Course Summary

The purpose of Math 322, Advanced Linear Algebra, is to delve deeper into the structure of vector spaces and their transformations. The abstraction and mathematical maturity developed in abstract algebra allow students to approach the content of this course with a new set of tools. The course progresses through Halmos' Finite dimensional vector spaces, with topics covering three main areas: vector spaces (including basic qualities of vectors, invariants of vector spaces, and canonical vector spaces constructions such as dual spaces, quotient spaces, and linear forms), transformations (including the formal construction of determinants and a review of canonical forms), and orthogonality (from the basics of inner product spaces to the spectral theorems). If time allows, the course will finish with a discussion of modules, a construction which generalizes vector spaces by replacing the scalar field with a scalar ring.

Aside from the content of the course, another distinguishing feature of this section of Math 322 is that lectures will primarily be delivered by students in the course. During the semester students will exercise a number of skills that extend far beyond the mathematical classroom: recognizing patterns; connecting ideas across disparate contexts; extending intuition from a familiar setting to solve problems in an unfamiliar setting; and communicating in a variety of ways and to a variety of audiences (ranging from informal discussions to very formal write-ups). Students will also find that the responsibility of giving lectures gives them a chance to engage with the material in new ways. For many it will be the first time that they are asked to learn material independently from a text; to distill content and make decisions about how it should (or shouldn't) be rearranged, amended, or supplemented to facilitate understanding by others; and to deliver mathematics for an extended amount of time at the blackboard in the semi-formal environment of a classroom.

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 9:45-11:00, Tuesdays from 2 to 3, Wednesdays from 2:30 to 3:30, 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").