MTH 420/520--Abstract Linear Algebra--Homework Assignments

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:
• https://www.dur.ac.uk/mathematical.sciences/teaching/gradescope/
• Note that you submit your exam as if it were homework.
• 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):

• TBA

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
• Topics: 1.4 - 1.6

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
• Topics: 1.6, 2.1, 2.2

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
• Topics: 2.4 - 3.1

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
• Topics:

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
• Topics: 3.2, 3.3, 3.4

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
• 11b is hard
• 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