #2(a), 4
Find all units and zero divisors in Z18
Compute 676(mod 13), 766(mod 120)
Compute φ(120), φ(384)
3/6 Lax page 171, #2, 3, 7, 8, 9
Supplement 2 page 425, #1, 2, 5, 6
some of these will be collected Thursday 3/13 Read Lax IV.5 (pages 164 - 170)
Read Supplement 2
3/11 Lax page 60, #1 - 8 (some collected later) Lax page 171, #7, 8
Supplement 2 page 425, #1
on Thursday 3/13
Read Lax III.1 and III.2
3/13 Lax page 66, #1, 3, 5 - 7, 11 - 13, 16
\[\text{Let}\ X=\begin{bmatrix} -1& -1\\ \phantom{-}1 & \phantom{-}0 \end{bmatrix}\ \text{and}\ Y=\begin{bmatrix} 0& 1\\ 1 & 0 \end{bmatrix}\ \text{and let}\ S\ \text{be the set of all (finite) }\] 'words' in X and Y, matrices of the form XaYbXcYd...XmYn, with a,b,c,d...m,n integers. Find the cardinality of S, and a multiplication table for S.
some of these and those from 3/11 will be collected Th. 3/20 Read Lax III.2 and III.3
3/18 Lax page 74, #5 - 13
Lax page 61 #6, page 67 #6, 12, 13 on Th. 3/20 Read Lax III.3
3/20 Lax page 74, #14, 15, 17 - 20
3/25 Lax page 79, #1 - 11 (some will be collected later) The matrix problem from 3/13
Lax page 74, #14, 17, 19
on Th. 3/27
Read Lax III.4
3/27 Lax page 115, #1, 2, 3, 5, 6, 8, 9 (some will be collected later) Read Lax III.8
4/1 Lax page 115, #10, 11 Lax page 79, #3, 9
Lax page 115, #1, 7
on Th. 4/3
Exam 2 will be Th. 4/10
covering encryption, Lax Ch. III, etc
4/3 Lax page 124, #1 - 8 Read Lax III.9, Supplement 3
4/8 Turn in Thursday 4/10:
Lax page 79 #3, 9
Lax page 115 #4, 6
Lax page 124 #3, 5
4/22 Lax page 144, #1 - 4, 7 - 10, 13, 14
Lax page 150, #3, 7, 9, 12, 17 - 19
some collected later Read Lax IV.1, IV.2
4/22 Lax page 213, #1 - 5
Lax page 223, #2, 4, 6, 8
Turn in Thursday 5/1: page 144 #9, page 150 #12, page 223 #2, 8 Read Lax V.1, V.2
4/29 Lax page 234, #1, 2, 8, 9
Lax page 242, #1, 2, 4
Read Lax V.3, V.4
5/1 Lax page 242, #5, 6
Lax page 249, #1, 2, 6
Read Lax V.5

Supplements

Supplement 1 on the integers.
Supplement 2 on the RSA cryptosystem.   Additional RSA reading: here and here.   Powers by successive squares reading: here
Supplement 3 on Burnside coloring.

Dan Cohen  Spring 2014   Back to MATH 4023; to my homepage.