Revised 12/06/2021 at 02:30 PM
MTH 419--Introduction to Abstract Algebra--Homework Assignments
Note: problems in brackets [ ] are to be done, but not turned in.
Homework: due in Gradescope before
class on Mondays
Quiz: due in Gradescope in recitation
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
Office Hours: TBA and by appointment
Textbook:
- 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
- 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
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
- 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
- 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
- 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