Tuesday, August 01, 2006

Come together, right now

Dog will hunt, y'all!

I've got the first nine days or so of the semester laid out.

This is hard.

Here's the condensed version (transcribed here with the hope that somewhere I will have a legible copy to which I myself can refer back to):

Day 1 (Monday, August 21st): Welcome! With no warning, let's get together and do the Markov Dance! For twenty or thirty minutes, we'll mimic the motion of people from Rich to Middle-Class to Poor, exploring population dynamics through simple linear systems. What does this mean? By the end of the day, we'll be able to see how linear equations, and maybe even vectors and matrices, fit into all of this! HW for Day 2: Read the syllabus, and fill out the questionnaire, both provided at the end of Day 1.

Day 2 (Wednesday, August 23rd): We'll spend our time working in groups, playing a little Toss 'n' Sort, and talking about what sort of teamwork I'll be expecting throughout the semester. We'll talk about expectations for research journals and research meeting notes, and how I would like folks to make use of the course blog and message board. HW for Day 3: Read Sections 1.1 and 1.2, and begin looking over the project descriptions, provided on-line.

Day 3 (Friday, August 25th): By this class, I'll have decided upon teams for the research projects. The first of many fun Two-part Quizzes will be given on this day, to give everyone a start in working with the teams they'll be in for the next few months. After that, we'll do some work with vectors. After briefly brainstorming properties of vectors, we'll look at some specific incarnations: RGB vectors, chemical equations, and realizations of abstract vectors in two- and three-dimensional Euclidean space. HW for Day 4: Read Section 1.3 of the text, re-read the project descriptions, this time as a group. Communicate with your group regarding these projects!

Day 4 (Monday, August 28th): After beginning Quiz 2 on vectors, we revisit the Markov Dance, in order to gain a deeper understanding of the steps we took. Specifically, we'll focus now on the matrices that arise in the Dance. The first of the "What If...?" exercises comes in at this point: what if we allow our matrices to vary over time? After using this exercise to examine the effects of matrix multiplication, we do some brainstorming on the various properties of matrices and their algebra. (The format for this brainstorming?: think-share-write-SHARE.) HW for Day 5: write in your journals about linear algebra so far, and get together with your teams to write rough drafts of your project proposals. You should have a rough draft in hand before class on Wednesday.

Day 5 (Wednesday, August 30th): Meta work! We spend the day investigating good and bad mathematical writing. After a little think-share-write-SHARE on what makes a good paper good, I'll pass out the rubric which will be used for the course's writing assignments. The fun then gets underway in earnest with the much-ballyhooed "Write a Bad Math Paper" exercise on something simple, like the definition of a vector. Each person will work with one other to write a horrifically bad paper, which will then be exchanged with that produced by another pair, who will then have the task of providing useful feedback. These are all skills that the teams'll wanna keep in mind when they do the...HW for Day 6: polish up those proposals for the various research projects. Also, read pages 51 through 56 and come ready for action involving systems of linear equations.

Day 6 (Friday, September 1st): Now that we know what systems of linear equations are, we'll revisit a couple that we've seen already, namely the Markov Dance and the Chemical Equations Balancing Act. How do we set up these linear systems? How are they translated into matrices? How do we solve them? We'll run a few examples, and we'll cap the week off by handing in those proposals on which you've worked oh so hard! HW for Day 7: Write in your journals regarding your proposals: do you feel good about them? Which project do you think you'll land? Also, finish reading Section 1.4, pages 57 through 73.

Day 7 (Wednesday, September 6th): Two-part Quiz 3 starts things off, covering the solutions to systems of linear equations. From there, we'll consider a new case study: the structure of a simple economy, with various inputs and outputs (resource: Lay, pp. 57-59). How can we understand this economy through what we've learned so far? HW for Day 8: Read pages 73 through 77, from Section 1.5.

Day 8 (Friday, September 8th): Two-part Quiz 4 gets us movin', where we're talkin' 'bout inverting elementary matrices. Once that's out of the way, we'll do some more complicated inversions with a step-by-step team exercise (Round Robin? Flock Around?), and then we'll go back to Applicationland by revisiting the simple economy constructed on Wednesday. HW for Day 9: Read pages 78 through 87, write in your journals about your team's work so far.

Day 9 (Monday, September 11th): Field trip! We'll meet with one of the university's reference librarians to learn more about the various research tools available for use on the projects. We'll also kick off the Reference Scavenger Hunt by breaking off into teams and tracking down a reference or two using MathSciNet and the Ramsey Library catalogue. HW for Day 10: Read pages 88 through 99 (Section 1.6), and complete the Reference Scavenger Hunt, handed out at the end of the day and posted on-line.

Dagnabbit, I need a break...more to come soon!

1 comment:

Anonymous said...

Job well done Patrick!
And I agree, you need a break! :)