Revised 12/09/14 at 5:07 PM
MTH 419/519--Introduction to Abstract Algebra--Homework Assignments
Note: problems in brackets [ ] are to be done, but not turned in.
Homework: due Wednesdays in lecture
Quiz(420 only): Mondays in recitation
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
Office Hours: Mon 2:00 PM, Wed 11:00
AM
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):
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.
- 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.
- 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 .
- 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