## Course Summary

Math 206, *Linear Algebra*, begins by investigating techniques for solving systems of linear equations. The methods we develop suggest deeper structures which are responsible for the phenomena we see, and much of the class is spent contemplating these driving forces abstractly. The benefit of this abstract approach is that it produces machinery which is useful in a wide variety of contexts, not simply when something ``looks like" a system of linear equations. We will spend much of the semester analyzing structures inside ``real $n$-dimensional Euclidean space" (your old friend $\mathbb{R}^n$ from multivariable calculus); later in the semester we will see that we can develop a more abstract notion of an $n$-dimensional space which has many of the attractive qualities of $\mathbb{R}^n$. One of the punchlines in linear algebra is that any $n$-dimensional space (over $\mathbb{R}$) is ``the same as" $\mathbb{R}^n$ (a statement we'll work to make more precise as the semester unfolds).

For many students this class will serve as an introduction to abstract mathematics, so in addition to the linear algebra knowledge you'll accumulate throughout the term, you'll also be developing the meta-skills of reading, writing and creating mathematical proofs. If time permits, we will also consider some ``real-world" applications of linear algebra.

## Course Instructor

The professor for this class is Andy Schultz. His office is on the third floor of the Science Center, room S352. His office hours are Mondays form 1-3, Tuesdays from 9 to 10:30, Wednesdays from 2:30 to 4, and Thursdays from 12:30 to 2. You are highly encouraged to attend office hours, and you never need an appointment to do so. If these office hours don't fit with your schedule, contact the instructor so that he can either adjust when ``official" office hours are held or set up an appointment to help you outside of office hours. Please come to my office or send me an email if you ever want to discuss material from the class or ask about homework problems!

You can contact the instructor at . Though he is always happy to receive emails from you with questions or concerns about the course, he can't guarantee that he'll be able to promptly reply to emails late at night or over the weekend. If you do contact the professor by email, please be sure to follow standard email etiquette. In particular, please make sure you include a greeting and signature and avoid abbreviations. If you're contacting him to ask about a problem, please be sure to specify what the problem asks (as opposed to asking something like ``I can't get problem 2 and need your help").