Revised 05/08/2020 4:40 PM
MTH 420/520--Abstract Linear Algebra--Homework Assignments
Homework: due Mondays in lecture
Quiz(420 only): Wednesdays in
recitation
Exams:
- Exam I: Wednesday, March 4
- Exam II: Wednesday, April 22--available at noon; due
April 24 at midnight.
- Final Exam: Monday, May 11, 2020, 11:45 AM - 2:45 PM
in Math 250 Not exactly
Office Hours: Mon, 12:30 - 1:20
PM; Wed, 1:30 - 2: 20 PM, and by appointment
Textbook:
- Linear Algebra (2nd Edition) by Kenneth M Hoffman and Ray Kunze
Note: problems in brackets [ ] are to be done, but not turned in.
Final Exam
- When: Monday, May 11, available in the morning, Due
in Gradescope by midnight on Wednesday
- preferably typed in LaTeX or word
- one page per question is ideal
- Be sure to assign a page or pages to each question in Gradescope. If
you do not know how to do this, here is a link that will be helpful:
- You can type your name when you sign the integrity pledge if the
rest of your exam is typed
- Where: in the cloud
- Covers: Sections 1.1 - 3.7, 4.2,
4.4, 4.5, 5.4, 6.2, 6.3
- 420 Format: 1 to 3 definitions or statements of
result, 6 - 10 problems/proofs
- proofs from the book or lecture, or pieces of proofs, may well be on
the exam
- 520 Format: 8 to 12
problems/definitions/proofs/statement of theorems
- No books, notes, internet resources (except for LaTeX or Word),
consultation, collaboration via any method
- No alphanumeric/programmable/graphing calculators and or computer
algebra systems allowed
Coming Attractions (very tentative list of upcoming assignments):
Week of January 27:
- Recitation for 420: Recitation
will meet Wednesday, January
29, at 8:00 AM in Math 250
- Read: Sections: 1.1 - 1.5
- Assignment 1:
- Due Monday, February 3
- problems listed for an assignment are to
be handed on the due date in
class.
- Notes must be typed, preferably in LaTeX (LaTeX required for
graduate students)
- LaTeX resources: UBLearns>Course Documents
- Lengthy computations may be handwritten (e.g. row reducing a
matrix)
- Section 1.2: 1 - 4, 6, 7
- Quiz for 420: Quiz this week on Wednesday, January 29
- Topics: Review of Matrix Multiplication, Linear
independence/dependence, inverse of a matrix
- Look at your notes from Linear Algebra or look up these topics on
the internet
Week of February 3:
- Read: Sections: 1.6 - 2.2
- Assignment 2:
- Due Monday, February 10
- Notes must be typed, preferably in LaTeX (LaTeX required for
graduate students)
- LaTeX resources: UBLearns>Course Documents
- Section 1.3: 3, 5, 7
- Section 1.5:
3, 4, 8 a hard problem
- Quiz for 420: Quiz on Wednesday, February 5
- Format:
- One statement or definition
- One problem or proof
- Topics: 1.1 - 1.3, 1.5 (through Theorem 9 on p. 20)
Week of February 10:
- Read: Sections: 2.1 -2.3
- Assignment 3:
- Due Monday, February 17
- Notes must be typed, preferably in LaTeX (LaTeX required for
graduate students)
- LaTeX resources: UBLearns>Course Documents
- Section 1.4: 1, 4, 8, 10 a hard problem
- Section 1.6: 1, 5 - 7, 10,
[11]. Look at 12 (extremely hard problem)
- Quiz for 420: Quiz on Wednesday, February 12
- Format:
- One statement or definition
- One problem or proof
Week of February 17:
- Read: Sections: 2.5 -2.6
- Assignment 4:
- Due Monday, February 24
- Section 2.1: 4, 6, 7
- Section 2.2: [1 - 2],
3, 5, 7, 9
- Quiz for 420: Quiz on Wednesday, February 19
- Format:
- One statement or definition
- One problem or proof
Week of February 24:
- Read: Sections: 2.4, 2.5,
2.6
- Assignment 5:
- Due Monday, March 2
- Section
2.3: [1],
4, 9 - 11, 13, 14 (a harder, but still doable problem)
- Note:
Problem 13
references Exercise 5 in Section 1.2, not 1.1
- Quiz for 420: Quiz on Wednesday, February 26
- Format:
- One statement or definition
- One problem or proof
- Topics: 2.2, 2.3 (through Cor. 2 on p 46)
- Exam I: Wednesday, March 4--covers through all of 2.3
Week of March 2:
