*

Homework Assignments

Assignment 1. Due Thursday, January 30.

• Chapter 1: # 2*, 3*, 17, 22*
• Chapter 2: # 6, 8* (read example 11 in chapter 2 first),  11, 14*, 18*, 22, 26*, 31(hint: RF cannot be a rotation, so it must be a reflection), 32, 34 (hint: use #31 and #32; also R^{-k}=R^{n-k}), 36*, 38 

Assignment 2. Due Thursday, February 6.

• Chapter 3: # 12*, 20*, 26*, 32, 36, 44*, 49, 50, 52, 54*, 60*
• Chapter 4: # 4*, 7

Assignment 3. Due Thursday, February 13.

   • Chapter 3: #62*

   • Chapter 4: # 10, 14*, 18*, 26, 32, 36*, 42, 45*, 50, 52*, 64*

   • Supplementary Exercises for Chapters 1- 4: #5*, 6*

Assignment 4. Due Thursday, February 20.

   • Supplementary Exercises for Chapters 1- 4: # 18, 26*, 35*

   • Chapter 5: # 2, 4, 7*(answer the question just for S_6), 11*,  18*, 20, 22*, 24, 36*, 38*, 40, 42* 48

Assignment 5. Due Thursday, March 12.

  • Chapter 5: # 54

  •      Chapter 6: # 10*, 12*, 16* (Hint: a^3-b^3=(a-b)(a^2+ab+b^2). You can also factor (a-b) in a^n-b^n for any n. See for example this page. ), 18, 25, 32*, 38*, 40*, 42*, 44 (Hint: you might need to use #42)

  •      Chapter 7: # 4, 6*

Assignment 6. Due Thursday, March 26 at 5:00pm. Submit in Moodle. 

  • Chapter 7: 14*, 24*, 38*, 40*,  16 (follow the proof of cor. 5), 29, 34*, 35*, 42*

Assignment 7. Due Thursday, April 2 at 5:00pm. Submit in Moodle. 

•        Chapter 8: # 2, 3*, 8*, 10*, 15*,  22, 24*, 32*, 34, 42, 44*, 47, 50*, 58*

Assignment 8. Due Thursday, April 16 at 5:00pm. Submit in Moodle. 

 • Chapter 9: # 4, 14*, 16, 24*, 38*, 40*, 48*, 50*, 54*, 58*, 75

Assignment 9. Due Thursday, April 23 at 5:00pm. Submit in Moodle. 

•    Chapter 9: #32*, 64 (hint: prove that HK is a subgroup of G and think about the order of HK.), 69* (Hint: Use Theorem 7.2), 70.

•    Chapter 10: #  6*, 8*, 9*, 10, 16, 18* (“onto” is the key word), 22*, 30, 36*, 46* (G’ is a homomorphic image of G if there exists a homomorphism f:G ->G’ such that f(G)=G’), 49 (the homomorphism to use is phi:G->G/N defined by phi(g)=gN)

Assignment 10. Due Thursday, April 30 at 5:00pm. Submit in Moodle. 

•    Chapter 10: #47, 54*, 62* (hint: use the fact the (m, n)=m(1,0)+n(0,1)).
•    Chapter 11: #2*, 6*, 8, 10*, 12*, 21,  30*