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

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

Exams:

• Exam I: Monday, Oct 4 completed
  
• Exam II: Monday, Nov 1 completed
• Exam III: Monday, Nov 29 completed
• Final Exam: Monday, December 13, 11:45AM - 2:45 PM in Math 150

• Contemporary Abstract Algebra, 9th edition, by Joseph Gallian

Assignment XIII--Week of November 29:

• Quiz D1 Wed recitation: No Quiz in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers:
  
• Quiz D2 Fri recitation: No Quiz in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers:
  
• Turn in Problem Set 12 (from the text book), due  Monday 12/06/2021, in Gradescope by 11:59 PM
• 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 that the homomorphism is supposed to be onto.
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment XIV--Week of December 6:

• Quiz D1 Wed recitation: Quiz XI  in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: Chapter 9, through Example 17; Chapter 10
  
• Quiz D2 Fri recitation: Quiz XI in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: Chapter 9, through Example 17; Chapter 10, beginning of Chapter 11 (depending on where we get on Wednesday)
  
• Turn in Problem Set 13 (from the text book), due  ->Saturday<- 12/11/2021, in Gradescope by 11:59 PM
• Chapter 10: 40 - 42, 49, 58
• Note: some problems ask if there is a homomorphism from G onto H, rather than from G to H. This means that the homomorphism is supposed to be onto.
• Chapter 11: 2, [6], 12, 21
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Final Exam--Monday, December 13

• When 11:45 - 2:45 PM in Math 150
  
• Covers: 
• Chapters 0 (through page 7 and related homework)
• Chapters 1 - 11
• Chapter 8: skip Examples 4 & 5, skip Theorem 8.3 to end of chapter 8
• Chapter 9: only through Example 16)
• Chapter 11: up to, but not including Lemma 1
• 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
• homework problems may well be on the exam
• properties left as exercises in class may well be on the exam
• Seating will be assigned
• Exam will be handed out in class
• Must be written in dark ink--black or blue; cross out anything you do not want graded
• Instructor will upload the exams to Gradescope
• Calculators: Only non-programmable, non-graphing, non-alphanumeric are allowed on exams
• Notes: None

Coming Attractions (tentative list of upcoming assignments): May be changed

• TBA

Assignment I--Week of August 30:

• No classes: Monday, Sept 6 (Labor Day)
• Quiz D1 recitation: Quiz I in recitation, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: Division algorithm
• Quiz D2 recitation: Quiz I in recitation, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: Division algorithm, Bezout's Lemma (GCD is a linear combination), Euclid's Lemma
  
• Turn in Problem Set 1: (from the text book), due Tuesday, 09/07/2021, in Gradescope by 11:59 PM
• Chapter 0: 4 - 9, 11- 13, 18 - 21, 30
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment II--Week of September 6:

• No classes: Monday, Sept 6 (Labor Day)
• NO LECTURE ON WEDNESDAY, Sept 8
  
• Lecture is recorded: UBlearns>Zoom -> cloud recordings sign in with sso. Two recordings from 09/05/21. Start with the older recording.
• Quiz D1 Wed recitation: Quiz II in recitation, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: Bezout's Lemma (GCD is a linear combination), Euclid's Lemma, Modular arithmetic
  
• Quiz D2 Fri recitation: Quiz II in recitation, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: Modular arithmetic, symmetries of a square
  
• Turn in Problem Set 2: (from the text book), due Monday, 09/13/2021, in Gradescope by 11:59 PM
• Chapter 1: [1], 2, 5, [6], 8, 10, 13, 15, 18 Problems in parentheses are to be done but not turned in
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment III--Week of September 13:

• Quiz D1 Wed recitation: Quiz III in recitation, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: symmetries of square, groups
  
• Quiz D2 Fri recitation: Quiz III in recitation, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: Groups, including U(n)
  
• Turn in Problem Set 3: (from the text book), due Monday, 09/20/2021, in Gradescope by 11:59 PM
• Chapter 2: 4 - 6, 9 - 12, 17, 22, 25, 26, [31], 32, 37
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date
• Note: Table 2.1 contains a typo. The inverse in C* should have a^2 + b^2 in the denominator for both terms.

