Math 412: Advanced Linear Algebra

Fall Term 2017
Lior Silberman

General Information

This is a second course in linear algebra, intended for honours students. There is no required textbook. The book by Halmos is very good, covers nearly everything, and is available in PDF form from the publisher for anyone on the UBC network; a lot of the material can also be found in any "abstract algebra" textbook. More details may be found in the syllabus.

References

  1. Halmos, Finite-dimensional Vector Spaces, available from SpringerLink
  2. Coleman, Calculus on Normed Vector Spaces, Chapter 1 (on SpringerLink)
  3. Higham, Functions of Matrices, available from SIAM
  4. [Your favorite author], Abstract Algebra

Problem Sets

  • Problem set grade statistics.
    1. Problem Set 1, due 14/9/2017.
    2. Problem Set 2, due 21/9/2017 (typo in 5(b) corrected).

    For your edification

    Lecture-by-Lecture information

    Section numbers marked § are in Halmos [1], section numbers marked N are in the course notes above.

    Week Date Material Reading Notes
    1 Th 7/9 Introduction §1,§2  
    2 T 12/9 Direct sum and product §19,§20 Note on infinite dimensions
    Th 14/9 (continued)   PS1 due
    3 T 19/9 Quotients §21,§22  
    Th 21/9 Duality §13,§15 PS2 due
    4 T 26/9 Bilinear forms
    Tensor Products
    §23
    §24,§25
     
    Th 28/9 (continued)    
      Th 19/10 Midterm exam    
      TBA Final exam    


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    Last modified Tuesday September 19, 2017