**
Math 223 Section 102 **
Linear Algebra
**Online Course Material**

NEWS

IÕll be back Monday Dec 8 and hope to be in my office say from 2-3. We have office hours Tuesday Dec 9 from in MATH ANNEX 1100 from 12-2 and again Wednesday Dec 10 in MATH ANNEX 1118 from 11-1. I have a meeting starting at 10 so cannot be sure when it will end but hope to be back around 11. Our final exam is scheduled for Wednesday Dec 10 from 7-10pm. The location is LSK 201. We should consider Safewalk given the late finish of our exam. The full schedule is at Exam Schedule.

First Midterm average was 77 with median of 80. Great work.

Second Midterm average was 71 with a median of 74. Great work.

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.

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 Thursdays in MATH ANNEX 1118 (near my office) and imagine many assignments will be due Fridays. 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 Friday Sept 12. Solutions. (grading scheme 1-2-1-3-3-2-2-3-3).
Assignment 2. Due Friday Sept 19. Solutions.
Assignment 3. Due Friday Sept 26. Solutions. (grading scheme 2-2-2-2-2-3-3-4).
Assignment 4. Due Friday Oct 3. Solutions. (grading scheme 4 2 4 2 2 2 4).
Midterm 1 solutions .
Assignment 5. Due Friday Oct 17.
Solutions.
Assignment 6. Due Friday Oct 24. Solutions.
Assignment 7. Due Friday Oct 31. Solutions.
Practice DE Problems. a little practice for midterm. Solutions.
Midterm 2 solutions .
Assignment 8. Due Friday Nov 14. Solutions.
Assignment 9. Due Friday Nov 21. Solutions.

Various Notes. Often for material not in text or at least not in the order we follow.

Some notes from Sept 3 lecture
Some notes from Sept 5 lecture
A challenging Putnam problem.
Induction as a proof technique. Basics only.
Different approaches to problems based on different levels of generality.
Linear Transformations from Sept 8 lectures.
Eigenvalues and eigenvectors from Sept 10 lecture.
Diagonalizable matrices and application to birds from Sept 12 lecture.
Fibonacci numbers from Sept 15 lecture.
with white/blue coordinate handout.
Gaussian Elimination from Sept 17,19, 22 lectures.
Basic results about determinants from Sept 24,26 lectures.
Interchanging first two rows changes sign of determinant from Oct 3 lecture.
Axioms for a Field and for a Vector Space from Oct 8 lecture. some additional remarks about Vector Spaces including `A vector is not a vector` comment.
Linear Independence and Bases from Oct 10,15,17 lectures.
Wronskian Notes
Some notes for Differential equations.
How many equiangular lines in d dimensions.
How to use an orthonormal basis. in proving results about orthogonal vector spaces using an inner product.
Some pictures from plotting 100 points that are relatively evenly spaced on a sphere
Back points, Front points, All points. The idea is how to obtain the rotation matrix by 10 degrees around an arbitrary axis.
Petersen Graph. Can the complete graph on 10 vertices be decomposed into 3 Petersen Graphs.
Symmetric and Hermitian matrices. Perhaps the computer should do the Gram Schmidt process.
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.
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.
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.
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.
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.