Assignment IV--Week of September 20:

• NO LECTURE ON WEDNESDAY, Sept 22
  
• Lecture is recorded: UBlearns>Zoom -> cloud recordings sign in with sso.
• Quiz D1 Wed recitation: Quiz IV in recitation, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: Groups, including U(n), subgroup tests
• Quiz D2 Fri recitation: Quiz IV in recitation, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: subgroup tests, cyclic groups
• Turn in Problem Set 4: (from the text book), due Monday, 09/27/2021, in Gradescope by 11:59 PM
• Chapter 3: [1 - 5], 13, 17, 19, 23, 31, [34], 44, 47, 70, 71, 73
• Chapter 4: 2, 3, [4], 5, 7
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment V--Week of September 27:

• NO LECTURE ON WEDNESDAY, Sept 29
  
• Lecture is recorded: UBlearns>Zoom -> cloud recordings sign in with sso.
• Quiz D1 Wed recitation: Quiz V in recitation, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: order of elements, cyclic groups
• Quiz D2 Fri recitation: No quiz this week
• Format for quizzes: one definition/statement, one problem/proof
• Covers:
• Turn in Problem Set 5: (from the text book), due -->Wednesday<-- 10/06/2021, in Gradescope by 11:59 PM
• Chapter 4: [8], 9, [12], 14, [23], 24, 31, 35, 50, 60, 77
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment VI--Week of October 4:

• Quiz D1 Wed recitation: No quiz in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers:
• Quiz D2 Fri recitation: Quiz V in recitation, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: Cyclic subgroups, generators
• Turn in Problem Set 6: (from the text book), due Monday 10/11/2021, in Gradescope by 11:59 PM
• Chapter 4: 13, 29, 53, 68, [Try 85]
• Chapter 4: 35, 70
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment VII--Week of October 11:

• Quiz D1 Wed recitation: Quiz VI in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: Cyclic subgroups, generators, subgroup lattice
• Quiz D2 Fri recitation: Quiz VI in recitation, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: subgroup lattice, beginning of permutations
• Turn in Problem Set 7: (from the text book), due ->>Tuesday<<- 10/19/2021, in Gradescope by 11:59 PM
• Chapter 5: 1 - 3, [4 - 8], 9, 13, [15], 16, 17, [19], 23, [26], 28, 29, [32]
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment VIII--Week of October 18:

• Quiz D1 Wed recitation: Quiz VII in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: Permutations, S_n, A_n
• order of permutations, even/odd permutations, writing a permutation as as a product of disjoint cylces
• writing a permutation as a product of transpositions
  
• Quiz D2 Fri recitation: Quiz VII in recitation, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers:
  
• Permutations, S_n, A_n
• order of permutations, even/odd permutations, writing a permutation as as a product of disjoint cylces
• writing a permutation as a product of transpositions
• isomorphisms and isomorphic groups
  
• Turn in Problem Set 8: (from the text book), due Monday 10/25/2021, in Gradescope by 11:59 PM
• Chapter 5: 35, 36, 53, 57, 61, 65
• Chapter 6: [1], [4, 5], 6, 7, 12, [22], 36, 39, 41
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment IX--Week of October 25:

• Quiz D1 Wed recitation: Quiz VIII in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• isomorphisms and isomorphic groups
• properties of isomorphisms
  
• Quiz D2 Fri recitation: no quiz this week
• Format for quizzes: one definition/statement, one problem/proof
• Covers:
  
• 
  
• Turn in Problem Set 8: (from the text book), due -->Tuesday<-- 11/02/2021, in Gradescope by 11:59 PM
• Chapter 6: 51, 53, [try 67]
• Chapter 6: 2, 9, 14, 17 -19, 26, 60
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment X--Week of November 1:

