MTH 419/519--Introduction to Abstract Algebra--Homework Assignments

Note: problems in brackets [ ] are to be done, but not turned in.

Exams:

• Exam I: Wednesday, Oct 7
  
• Exam II: Wednesday, Nov 4
• Exam III: Wednesday, Dec 2
  
• Final Exam: Monday, December 14, 11:45AM - 2:45PM, NSC 218

• Contemporary Abstract Algebra, 8th edition, by Joseph Gallian

Final Exam

• When: Monday, December 14 at 11:45-2:45
• Where: NSC 218
• Covers: 
  
• Chapter 0 (Well Ordering, Division Algorithm, Modular Arithmetic)
  • the dihedral group D_n (from Chapter 1) 
  Chapters 2 - 15 (not RSA, not field of quotients)
  
• Includes all the homework problems assigned (whether to turn in or not turn in)
• Here is a link to Gallian's advice for studying for this course www.d.umn.edu/~jgallian/advice.html
  
• Format: 2 or 3 statements of theorems/definitions; 6 to 12 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed

Coming Attractions (tentative list of upcoming assignments):

• Winter Break

Assignment 1--Due Friday, September 11:

• Recitation: will meet Wednesday, Sept 2, at 8:00 AM in Math 150
• Required for undergraduates (419)
• Graduate students are encouraged to attend recitation on September 2
  
• No classes: Monday, Sept 7 (Labor Day)
• Quiz (419): Quiz I on Wednesday, Sept 9
• Format for quizzes: one definition/statement, one problem/proof
• Covers: topics covered in Chapter 0
  
• Chapter 0: 4 - 9, 11- 13, 18 - 21, 30
• Chapter 2: 4 - 6, 9, 10, 12, 15, 17
• Note: problems listed for an assignment are to be handed in
• Note: Table 2.1 contains a typo. The inverse in C* should have a^2 + b^2 in the denominator for both terms.
  

Assignment 2--Due Friday, September 18:

• Quiz (419): Quiz II on Wednesday, Sept 16
• Format for quizzes: one definition/statement, one problem/proof
• Covers: Chapters 2 and 3
  
• Chapter 2: 22, 25, 26
• Chapter 2: 31, 32, 37, [39] (do, but don't turn in), [51]
• Chapter 3: [1 - 5], 13, 17, 19, 23, 31, [32], 42, 45, 75

Assignment 3--Due Friday, September 25:

• Quiz (419): Quiz III on Wednesday, Sept 23
• Covers: Chapter 4 (but not the material on the Euler phi function)
• "students ... who are absent to observe religious holy days can do so with no negative consequences."
• Chapter 4: 2, 3, [4], 5, 7
• Chapter 4: [8], 9, [12], 13, 14, [23], 24, 29, 31, 37, 52, 55, 62, 70, 76

Assignment 4--Due Friday, October 2:

• Quiz (419): Quiz IV on Wednesday, Sept 30
• Covers: Chapter 4 (Euler phi function) and Chapter 5
  
• Chapter 4: [Try 85]
• Chapter 5: 1 - 3, [4 - 8], 9, 10, [11], 13, [15], 16, 17, [19], 23, [26], 28, 29, [32], 35, 36, 61, 66, 77

Assignment 5--Due Friday, October 9:

• Quiz (419): No quiz on Wednesday, October 7
• Chapter 6: [1], [4, 5], 6, 7, 10, [20], 34, 37, 39, 48, 49, 51, [try 63]

Assignment 6--Due Friday, October 16:

• Quiz (419): Quiz V on Wednesday, October 14
• Covers: Chapter 6
  
• Chapter 6: 2, 9, 12, 15 -17, 24, 42, 52
• Chapter 6: 56
• Chapter 7: 1, [2], 3, [5], 6 - 10
• #10 has a misprint. Should have the definition: HK = {hk | h in H, k in K}.

