Math 223 Section 102
Linear Algebra
Online Course Material 

NEWS
Our final exam is scheduled for Tuesday December 20, 3:30 in MATH 204. Our exam is 3 hours long. Two practice tests have been posted, from 2008 and 2009. I will be available for questions Monday Dec 19 and Friday Dec 16 with times and room yet to be decided.

Comments for midterm 2. The class average was 68%. Great job.
Comments for midterm 1. The class average was 70%. Great job.

Our class is now scheduled to meet in MATH 204 9-10 MWF. This should be much more suitable for our small class. Also note that Assignment 1 due Wednesday Sept 14 is now posted. I will try to follow a Wednesday due date for assignments and then our Tuesday office hour 4-5 in MATH ANNEX 1118 will be especially useful.

This is an Honours level course that both covers the material of MATH 221 and MATH 152 but adds some theoretical material. The grading standards (for me) are roughly those of MATH 221 and so some judicious scaling will be used. It will be substantially more work than MATH 221 but hopefully much more interesting. There is another section of MATH 223 at 10 MWF but our section will be run independently of that section with slightly different topics and different tests.


I will be putting course materials on the web in pdf format to supplement the text. The text has some excellent explanations but the problems tend to be much too elementary.
The notes look authoritative when typed so be wary. They may look perfect but may still contain errors! I don't have an editor.
I arrive most days by 9:00. Obviously I'll have to arrive a little earlier than that for teaching! I have an office hour 4-5 on Tuesdays in MATH ANNEX 1118 (near my office) and imagine many assignments will be due Wednesdays. Other office hours will be available. I do not reliably read my email from home (i.e. evenings and weekends) nor every hour at work.

  • Course Outline: grading scheme etc. 
  • Assignment 1.due Wednesday Sept 14.  
  • Assignment 1 Solutions .  
  • Assignment 2.due Wednesday Sept 21.  
  • Assignment 2 Solutions .  
  • Assignment 3.due Wednesday Sept 28.  
  • Assignment 3 Solutions .  
  • Assignment 4.due Wednesday Oct 5.  
  • Assignment 4 Solutions .  
  • Assignment 5.due Wednesday Oct 19.  
  • Assignment 5 Solutions .  
  • Assignment 6.due Wednesday Oct 26.  
  • Assignment 6 Solutions .  
  • Assignment 7.due Wednesday Nov 2.  
  • Assignment 7 Solutions .  
  • Assignment 8.due Tuesday Nov 8 by noon under my office door. Solutions posted at noon so no solutions after noon. Midterm Wednesday Nov 9. See second sample midterm below.  
  • Assignment 8 Solutions .  
  • Assignment 9.due Friday Nov 18.  
  • Assignment 9 Solutions .  
  • Assignment 10.due Friday Nov 25.  
  • Assignment 10 Solutions .  
  • Sample midterm 1 This sample midterm is a study aid. It may be too early for you to use it profitably. I will NOT post solutions. You can come and show me your solutions and ideas if you want feedback. Reading solutions (unless you have done the problems) is not a valuable study aid in my opinion.  
  • Midterm 1 Solutions  
  • Sample midterm 2 This sample midterm is a study aid. I will NOT post solutions. You can come and show me your solutions and ideas if you want feedback. Reading solutions (unless you have done the problems) is not a valuable study aid in my opinion.  
  • Midterm 2 Solutions .  
  • 2008 Sample Final Exam This sample exam is a study aid. It may be too early for you to use it profitably. I will NOT post solutions. You can come and show me your solutions and ideas if you want feedback. Reading solutions (unless you have done the problems) is not a valuable study aid in my opinion.  
  • 2009 Sample Final Exam This sample exam is a study aid. It may be too early for you to use it profitably. I will NOT post solutions. You can come and show me your solutions and ideas if you want feedback. Reading solutions (unless you have done the problems) is not a valuable study aid in my opinion.  


  • Course Notes of material (often not in text or at least not in this order)

  • Notes from Sep 7.
  • Notes from Sep 9.
  • Putnam problem from Sep 9.
  • Linear Transformations (Sep 12).
  • Eigenvalues and Eigenvectors (Sep 14,16).
  • Fibonacci Numbers.
  • Interchanging first two rows changes determinant by factor -1.
  • Some notes on vector spaces
  • Axioms for Fields and also for Vector Spaces.
  • Partial Fractions.
  • Equiangular Lines. Notes (from Aart Blokhuis) from class and other information.
  • Petersen Graph . some applications of the symmetric adjacency matrix.
  • Levels of generality. Our problems can be studied at at least three levels: at the entry by entry level, at the level of matrices and at the level of linear transformations. It is suprising for students to discover that tackling a problem in greater generality often results in a simpler proof.
  • Matrix multiplication and some possible interpretations other than as linear transformations. Multiplication on the left is a row operation, multiplication on the right is a column operation etc. We discuss other interpretations later in the course.  
  • An interactive 2x2 matrix multiplication: A java program that allows you to move input point A around and see the output after a 2x2 matrix multiplication. The matrix entries are a,b,c,d and the java program gives you sliders to change their values if you wish. The initial data for a,b,c,d corresponds to the matrix for the fiboacci numbers. This demo was created with GeoGebra in about 1 hour with no knowledge of Java except the idea of jar files. You can play with this free software at www.geogebra.org (NOT www.geogebra.com)  


  • How to slice a bagel Use edible ink.