- Read: Sections: 3.1, 3.2
- Assignment 6:
- Due Monday, March 9
- Section
2.3: 2,
7
- Section 2.4: 2, 6 (don't do
4)
- Quiz for 420: No Quiz on Wednesday, March 4
Week of March 9:
- Read: Sections: 3.3, 3.3
- Assignment 7:
- Due Monday, March 23
- Section 2.6: 1, [2], 3, 5
- For Problem 1:
Theorem 4 is on p 44
- Section 3.1: 4, 5, 8, 10, 12
- Quiz for 420: Quiz on Wednesday, March 11
- Format:
- One statement or definition
- One problem or proof
Week of March 23
- Read: Sections: 3.4
- Assignment 8:
- Due Wednesday, April 1 through Gradescope
- Section 3.2: 3
- 6, 8
- Section
3.2: 10, 11
- Section 3.3: 2,
3, 5, 7
- Quiz for 420: no quiz on Wednesday, March 25
- Format:
- One statement or definition
- One problem or proof
Week of March 30
- Read: Sections: 3.5 - 3.6
- Assignment 9:
- Due Monday, April 6 through Gradescope
- Section 3.4:
2, 5, 10, 12
- Quiz for 420: Quiz available noon Wednesday, April 1,
due midnight Thursday, April 2
- Format:
- One statement or definition
- One problem or proof
Week of April 6
- Read: Sections: 3.5 - 3.6
- Assignment 10:
- Due Monday, April 13 through Gradescope
- Section 3.5: 1 - 5
- For problem 2, the answer should be in terms of the standard
ordered basis for the dual space
- where the standard ordered basis for the dual space is the
dual basis to the standard ordered basis for C^3.
- Alternatively, the book thinks of C^3 as row vectors, so the
dual basis should be actual column vectors
- that give \delta_{ij}, the Kronecker delta, when applied to
the given basis.
- Quiz for 420: Quiz available noon Wednesday, April 8,
due midnight Thursday, April 9
- Format:
- One statement or definition
- One problem or proof
- Topics: 3.4, 3.5 up to, but not including, Example 22
Week of April 13
- Read: Sections: 3.6, 3.7
- Assignment 11:
- Due Monday, April 20 through Gradescope
- Section 3.5: 6 - 9, 11, 12
- Quiz for 420: Quiz available noon Wednesday, April
15, due midnight Thursday, April 16
- Format:
- One statement or definition
- One problem or proof
- Topics: 3.5 including Example 22, beginning of 3.6 (not double dual,
but Theorem 18 etc)
- annihilator, pre-annihilator (not a term used in the book, but the
concept is there just above theorem 18)
Week of April 20
- Read: Sections: 4.2, 4.4,
4.5
- Assignment 12:
- Due Tuesday, April 28 through Gradescope
- Section 3.7: 2 - 5, 8
- Section 3.6: 3 just
look at
- Quiz for 420: no quiz this week
- Format:
- One statement or definition
- One problem or proof
Week of May 4
- Read: Sections: 5.4, 6.2,
6.3
- Assignment 13:
- Due Friday, May 8 through Gradescope
- Section
4.2: 6 - 8
- Section
4.4: 1, 3
- Section 5.4: 3, 5, 8
- Section 6.2: 5, 8, 9, 13
- Quiz for 420: Quiz on Wednesday, May 6 Cancelled
- Format:
- One statement or definition
- One problem or proof
- Topics: 5.4, 6.2
Exam I
- When: Wednesday, March 4 at 11:00-11:50 AM
- Where: Math 250
- Covers: Sections 1.1 - 2.3
- including the
corresponding material on the lecture slides/notes
- Format:
- 420: 1 or 2 statements/definitions; 3 or 4 problems/proofs
- 520: 4 or 5 problems/definitions/proofs/statement of theorems
- 420/520: 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, April 22, released tentatively at
noon
- Due in Gradescope: Friday, April 24 at 11:59 PM
- Covers: Sections 2.4 - 2.6, 3.1 - 3.5, beginning of
3.6 (not double dual, but Theorem 18 etc)
- including the
corresponding material on the lecture notes
- Format:
- designed to be a sixty minute exam
- preferably typed
- 420: 1 or 2 statements/definitions; 3 - 5 problems/proofs
- 520: 4 - 6 problems/definitions/proofs/statement of theorems
- 420/520: proofs from the book or lecture, or pieces of proofs, may
well be on the exam
- No books, notes, internet resources (except for LaTeX or Word),
consultation, collaboration via any method
- No alphanumeric/programmable/graphing calculators and or computer
algebra systems allowed