• Quiz D1 Wed recitation: no quiz this week
• Format for quizzes: one definition/statement, one problem/proof
• Quiz D2 Fri recitation: Quiz VIII in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: automorphisms
• including Inn(G), Aut(G), Aut(Z), Aut(Z_n)
  
• Turn in Problem Set 9: (from the text book), due  Monday 11/08/2021, in Gradescope by 11:59 PM
• Chapter 7: 1, [2], 3 - 8, 12, 13, [15, 16], 17 - 19, 22, 26
• Problem 8 has a misprint. Should be: HK = {hk |  h in H, k in K}.
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment XI--Week of November 8:

• Quiz D1 Wed recitation: Quiz IX in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: automorphisms and cosets
  
• including Inn(G), Aut(G), Aut(Z), Aut(Z_n)
• Quiz D2 Fri recitation: Quiz IX in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: cosets
• including normalizer-stabilizer theorem
  
• Turn in Problem Set 10 (from the text book), due  ->Tuesday<- 11/16/2021, in Gradescope by 11:59 PM
• Chapter 7: 30, 33, [45], 53, [58], 59
• Chapter 8: 1, 5 - 7, 14, 16, 27. Note: 11, 34 have been deleted from the assignment.
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment XII--Week of November 15:

• Quiz D1 Wed recitation: Quiz X in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: cosets, direct product of groups
  
• including orbit-stabilizer theorem
• Quiz D2 Fri recitation: Quiz X in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers: direct product of groups, normal subgroups
  
• Turn in Problem Set 11 (from the text book), due  Monday 11/22/2021, in Gradescope by 11:59 PM
• Chapter 9: 2, 5, 6, 9, [10 - 12], 17, [18, 19], 22, 37, [43], 51, 59, 61, 67, [71]
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment XIII--Week of November 29:

• Quiz D1 Wed recitation: No Quiz in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers:
  
• Quiz D2 Fri recitation: No Quiz in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Covers:
  
• Turn in Problem Set 12 (from the text book), due  Monday 12/06/2021, in Gradescope by 11:59 PM
• 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 that the homomorphism is supposed to be onto.
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Exam I--Monday, October 4

• When 11:30 - 12:20 PM in Math 150
  
• Covers:  Chapters 0 (through page 7 and related homework), 1 - 4 (through Theorem 4.1 only)
• Format:
• 1 or 2 statements/definitions; 3 or 4 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• homework problems may well be on the exam
• Seating will be assigned
• Exam will be handed out in class
• Must be written in dark ink--black or blue; cross out anything you do not want graded
• Instructor will upload the exams to Gradescope
• Calculators: Only non-programmable, non-graphing, non-alphanumeric are allowed on exams
• Notes: None

Exam II--Monday, November 1

• When 11:30 - 12:20 PM in Math 150
  
• Covers:  Chapters 4 - 6 (up to, but not including Automorphisms on  page 128)
• 1 or 2 statements/definitions; 3 or 4 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• homework problems may well be on the exam
• properties left as exercises in class may well be on the exam
• be sure to review center, centralizer, order of a group
• Seating will be assigned
• Exam will be handed out in class
• Must be written in dark ink--black or blue; cross out anything you do not want graded
• Instructor will upload the exams to Gradescope
• Calculators: Only non-programmable, non-graphing, non-alphanumeric are allowed on exams
• Notes: None

Exam III--Monday, November 29

• When 11:30 - 12:20 PM in Math 150
  
• Covers:  Chapters 6 - 9 (Chapter 8: skip Examples 4 & 5, skip Theorem 8.3 to end of chapter 8; Chapter 9: only through Example 16)
• 1 or 2 statements/definitions; 3 or 4 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• homework problems may well be on the exam
• properties left as exercises in class may well be on the exam
• Seating will be assigned
• Exam will be handed out in class
• Must be written in dark ink--black or blue; cross out anything you do not want graded
• Instructor will upload the exams to Gradescope
• Calculators: Only non-programmable, non-graphing, non-alphanumeric are allowed on exams
• Notes: None