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

Homework:

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

Exams:

• Exam I: Wednesday, Sep 28 completed
  
• Exam II: Monday, Oct 24 completed
• Exam III: Wednesday, Nov 30
• Final Exam: Monday, December 12, 8:00 AM - 11:00 AM, Math 150

Office Hours:

• Monday and Wednesday at 1:30 - 2:20
• by appointment

Textbook: 

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

Final Exam

• When: Monday, December 12, 8:00 AM - 11:00 AM
• 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, 13.4
  
• Includes all the homework problems assigned (whether to turn in or not turn in)
• Format: 8 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

Coming Attractions (tentative list of upcoming assignments):

• Monday, December 12, 8:00 AM - 11:00 AM

Assignments I--Week of August 29

• Read Chapter 0
• Course will begin with Chapter 1.
• No classes: Monday, Sept 5 (Labor Day)
• Chapter 0 Problems:  Due Friday, Sept 2
• 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, 10 - 14 [[For future reference, 10 is not a good problem]]
• All problems to be turned in must be typed in LaTeX. A template is available in UBLearns.

Assignments II--Week of September 5

• No classes: Monday, Sept 5 (Labor Day)
• Chapter 1 Problems:  Due Friday, Sept 9
• 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
• 1.4: 4, 5, 8, [10, 11]

Assignments III--Week of Sept 12

• Problems:  Due Friday, Sept 16
• 1.6: 9, 13, 14
• 1.7: 17, 18, 19
• 2.1: [1], [2], 5--8, 15
• 2.2: [2, 5a, 5b], 6a, 14

Assignments IV--Week of Sept 19

• Problems:  Due Friday, Sept 23
• 2.3: [1], [3], 8, 9, 12, 16, [20], 21, 24
• For 21: Use induction and the binomial theorem ...
• 3.1: 1, 5, [30], 36, 41

Assignments V--Week of Sept 26

• Exam I: Wednesday, Sept 28
  
• Problems:  Due Friday, Sept 30
• 2.4: 3, 14, 15
• 3.2 Additional Problems: 1
• Additional Problems are in UBLearns > Course Documents
• 3.2: 11, 18, 19

Assignments VI--Week of Oct 3

• Problems:  Due Friday, Oct 7
• 3.3: 3, 7, 8
• 3.4: 4
• 3.5:  3, 4, 12

Assignments VII--Week of Oct 10

• Problems:  Due Friday, Oct 14
• 4.1: [1], 2, 3, 10
• 4.2: [3], 8, 9
• 4.3: 5, 6
• 4.4: 1, 2, 6

Assignments VIII--Week of Oct 17

• Problems:  Due Friday, Oct 21
• 4.5: 4, 8, 13, 16, 46
• 5.1: 1, 4, 11

Assignments IX--Week of Oct 24

• Problems:  Due Friday, Oct 21
• 5.2: [2], 6, 8
• 5.4: 1, 2, [3], [10], 11, 15, 16

Assignments X--Week of Oct 31

• Problems:  Due Friday, Nov 4
• 7.1: [11], 15, 16, [17], [21], 22
• 7.2: [2], [3a], 3b, 3c, 4
• 7.3: 16, 19, [25], [26a], 26b, 26c, 34, 35, 37

Assignments XI--Week of November 7

• Problems:  Due Friday, Nov 11
• 7.4: 5, 7, [8], 11, 19, 23, 30 [Note: 23 added to list of problems]
• 7.5: 3
• 7.6: 1, 2, 3 [4]

Assignments XII--Week of November 14

• Problems:  Due Friday, Nov 18
• 8.1: 3, 6, 7 [6 was added]
• 7 is a calculation. You may use Mathematica or another CAS to simplify the calculations, but not to actually do the problem, or to actually do the division algorithm in Z[i]
• Attach calculations to the rest of your assignment or export calculations as pdf and import into LaTeX
• 8.2: 1, 3, 4
• 8.3: Look at 8a
• 9.1 2, 4, 6, 8a

Assignments XIII and XIV--Weeks of November 21 and 28

• Problems:  Due Friday, Dec 2
• 9.2: [2], [4], 5, [6a, b, c], 6d
• 4 presupposes that you know how to prove there are infinitely many prime numbers
• 9.3: 2, 3
• 9.4: [1], 2d, 3, [6], [7]
• 13.1: 2, [3], [4], 5, [6], 7

Assignments XV--Week of December 5

• Problems:  Due Friday, Dec 9
• 13.2: [3], 4, 5, 7
• You may use Mathematica to do calculations for #7, but not to just solve the problem completely.
• 13.4: 1, 2, 5, 6

Exam I

• When: Wednesday, September 28 at 11:00-11:50 AM
• Where: Math 150
• Covers: 
  
• 0.1 - 2.3, 3.1 [2.4 will be covered on the next exam]
  
• 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: Monday, October 24 at 11:00-11:50 AM
• Where: Math 150
• Covers: 
  
• 2.4, 3.2, 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 30 at 11:00-11:50 AM
• Where: Math 150
• Covers: 
  
• 5.2, 5.4, 7.1 - 7.6, 8.1 - 8.3, 9.1, 9.2, 9.4, 13.1
  
• 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