Fall 2017, MTH 309-001: Linear Algebra I

  • Course syllabus: click here. Make sure to read this! The content of this page is merely a condensed version of the syllabus.
  • Meeting information: MWF, 10:20 AM -- 11:10 AM, Wells Hall A320
  • Exam information:
    • Midterms:
      • Friday, October 6, 2017, in-class
      • Wednesday, November 1, 2017, in-class
    • Final: Friday, December 15, 2017, 7:45 AM -- 9:45 AM, Wells Hall A320
  • Textbook: Although it is not strictly required, I recommend following along with the book Linear Algebra with Applications, 8th edition or newer, by Steven J. Leon.
  • As the course progresses, I will add notes to this section for you to use as references. While I've done my best to avoid any typos, they do occasionally slip in. Let me know if you have found one (or think you might have) and I will correct it as soon as possible.
  • Online Discussion: Piazza is a very nice communication platform for classes (especially math classes). Instead of sending me questions by email, I encourage you to post questions and/or answers using Piazza, so that everyone in the class can see both the questions and answers. Piazza also allows you to post anonymously, in case you are reluctant to have your name attached to a post. You will receive an invitation in the beginning of the semester inviting you to join. Our Q&A page is
  • Homework: Homework sets will be posted in this section regularly, so make sure to check back for any new assignments. All homework must be typed using LaTeX; I recommend all students use www.sharelatex.com for their homework, as it is easy to get started with and many of you have used it in a previous class. Each assignment will be collected at the beginning of class, and late work will not be accepted under any circumstances. To offset this strict policy, your three lowest homework scores will be dropped automatically.
  • LaTeX: some information about getting started with LaTeX can be found here ( .pdf | .tex ). You can learn not only from the content of the .pdf file, but from looking at how some of the formatting was done by looking at the .tex file itself. If you want to brush up on using it, or learn how to use it at all, there will be a help session on Thursday, 8/31 at 6:00 pm -- 7:00 pm in Wells Hall, room A320.
  • Tentative schedule of topics:
    • Week 1
      • 8/30: Introductions; what is linear algebra?
      • 9/1: Review of notation, logic, and proof techniques
    • Week 2
      • 9/4: Labor Day -- no class
      • 9/6: Systems of linear equations
      • 9/8: Row reduction and echelon forms
    • Week 3
      • 9/11: (cont'd)
      • 9/13: Vector equations
      • 9/15: The matrix equation Ax = b
    • Week 4
      • 9/18: Homogeneous and non-homogeneous systems
      • 9/20: Linear independence
      • 9/22: Intro. to linear transformations
    • Week 5
      • 9/25: The matrix of a linear transformation
      • 9/27: Matrix operations
      • 9/29: The inverse of a matrix
    • Week 6
      • 10/2: Characterizations of invertible matrices
      • 10/4: Review
      • 10/6: Midterm Exam 1
    • Week 7
      • 10/9: Intro. to Determinants
      • 10/11: Vector spaces and subspaces
      • 10/13: Null spaces, column spaces, and linear transformations
    • Week 8
      • 10/16: Linearly independent sets and bases
      • 10/18: Coordinate systems
      • 10/20: The dimension of a vector space; Rank
    • Week 9
      • 10/23: Eigenvalues and eigenvectors
      • 10/25: The characteristic equation
      • 10/27: (cont'd)
    • Week 10
      • 10/30: Review
      • 11/1: Midterm Exam 2
      • 11/3: Diagonalization
    • Week 11
      • 11/6: Eigenvectors and Linear Transformations
      • 11/8: (cont'd)
      • 11/10: Inner product, length, and orthogonality
    • Week 12
      • 11/13: Orthogonal sets
      • 11/15: Orthogonal projections
      • 11/17: Gram-Schmidt orthonormalization
    • Week 13
      • 11/20: Gram-Schmidt practice
      • 11/22: TBD
      • 11/24: Thanksgiving Break -- no class
    • Week 14
      • 11/27: Direct sums of vector spaces
      • 11/29: Tensor products of vector spaces
      • 12/1: class canceled
    • Week 15
      • 12/4: (cont'd)
      • 12/6: Review
      • 12/8: Review