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

__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 pages 1-19

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**1,3,4,5,10a,11,12,

Page 45**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 Z_{3}is isomorphic with the three root of z^{3}= 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**Do all 12 problems.

From Homework Sheet**Turn in any five you want!.****September 17**1-13, 20,21,

Page 55**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 S**_{n}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**1,4,6,12,15,17,18,21,22,23,24,33,

Page 101**34,37**,40**October 20**1-20

Page 110**turn in 4,6,11****Page 110**21,23,24,26,29,**39**,40,41,47,48,49,**52****October 26**1,3,5,

Page 133**8**,9,**10,11****October 31**

Finish the proof started in class**November 5**1-16

Page 142**Turn in 8,14,24****November 19****Exam 2****December 12 (10:30-12:30)****Final**