Course plan update

I've got a few more weeks' worth of classes planned now, taking me most of the way to the midpoint of the semester. Feast your eyes on the following:

Day 10 (Wednesday, September 13th): things get rolling with Quiz 5, on spaces, subspaces, and spans. From there we'll split into teams and work in Round-robin fashion on solving homogeneous equations. [Note to self: I need to come up with a good application exercise here!] HW for Day 11: Read pages 91 through 99, finishing off Section 1.6.

Day 11 (Friday, September 15th): No quiz, but teams should sign up to come by sometime in the following week to send a couple of representatives to my office to provide a progress report on the team's project. The goal for the day is to work through one of those awful "equivalence" theorems which are all the rage in linear algebra: we'll spend most of the day putting together our own proof of Fraleigh-Beauregard's Theorems 1.16 and 1.17 on various equivalent forms of uniqueness of solution. HW for Day 12: Read pages 125 through 134 (Section 2.1), and make some noise in your journals about what's going on in your math world.

Day 12 (Monday, September 18th): Quiz 6, on linear independence, starts us off, and from there we go into some examples of finding spans and verifying linear independence. HW for Day 13: Read pages 136 through 140 (Section 2.2) of the text, and take a gander at the worksheet for the Pipe Problem which will be the focus of class on Day 13!

Day 13 (Wednesday, September 20th): Quiz 7, on matrix ranks, starts things off. But the pace quickens with quickness, and we spend the rest of the day on the Pipe Problem, in which we try our darnedest to get the right levels of salt solutions in a tank in a constant state of flux. Oh, the salinity! More than linear combinations, we're starting to talk about convex combinations! HW for Day 14: Read pages 179 through 186 (Section 3.1), paying careful attention to the first four examples from that section, and read through the worksheet on A Variety of Vector Spaces. You'll wanna know these forwards, backwards, and put together in any linear combination!

Day 14 (Friday, September 22nd): Vector spaces, vector spaces, vector spaces! You want 'em, we got 'em! We'll spend the first part of the class in a think-share-write-SHARE exercise meant to brainstorm the properties we want these "vector spaces" to have. From there we'll launch into an examination of each of the eight examples from the homework (four from the book, four from the worksheet): one per team, we'll have some mini-presentations on what makes each of these guys a vector space. HW for Day 15: Read pages 190 through 201 (Section 3.2), and let your journals know about vector spaces. How do these relate to your research project?

Day 15 (Monday, September 25th): After Quiz 8 (on vector spaces), we'll revisit the examples from Friday in order to examine their dimensions, bases, subspaces, and so forth. Trying to anticipate what might go on on Day 16, what do you notice about all but two of the examples from Day 14? HW for Day 16: Read pages 204 through 211 (Section 3.3) of the text. Pay special attention to how you might apply these ideas to the examples from the last few classes.

Day 16 (Wednesday, September 27th): We'll spend yet another day on the examples at which we've been pounding away since Friday. In particular, note how all but two of those examples look a heckuva lot like real Euclidean space! And what, indeed, about those last two? Can we "fix" them somehow, by chucking the set of real numbers out of the window? Hmm...! HW for Day 17: read over the worksheet Flyin' High (projective geometry and computer graphics).

Day 17 (Friday, September 29th): We start off with Quiz 9, on the worksheet from the previous class. We'll then spend the next half hour or so talking more about this worksheet: what's really going on here? Lines became other lines, or points, even! Things got squashed from three dimensions down to two, just like when 3-D objects are rendered in 2-D by a computer's graphical display. What's at work here are linear transformations, which will be dealt with formally in the HW for Day 18: read pages 142 through 152 (Section 2.3) of your text, taking care to note how linear transformations relate to matrices: is there really any difference?

It's comin' together! Now I'm off to pester my colleagues...