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

Homework:

• usually due Fridays in lecture
• must be typed in LaTeX double spaced; a template is available in UBLearns > Course Documents
• Diagrams may be handwritten
• problems in brackets [ ] are to be done, but not turned in

Exams:

• Exam I: Friday, Oct 6 completed
  
• Exam II: Wednesday, Nov 1 completed
• Exam III: Wednesday, Nov 29 completed
• Final Exam: Monday, December 11, 11:45 AM - 2:45 PM, Math 150

Office Hours:

• Monday 1:00 - 1:50, Wednesday 1:30 - 2:20
• By appointment

Textbook: 

• Abstract Algebra, 3rd edition, by David Dummit and Richard Foote

Final Exam

• When: Monday, December 11, 11:45 AM - 2:45 PM
• Where: Math 150
• Covers: 
  
• 0.1 - 2.4, 3.1- 3.3, 3.5, 4.1 - 4.5, 5.1, 5.2, 5.4, 7.1 - 7.6, 8.1 - 8.3, 9.1, 9.2, 9.4, 13.1, 13.2
  
• Includes all the homework problems assigned (whether to turn in or not turn in)
• Format: 9 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

Assignments XIII--Week of December 4

• Chapter 9 Problems: Due Friday, December 8
• 9.3: [Look at 3]
• 9.4: [1], 2d, 3, [7]

• Chapter 13 Problems: Due Friday, December 8
• 13.1: 2, [3], 5, [6], [7]
• 13.2: [3], 4, 5, 7
• You may use Mathematica to do calculations for #7, but not to just solve the problem completely.

Coming Attractions (tentative list of upcoming assignments):

• TBA

Assignments I--Week of August 28

• Read Chapter 0
• Course will begin with Chapter 1.
• No classes: Monday, Sept 4 (Labor Day)
• Chapter 0 Problems:  Due Friday, Sept 1
• 0.1: 5 - 7
• 0.2: [1], 6, 7, 10 Note: 10 has two parts; treat them as separate questions (10a and10b). You may answer 10b even if you cannot solve 10a.
• 0.3: [2], 6, 7, 11 - 14
• All problems to be turned in must be typed in LaTeX. A template is available in UBLearns > Course Documents.

Assignments II--Week of September 4

• No classes: Monday, Sept 4 (Labor Day)
• Chapter 1 Problems:  Due Friday, Sept 8
• 1.1: [19], [24], 25, [26], 27, [28], 30 - 33a, [33b], 34, 35 Problems in brackets are to be done, but not turned in
• 1.2: 4, 5
• 1.3: [2], 10, 15, 18

Assignments III--Week of September 11

• Chapter 1, 2 Problems:  Due Friday, Sept 15
• 1.4: 4, 5, 8, [10, 11]
• 1.6: 9, 13, 14
• 1.7: 17, 18, 19
• 2.1: [1], [2], 5--8, 15

Assignments IV--Week of September 18

• Chapter 2 Problems:  Due Friday, Sept 22
• 2.2: [2, 5a, 5b], 6a, 14
• 2.3: [1], [3], 8, 9, 12, 16, [20], 21, 24
• For 21: Use induction and the binomial theorem ...
• 2.4: 3, 14, 15

Assignments V--Week of September 25

• Chapter 3 Problems:  Due Friday, Sept 29
• 3.1: 1, 5, [30], 36, 41
• Note: 41 is subgroup generated by ...
• 3.2 Additional Problems: 1
• Additional Problems are in UBLearns > Course Documents
• 3.2: 11, 18, 19
• 3.3: 3, 7, 8

Assignments VI--Week of October 2

• Chapter 3 Problems:  Due Monday, October 9 [note change from usual due date]
• 3.4: 4
• 3.5: 3, 4, 12
• Chapter 4 Problems:
• 4.1: [1], 2, 3, [10]

Assignments VII--Week of October 9

• Chapter 4 Problems: Due Friday, Oct 13
• 4.2: [3], 8, 9
• 4.3: 5, 6

Assignments VIII--Week of October 16

• Chapter 4 Problems: Due Friday, Oct 20 [Changed to Monday, Oct 23]
  
• 4.4: 1, 2, 6
• 4.5: 4, 8, 13, 16, 46 (a hard problem)
• Chapter 5 Problems: Due Friday, Oct 20 [Changed to Monday, Oct 23]
• 5.1: 1, 4
• Note: 11 will be on the next assignment

Assignments IX--Week of October 23

• Chapter 5 Problems: Due Friday, Oct 27
• 5.1: 11
• 5.2: [2], 6, 8 (a more difficult problem)

Assignments X--Week of November 6

• Chapter 5 Problems: Due Friday, Nov 10
• 5.4:[[1-3], [10], 11, 15, 16
• Chapter 7 Problems: Due Friday, Nov 10
• 7.1: [11], 15, 16, [17], [21], 22
• 7.2: [2], [3a], 3b, 3c, 4

Assignments XI--Week of November 13

• Chapter 7 Problems: Due Friday, Nov 17
• 7.3: 16, 19, [25--just read], [26a], 26b, 26c, 34, 37
• 7.4: 5, [8], 11, 19, 30 (a harder problem)
• 7.5: 3
• 7.6: 1, 3, [4]

Assignments XII--Week of November 20

• Chapter 8 Problems: Due Monday, Nov 27
• 8.1: 3, 6 [an interesting but harder problem]
• 8.2: 1, 3, 4
• 8.3: Look at 8a
• Chapter 9 Problems: Due Monday, Nov 27
• 9.1: 4, 6
• 9.2: 2, 4
• #4 presupposes that you know how to prove there are infinitely many prime numbers

Exam I

• When: Friday, October 6 at 11:00-11:50 AM
• Where: Math 150
• Covers: 
  
• 0.1 - 2.4, 3.1 - 3.3
  
• Includes all the homework problems assigned (whether to turn in or not turn in)
• Format: 4 or 5 problems/definitions/proofs/statement of theorems
• 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 1 at 11:00-11:50 AM
• Where: Math 150
• Covers: 
  
• 3.3, 3.5, 4.1 - 4.5, 5.1
  
• Includes all the homework problems assigned (whether to turn in or not turn in)
• Format: 4 or 5 problems/definitions/proofs/statement of theorems
• 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, November 29 at 11:00 -11:50 AM
• Where: Math 150
• Covers: 
  
• 5.2, 5.4, 7.1 - 7.6, 8.1, 8.2, 9.1, 9.2
• Includes all the homework problems assigned (whether to turn in or not turn in)
• Format: 4 or 5 problems/definitions/proofs/statement of theorems
• 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