Algebra II

Instructor: Joel Kamnitzer,
Office: 6110 Bahen 416-978-5163
Office Hours: Wednesdays 10:00 am - 12:00 pm

TAs: Mikhail Gudim, and Jesse McKeown,
Office Hours: Mondays 2:30 pm - 4:30 pm, Wednesdays 5 pm - 7 pm, BA 6283.

Lectures: Monday 1-2 pm, Tuesday 2-3 pm, Thursday 1-2 pm in BA 1220
Tutorial: Tuesday 1-2 pm BA 1220

Grading scheme:

  • Homework (8-10 assignments) 30%
  • Term test (Tuesday February 15) 20%
  • Final 50%

  • Text: Linear Algebra done right, Sheldon Axler

    Other useful references:
  • Freidberg, Insel, and Spence, Linear algebra
  • Hoffman and Kunze, Linear algebra
  • Treil, Linear algebra done wrong
  • Charles W. Curtis, Linear algebra: an introductory approach

  • Syllabus:
    Inner products (Axler 6, Curtis 4, Treil 5)
    Operators on inner product spaces (Axler 7, Curtis 9, Treil 6)
    Bilinear forms (Friedberg Insel Spence 6.8, Curtis 27 and 31, Treil 7)
    Duals and tensor products (Curtis 8, Treil 8)

    Assignment 1 (pdf, tex) due Thursday January 20.
    Assignment 2 (pdf, tex) due Thursday January 27.
    Assignment 3 (pdf, tex) due Thursday February 3.
    Assignment 4 (pdf, tex) due Thursday February 10.
    Assignment 5 (pdf, tex) due Thursday March 3.
    Assignment 6 (pdf, tex) due Thursday March 10.
    Assignment 7 (pdf, tex) due Thursday March 17.
    Assignment 8 (pdf, tex) due Thursday March 25.
    Assignment 9 (pdf, tex) due Tuesday April 5.
    Bring assignments to class or email them (typed in latex) to one of the TAs. No late homeworks accepted.

    Final Info:
    The final exam will be held in EM 119 on Tuesday April 19 from 9:00 am to 12:00 pm. I will be holding office hours Wednesday April 13 and Monday April 18 from 9:00 am to 11:00 am. We will also have an exam review session on Friday April 15 from 2:00 pm to 4:00 pm in BA 6183. Here are some study suggestions.

    Notes from class:
    I will be posting notes about bilinear forms and tensor products every week.
    Bilinear forms and their matrices, posted March 8, 2011 (reposted with corrections, March 11).
    Symmetric bilinear forms, posted March 14, 2011.
    Symplectic forms, posted March 24, 2011.
    Multilinear forms, posted April 1, 2011.
    Tensor products, posted April 5, 2011.

    Chris Guibault has kindly made available his typed notes. They are on the wiki. Hopefully these notes will be useful. Keep in mind, however, that these are not "official" notes and neither Chris nor I certify that they are free of typos or mathematical errors.
    If you have anything else to contribute to the wiki, please do so (you may first have to contact me in order to become a confirmed user).

    Midterm Info:
    The midterm will be held in UC 266 (East Hall) from 1:15-3:00 pm on Tuesday February 15. The midterm covers all the material from class (except for the lecture on quantum mechanics) up to and including the February 8 lecture. This corresponds to chapter 6 and 7 from Axler, with the exception of the sections on normal operators on real inner product spaces, positive operators, and polar decompositions.

    Suggested study questions from Axler: 6.5, 6.13, 6.16, 6.17, 6.21, 7.3, 7.4, 7.10, 7.15, 7.21.

    On Monday February 14, there will be TA office hours 2:30-4:30 pm in BA 6283 and 5 - 7 pm in the math lounge (on the 6th floor of Bahen).

    The midterm has been marked and I believe that you should be able to view the marks on portal. I will hand back the midterms in class on Thursday. There was quite a spread of marks: 5 people got 50/50, but the average was only 32/50.
    If you received less than 30/50, you should make some changes to improve your performance in the class. Here are some suggestions: come to every class, come to tutorials, come to TA or professor office hours, spend more time reading your notes from class, spend more time working on assignments. If you received less than 20/50, then perhaps you are not getting much out of the course and should consider dropping it.

    Here is the midterm and the solutions.