Assignment 7--Due Friday, October 23:

• Quiz (419): Quiz VI on Wednesday, October 21
• Covers: Chapter 7
  
• Chapter 7: 12, 13, [15, 16], 17 - 19, 22, 26, 30, 33
• Chapter 7: [45], 53, [58], 59

Assignment 8--Due Friday, October 30:

• Quiz (419): Quiz VII on Wednesday, October 28
• Covers: Chapter 8 [not "Applications"]
• Chapter 8: 1, 5 - 7, 11, 14, 16, 27, 34, 41, 48, 63, 65
• Chapter 8: 49, 50 , 69, 75, 78
• Note: in problem 50, `determine' means: what familiar group is this isomorphic to and why?

Assignment 9--Due Friday, November 6:

• Quiz (419): No quiz on Wednesday, November 4
  
• Covers:
• Chapter 8: 54, 55, 83, 88, 89
• Chapter 9: [1], 2, [4], 6, 9 - 11, [12 -14], 15, 17, [18, 19], 20, 22, 37, [43], 72

Assignment 10--Due Friday, November 13:

• Quiz (419): Quiz VIII on Wednesday, November 11
  
• Covers: Chapter 9
• Chapter 9: 5, 21, 34, 51, [58], 59, 61, 67
• Chapter 10: [5], 6, 7, [8], 9, [14], 16, [19], [35]
• Note: some problems ask if there is a homomorphism from G onto H, rather than from G to H. This means the homomorphism is supposed to be onto.

Assignment 11--Due Friday, November 20:

• Quiz (419): Quiz IX on Wednesday, November 18
  
• Covers: Chapter 10
• Chapter 10: 11, 13, 20, 26, 28, 32, 40 - 43, 49, 51, 58
• Note: some problems ask if there is a homomorphism from G onto H, rather than from G to H. This means the homomorphism is supposed to be onto.

Assignment 12--Due Friday, December 4:

• Quiz (419): No quiz on Wednesday, December 2
  
• Covers:
• Chapter 11: 2, [6], 12, 21, 26, 28, 30, 31, 38
• Note: the Chapter 11 homeworks are covered on Exam III
  
• Chapter 12: 1, [2], 8, 19, 22, 25, 32, 44, [49], 50, 51

Assignment 13--Due Friday, December 11:

• Quiz (419): Quiz on Wednesday, December 9
  
• Covers: Chapters 11 - 15 (through Theorem 15.4)
• Chapter 13: [3], 5, 11, 15, [18], 24, [29], 30, 31, 35, 47, 49 (Hint: use the Binomial Theorem), 51
• Chapter 14: 3, 6, 10, [11], 12, [13], 19, 33, 39, 41, 45, 46 (hard part is closed under addition), [47], [48], 51
• Chapter 15: 8, 12, 14, 26, 44, 56

Exam I

• When: Wednesday, October 7 at 11:00-11:50 AM
• Where: Math 150
• Covers: 
  
• Chapter 0 (Well Ordering, Division Algorithm, Modular Arithmetic)
• the dihedral group D_n (from Chapter 1)
• Chapters 2 - 5
• Includes all the homework problems assigned (whether to turn in or not turn in)
• Here is a link to Gallian's advice for studying for this course www.d.umn.edu/~jgallian/advice.html
  
• Format: 1 or 2 statements of theorems/definitions; 3 or 4 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed

Exam II

• When: Wednesday, November 4 at 11:00-11:50 AM
• Where: Math 150
• Covers: 
  
• Chapters 6 - 8 [not "Applications" in 8]
  
• Includes all the homework problems assigned (whether to turn in or not turn in)
• Here is a link to Gallian's advice for studying for this course www.d.umn.edu/~jgallian/advice.html
  
• Format: 1 or 2 statements of theorems/definitions; 3 to 5 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed

Exam III

• When: Wednesday, December 2 at 11:00-11:50 AM
• Where: Math 150
• Covers: 
  
• Chapters 9 - 11
  
• Includes all the homework problems assigned (whether to turn in or not turn in)
• Includes homework on Chapter 11 due on Friday, December 4
  
• Here is a link to Gallian's advice for studying for this course www.d.umn.edu/~jgallian/advice.html
  
• Format: 1 or 2 statements of theorems/definitions; 3 to 5 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed