MA253 — Linear Algebra
This page contains various course materials for MA253 and links to
web sites that might be of interest. Most materials are in pdf format.
Technology
You do want to learn to do the basic operations by hand. In a pinch
(or for that matter, in an exam), you need to be able to do a quick
row-reduction and get the answer right. That said, however, once you do
know how to do it you'll find that doing things by hand is tedious and
prone to errors in arithmetic. That's why God created software. I list
below several software options.
1. You may already own a fancy calculator. If so, it's worth your
while to check the manual to find out whether it does linear algebra
calculations. There's no need to reinvent the wheel, after all.
Most calculators can do the basic linear algebra operations, and fancier
ones (e.g., the TI-89) can do quite a bit more. Read the friendly manual!
2. One of the friendliest software packages for doing basic linear
algebra is online:
the Linear Algebra
Toolkit. This includes tools for doing row operations, for solving
linear systems, and a lot more. These software tools are easy to use, and
they make life a lot easier for you, especially later in the course.
3. Many computers on campus have Mathematica installed. This
is a very powerful mathematics program. It takes a while to learn. On the
other hand, it can do pretty much all the kinds of computations we are
likely to run into. Don't be afraid to play with it.
Some useful Mathematica commands:
- To enter a matrix, use the "Input" menu.
- RowReduce[ ] will perform Gaussian elimination on the matrix you
enter inside the square brackets.
- EigenSystem[ ] will find eigenvalues and the corresponding
eigenvectors.
Use the Mathematica help system to find many more matrix-related
commands.
Interesting Links
I'll be adding more of these as the course progresses.
- Need help with your homework?
Maybe Wolfram|Alpha can help.
- Wolfram MathWorld is more like an online encyclopedia of mathematics.
- Another nice one is PlanetMath.
- There are, of course, tons of sites that have linear algebra information, including many that have course notes, problems, and solutions. For example, I find the notes you can get at Peter Taylor's site very nice. He takes an incredibly applied and concrete point of view. If you don't like it when I get too abstract, check out Peter's approach.
- There's also tons of free software out there in addition to the Linear Algebra Toolkit. The quality varies, of course, but free stuff is always fun.
- Check out the MAA's online journal Loci, which has articles and a huge collection of mathematical applets.
- The hardest way to make a million dollars: the Clay Institute's Millennium Prize Problems.
Fernando Q. Gouvêa ---- fqgouvea@colby.edu
Last modified: Sun Sep 06 14:46:46 Eastern Daylight Time 2009