TOP TEN SUGGESTIONS ON TEACHING LINEAR ALGEBRA

In article , jvogel@math.rutgers.edu (jeff vogel) writes:
|> I'm teaching my first class, starting in two weeks. A full first semester
|> of linear algebra, stuffed in six weeks (MWF 6:15 - 8:45).
|> 
|> Any suggestions?
|> 
|>                                      - Jeff Vogel
|>                                      Rutgers math, and damn
|>                                      proud of it!

TOP TEN SUGGESTIONS ON TEACHING LINEAR ALGEBRA:

9. Linear algebra consists of two parts: matrix algebra and vector space theory. Do the matrix algebra part first, with emphasis on LU factorization, Gauss-Jordan elimination, and Jordan canonical form. Then do the vector space theory, with the four fundamental subspaces of a matrix as the climax.

8. Mumble something on the first day of classes about always being turned on when you hear the word "matrix".

7. Never make eye contact.

6. When your students complain about having to invert a four by four matrix, yell: "Yeah? Well, when I was back in 'Nam, I had to invert ten by ten matrices with nothing but tree bark and my own blood for ink!" Then look dazed and clutch the nearest notebook firmly to your chest.

5. Find out from previous teachers of the course what the expected level of mathematical maturity of the students is. Some schools use linear algebra as their intro to proofs & rigour course for math majors. Also, find out whether they've had third semester calculus yet, as this can be a major source of examples.

4. You may already be locked into a textbook, but if not, I recommend Strang's book. Avoid Banchoff & Wermer's _Linear Algebra through Geometry_ like the plague.

3. If your class starts at 6:15 a.m., then the only way your students are going to make it to class on time is if you give them daily wake up calls. Come to think of it, this isn't a bad idea, even if it starts at at 6:15 pm. If it starts at 6:15 p.m., you can create a nurturing learning enviornment by having the students rotate bringing deserts to class. Be sure to use one of the students as your taster.

2. When saying the phrase "least squares fit", make a little Elvis-esque pelvic thrust on the word "fit".

1. Have Jeff Goldblum make a special guest appearance. Tell him there are some cute looking babes in the class.