8/27-29

Vector spaces

1.1-1.2

homework 1

Please read the webpage for this course carefully. If you see any problems with the way things are scheduled (e.g. midterm on bad date, etc, etc), you need to bring them to my attention in the 1^st week.

Also, we need to schedule a (likely evening) time for a weekly help session. I propose Mondays 7:30-8:30 PM. And I need to schedule some office hours. How about Tuesdays 3-5 PM?

9/1-9/5

Linear transformations

1.3-1.6

homework 2

Help session this week in HH125 from 7:30-8:30 PM Monday. If it's generally agreeable, I'll make this the time & day for help sessions the entire term.

9/8-9/12

More linear transformations

homework 3

I've scheduled the weekly help session for 7:30-8:30 every Monday in Hayes-Healy 231 (different room from the 1^st week). This week will be a slight exception, however: the time of the session will be 8-9 on Monday in order to accommodate a glitch in Josh's schedule.

My colleague has gone and scheduled an interesting looking seminar from 3-5 on Tuesdays. Hence, starting this week, I'll try 1-3 PM and 5-6 PM Tuesdays for office hours.

9/15-9/19

subspaces

linear systems

2.1-2.2

homework 4

Help session at 7:30 PM Monday, office hrs 1-3 PM, 5-6 PM Tuesday. These are now the official times (til further notice).

9/22-9/26

applications of solving systems

2.3, 2.5-2.6

homework 5

9/29-10/3

linear systems and linear transformations

2.4, 2.7-2.8

homework 6

On sale in paperback now at the bookstore: “Linear Algebra Done Right” for 29.50.

Here's a redo of the proof I messed up in class on 10/1.

10/6-10/10

Inner product spaces

5.1-5.3

homework 7

10/13-10/17

the dual space, adjoints, and least squares

5.4-5.5 My treatment will differ from the book's. I follow Axler's book (page 117 til end of chapter) more closely.

homework 8

Review sheet for the midterm

10/27-10/31

review for midterm (10/27)

finish up adjoints (for now) and least squares.

no new hwk this week; hwk 8 due next week

Midterm exam Tuesday 10/28 from 8-10 PM in HH 117

The help session will meet as usual on Monday 10/27, and I'll hold my regular office hours on 10/28.

11/3-11/7

determinants

3.1-3.5

homework 9

Class starts 20 minutes earlier each day this week

11/10-11/14

No class this week. Josh will still hold his help session, but in deference to the undergrad math research conference on Monday and Tuesday evenings, the help session will meet Sunday, Nov 9 from 7:30-8:30 PM.

11/16-11/20

more determinants, eigenvalues

4.1-4.2

homework 10

Class starts 20 minutes earlier each day this week

11/23-11/24

eigenvalues (cont)

No homework due this week—Thanksgiving break.

Here's a version of the Mathematica computation I did in class on Monday.

12/1-12/5

complex eigenvalues,

invariant subspaces and an alternative method for finding characteristic polynomials

The book doesn't treat these topics much, so you'll be more dependent than usual on my lectures. You might also see what the reserve books have to say.

homework 11

The book by Treil doesn't really discuss complex eigenvalues for real linear operators much. However, here's the Mathematica demo I did concerning this topic.

Note the change in plans here. I'm going to forego the stuff about operators on inner product spaces til next term. Instead, I'll discuss invariant subspaces and the Cayley-Hamilton theorem.

12/8-12/11

The Cayley-Hamilton Theorem.

8.1 (though my treatment will differ somewhat)

Here's the Mathematica demo from class on 12/8.

Review sheet for final exam.

A writeup of the computation I messed up on Monday.

Don't forget to fill out course evaluations. These are now online. Filling them out is voluntary of course, but there have been unsubstantiated reports that non-participants have been inexplicably receiving electric shocks when touching metal surfaces on campus.