# Fall 2007

NOTE:  Final exam time change to Wednesday December 12, 10:30-12:30.

Syllabus

Homework:  Homework is to be turned at the beginning of class on the days indicted below. Follow the guidelines at http://www.math.unt.edu/~brand/class/3510/2007Fall/homeworkexp.htmll when preparing your homework to be graded.  Soon after class each day the homework assignments will be posted here.  You should do all the homework listed, but turn in only the problems listed in bold face type.

• August 27
First day of class
• August 29
Read all the problems in the set that starts on page 19 and turn in 7,11,18,25,31,33
• August 30
Page 26 7-13 (Turn nothing in)
• September 5
Page 45
1,3,4,5,10a,11,12,19,22,29,31,32,35
• September 7
Using group tables, find a group of order 5 and then show that any other group with five elements is isomorphic with the group you found.
• September 10
Prove the rest of the theorem  covered in class that says the isomorphic image of the inverse of an element is the inverse fo the image of the element.
Prove that Z3 is isomorphic with the three root of z3 = 1 in the complex plane (using the operation of multiplication).
Prove that the group of polynomials of degree less than or equal to 2 is isomorphic with the group of vectors in three space under addition.
• September 14
From Homework Sheet
Do all 12 problems.  Turn in any five you want!.
• September 17
Page 55
1-13, 20,21,25,27-45,47,49,54
• September 28
Page 66  3,7,11,12,15,16,17,18,20,27,28,29,30,32,33,34,35,36,37,44,45,48,49,50,51
• October 1
Write the following permutations as a product of disjoint cycles. (In other words, multiply them!)
1)  (1,3,5,2)(2,5,1,3)(3,2)
2)  ([1,5,2,4)(2,3)]-1
3)  (1,2,3,4,5,6)3
4)  (4,6)(2,3)(1,5)(2,3)(1,4)(2,3)(5,1)(2,5)
5)  [(1,2)(3,4)(5,6)]-1
6)  (1,5,2)(1,5,2,3)(1,5,2)-1
7)  (4,1,2)(2,5,3)(4,1,2)-1(2,5,3)-1
Determine if the element of Sn is even or odd.
8)  (1,2,5,4)
9)  (1,2,3)
10)  (1,3,4,5,6)(2,4,1,5)(1,2,3)(5,6)
11)  (1,2,3,4,5,6,7,8,9)-1

Find the order of the permutation.
12)  (1,5,3,8)(2,4,6,9,7)
13)  (1,5,2)(2,4,9)(9,1,4,5)(3,2,1,4)
14)  (1,2,3)(4,5,6,7)(8,9,10)(11,12,13,14,15)(16,17,18,19,20,21,22)
• October 3
Page 83  46,47,52
• October 5
Exam 1
• October 8
Page 83  46,47,52
• October 16
Page 101
1,4,6,12,15,17,18,21,22,23,24,33,34,37,40
• October 20
Page 110
1-20 turn in 4,6,11
• Page 110  21,23,24,26,29,39,40,41,47,48,49,52
• October 26
Page 133
1,3,5,8,9,10,11
• October 31
Finish the proof started in class
• November 5
Page 142
1-16 Turn in 8,14,24
• November 19
Exam 2
• December 12 (10:30-12:30)
Final