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

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

Exams:

• Exam I: Friday, Oct 3 completed
  
• Exam I: Friday, Oct 31 completed
• Exam I: Friday, Nov 21 postponed to Monday, Nov 24. completed
  
• Final Exam: Wednesday, Dec 10, 11:45 AM - 2:45 PM, in NSC 205

Textbook: 

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

Assignment 14--Practice problems on the last material (do not hand in):

• 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,

Final Exam

• When: Wednesday, December 10 at 11:45-2:45
  
• Where: NSC 205
• Covers:  Through Chapter 15 (up to, but not including, Field of Quotients on p 290)
  
• Format: 2 or 3 statements of theorems/definitions; 6 to 10 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• homework problems or variations on them
• some new problems might appear
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed
• calculator might actually be needed
• Review Session: TBA

Coming Attractions (tentative list of upcoming assignments):

• Chapter 14: TBA

Assignment 1--Due Wednesday, September 3:

• Recitation for 419: Recitation will not meet Monday, August 25, at 8:00 AM in Math 150
• No classes: Monday, Sept 1 (Labor Day)
• Quiz (419): Quiz I on Monday, Sept 8
  
• Chapter 0:  4 - 9, 11- 13, 18 - 21, 30
• Note: problems listed for an assignment are to be handed in

Assignment 2--Due Wednesday, September 10:

• Quiz (420): Quiz I on Monday, Sept 8.
  
• Format for quizzes: one definition/statement, one problem/proof
• Covers: topics covered in Chapter 0, definition of Group
  
• Chapter 2: 4 - 6, 9, 10, 12, 15, 17, 20, 22, 25 - 27
• Chapter 2: 31, 32, 36, 37, [39] (do, but don't turn in), 47, [51]

Assignment 3--Due Wednesday, September 17:

• Quiz (419): Quiz II on Monday, Sept 15.
  
• Format for quizzes: one definition/statement, one problem/proof
• Covers:  Chapters 2, including definitions of the groups in examples, especially the ones we have been using in class.
  
• Chapter 3: [1 - 5], 13, 17, 19, 23, 31, [32], 42, 45, 75
• Chapter 4: 1 - 4, 7, 17

Assignment 4--Due Wednesday, September 24:

• Quiz (419): Quiz III on Monday, Sept 22.
  
• Format for quizzes: one definition/statement, one problem/proof
• Covers:  Chapters 3 & 4 (up to Classification of Subgroups on p. 82)
  
• Chapter 4: 5, 8, 9, 12 - 14, 23, 24, 29, 31, 37, 52, 55, 62, 70, 76, [Try 85]

Assignment 5--Due Wednesday, October 1:

• Quiz (419): Quiz IV on Monday, Sept 29.
  
• Covers:  Chapter 4
  
• 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 6--Due Wednesday, October 8:

• Quiz (419): No Quiz on Monday, Oct 6.
  
• 
  
• Chapter 6: [1], [4, 5], 6, 7, 10, [20], 34, 37, 39, 48, 49, 51, [try 63]
• Note: only some of the problems from previous Coming Attractions were assigned for Oct 8.

Assignment 7--Due Wednesday, October 15:

• Quiz (419): Quiz V on Monday, Oct 13.
  
• Covers: Chapter 5 and Chapter 6 (up to, but not including, automorphisms)
  
• Chapter 6: 2, 9, 12, 15-17, 24, 42, 52 [note: 39 has been removed, since on previous assignment]
• Chapter 6: 56

Assignment 8--Due Wednesday, October 22:

• Quiz (419): Quiz VI on Monday, Oct 20.
  
• Covers: Chapter 6
  
• Chapter 7: 1, [2], 3, [5], 6 - 10, 12, 13, [15, 16], 17 - 19, 22, 26, 30, 33
• #10 has a misprint. Should have the definition: HK = {hk | h in H, k in K}.

Assignment 9--Due Wednesday, October 29:

• Quiz (419): Quiz VII on Monday, Oct 27 .
  
• Covers: Chapter 7
• Chapter 7: [45], 59
• Chapter 8: 1, 5 - 7, 11, 14, 16, 27, 34, 41, 48, 63, 65

Assignment 10--Due Wednesday, November 5:

• Quiz (419): No quiz on Monday, Nov 3 .
  
• Chapter 8: 49, 50, 54, 55, 69, 75, 78, 83, 88, 89

Assignment 11--Due Wednesday, November 12:

• Quiz (419): Quiz VIII on Monday, Nov 10 .
  
• Covers: Chapter 8 (from page 166), Chapter 9 (up to Applications of Factor Groups on page 193)
  
• Chapter 9: [1], 2, [4], 5, 6, 9 - 11, [12 -14], 15, 17, [18, 19], 20 - 22, 34, 37, [43], 51, [58], 59, 61, 67, 72

Assignment 12--Due Wednesday, November 19:

• Quiz (419): Quiz IX on Monday, Nov 17 .
  
• Covers: Chapters 9 and 10
  
• Chapter 10: [5], 6, 7, [8], 9, 11, 13, [14], 16, [19], 20, 26, 28, 32, [35], 40 - 43, 49, 51, 58
• Note: some problem ask if there is a homomorphism from G onto H, rather than from G to H. This means the homomorphism is suppose to be onto.
• Exam III: Friday, November 21 [changed to Monday, November 24]

Assignment 13--Due Wednesday, December 3:

• Quiz (419): Quiz X on Monday, December 1 .
  
• Covers: Chapters 11 (statement of Fundamental Theorem and consequences) and 12
  
• Chapter 11: 2, [6], 12, 21, 26, 38
• Chapter 12: 1, [2], 8, 19, 22, 25, 32, 44, [49], 50, 51
• Chapter 13: [3], 5, 11, 15, [18], 24, [29], 30, 31, 35, 49 (Hint: use the Binomial Theorem), 51

Exam I

• When: Friday, October 3 at 12:00-12:50 PM
• Where: Math 150
• Covers: 
  
• Chapter 0 (Well Ordering, Division Algorithm, Modular Arithmetic)
• Chapter 1 (the dihedral group D_n)
• Chapters 2 - 4
• 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
• Review Session: Wednesday, Oct 1, 2:30 PM in Math 205

Exam II

• When: Friday, October 31 at 12:00-12:50 PM
• Where: Math 150
• Covers:  Chapters 5 - 8 (up to new topic on page 166)
  
• 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
• homework problems or variations on them
• some new problems might appear
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed
• calculator might actually be needed
• Review Session: Wednesday, October 29, 2:30 PM in Math 122

Exam III

• When: Monday, November 24 at 12:00-12:50 PM [date changed due to UB closing]
  
• Where: Math 150
• Covers:  End of Chapter 8, Chapters 9 & 10
  
• 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
• homework problems or variations on them
• some new problems might appear
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed
• calculator might actually be needed
• Review Session: Wednesday, November 19, 2:00 PM in Math 122