MAT 531 - M002 - Second Course in Linear Algebra - Fall 2019

The course will cover Chapters 1,2,5, and 6 in the textbook as well as some additional topics if time permits. Mathematically, the course will be similar to MAT 331. However, it is not intended to be an immediate continuation of MAT 331. Rather, it will reintroduce important concepts of linear algebra in a more abstract, coordinate-free setting. Consequently, the focus of this course will be on proofs and concepts, not on calculations. The course will cover the following topics:

  • Abstract vector spaces and bases
  • Linear transformations and their matrix representations
  • Eigenvalues and eigenvectors
  • Inner product spaces
  • Applications

More information can be found below:

  • Text: Linear Algebra, by Friedberg, Insel, and Spence, Fourth Edition, Prentice Hall, 2003.
  • Classes: TuTh 12:30 - 1:50 PM, 100 Carnegie
  • Office Hours: TuTh 3:10 - 4:10 PM or by appointment
  • Course Syllabus: A PDF version of the course syllabus can be found here.
  • Midterm Exam: There will be one midterm exam, which will tentatively be given on Tuesday, October 15.
  • Final Exam: The final exam will cover the entire course and will be given on Thursday, December 12, from 5:15 - 7:15 PM. The location of the exam will be announced later.
  • Homework: Written assignments will be announced weekly at the bottom of this page. Working independently on the assignments will probably help you to learn the material more effectively and to do better on exams. However, you may (and sometimes should) work with others to fully understand the material. You must write your own solutions to homework problems. Homework is due on Thursdays at the beginning of class.
  • Grading: The midterm exam will count for 30% of your course grade and the final exam for 40%. The remaining 30% will come from the homework.
  • Calculator Policy: Calculators will not be allowed on the exams.
  • Academic Integrity: See Syracuse University's Academic Integrity Policy
  • Students with Disabilities: If you believe you need an accommodation for a disability, please talk to me at the beginning of the semester or contact the Office of Disability Services (ODS), located in Suite 303 of 804 University Avenue, or call (315) 443-4498
  • Religious Observances Notification: Students who will be observing religious holidays during the semester are required to fill out their notification form on MySlice by the end of the second week of classes.

Homework Assignments:

    • Homework 1, due in class on Thursday, September 5:
      Section 1.2, Exercises 1 (only parts a through i), 4 (only parts b, c), 6, 13
      Additional Exercise (required for full credit): How many vectors are there in F3 for F=Z2?
      (Here Z2 denotes the field with two elements defined in Example 4 on page 553.)
    • Homework 2, due in class on Thursday, September 12:
      Section 1.3, Exercises 8 (only parts b and c), 11, 15 (here C(R) is defined as in Example 2 on page 18)
      Section 1.4, Exercises 3 (only part a), 4 (only part a), 5 (only part g)
      Additional Exercise (required for full credit): How many subspaces are there in F2 for F=Z2?
    • Homework 3, due in class on Thursday, September 19:
      Section 1.5, Exercises 1, 2 (only parts d, e), 8 (in part b, assume F=Z2), 9
      Section 1.6, Exercises 1 (only parts a through g), 2 (only part a)
    • Homework 4, due in class on Thursday, September 26:
      Section 1.6, Exercises 4, 6, 7, 10 (only part a), 16, 26
      Section 1.7, Exercise 3
    • Homework 5, due in class on Thursday, October 3:
      Section 2.1, Exercises 2, 3, 9, 12, 16
    • Homework 6, due in class on Thursday, October 10:
      Section 2.1, Exercise 1
      Section 2.2, Exercises 2 (only part b), 3, 4, 9
      Section 2.4, Exercise 3
    • Homework 7, due in class on Thursday, October 17:
      Section 2.3, Exercises 1 (only parts a through f), 3 (only part a)
      Section 2.4, Exercise 6
    • Homework 8, due in class on Thursday, October 24:
      Section 2.5, Exercises 1, 2 (only parts b and c), 6 (only part b), 7 (only part a)
    • Homework 9, due in class on Thursday, October 31:
      Section 2.6, Exercises 2, 6 (only part a)
      Section 4.3, Exercise 12
      Section 4.4, Exercises 1, 2 (only part a), 3 (only part b)
    • Homework 10, due in class on Thursday, November 7:
      Section 5.1, Exercises 2 (only part a), 3 (only parts a, c), 15 (only part a)
      Section 5.2, Exercises 1 (only parts a through f), 2 (only part f)
    • Homework 11, due in class on Thursday, November 14:
      Section 5.2, Exercises 3 (only part b), 7, 14 (only part a)
      Section 5.4, Exercises 2 (only parts b, c), 18 (only part b)
    • Homework 12, due in class on Thursday, November 21:
      Section 6.1, Exercises 1 (only parts a through e), 2, 11, 16 (only part b)
      Section 6.2, Exercise 2 (only part a)
      Remark: In Exercise 6.1.16(b), C([0,1]) denotes the space of real-valued continuous functions on [0,1].