New Course Page and Syllabus: Differential Equations

I have just finished putting together the course web page and syllabus for my third course of the fall term: Math3425/5425 Differential Equations. The course is cross-listed as an undergraduate and a graduate class, so there is a little wrinkle to this. Basically, the grad students have to do two longer-term, larger projects.

If you are curious for details, you can find the pages here:

Now that this course and geometry are ready to go for a few weeks, I will move back to preparing materials for linear algebra. I still have a lot of stuff to  write.

Fall 2017 Workload Balancing

Here is a lesson I learned the hard way, which I present as a tip for newer faculty:

It pays to plan out your due dates for the entire term in advance. Spread the due dates around, so that that assignments from different classes come in at different times. Try to avoid having major assignments come it all at once.

I finally figured this out about two years ago (I am not that bright), and I have been conscious of it every term since. The “day to balance things” has become a regular part of my pre-term planning process. I just finished the plan for this term, and here it is, as a convenient Google Doc. I haven’t ever done it quite so formally as this table, but it feels natural now.

Note that I also have a column dedicated to what weekend commitments I have. That way, I can try to avoid having bad work vs family conflicts. This term, I have a weekend where my in-laws will visit, the Iowa Section of the MAA meeting to attend, and seven different travel days for my daughter’s soccer commitments. I don’t want a situation where I have a big stack of work to do when I have to drive the whole family to St Louis for the weekend to watch soccer games.

Of course, nothing is ever perfect. On September 22 I am collecting something big from two of my three courses right as family shows up. Sigh.

I am NOT worried about the big collection right before Thanksgiving. I get a whole week off, but my kids go to school on the next Monday and Tuesday. That means I have a few days of quiet office time.

If everything goes according to plan, I should be able to keep up with my grading work during the regular business day and still return papers either the next class meeting or the one after.

 

Euclidean Geometry: New Course Web Page and Syllabus and…

I just finished prep work on my Euclidean Geometry course. This involved rewriting or rebuilding lots of fiddly little things, so even though it was the “easy” one with minimal changes, it still took a whole day to do. (8-10 hours?) You can find the course web page here:

Course Web Page for Euclidean Geometry

That has everything. All of the assignments are written. Even the exams are written, but I am not going to post those publicly. If you want to skip to the core of things, you can just look at the new syllabus and maybe the first assignment page.

Euclidean Geometry Syllabus for Fall 2017

I am feeling super cool, now, so I chose to decorate this post with a different version of Count Vertigo.

cropped-countvertigo-flip.jpg

New Syllabus for Linear Algebra

I last posted about how I was rethinking the content expectations for linear algebra, so that I could write my own text. I took another step towards getting class ready today: I finished my syllabus.

This was inspired by examples that Susan Hill, our CETL director, handed out at this summer’s Course Design Academy. She had several different syllabus pairs in a before/after set-up. I really liked the way that most of the redesigned and reworked documents looked, so I wanted to write my own, better, syllabus document.

Here it is. I guess you can comment, but I am done with this for now. I have other things to do.

My New Linear Algebra Syllabus

The primary changes for me are these:

  • I am not doing SBG/SBAR this term, since I have so much else to manage.
  • I have streamlined my list of outcomes into four “process goals” and five “Big Questions.”
  • I am going to try out some peer grading for the first time.
  • I am definitely going to use an IBL scheme which is “individual work at home; group discussion in class; solo presentation in class,” but I have not made a big deal of this on the syllabus as being an IBL environment.

Anyway, you can do this too. It just takes several years of flailing about and thinking hard, two weeks of digesting the University, Department, and MAA learning goals, and then about 12 hours of writing and editing over two days.

Major Results of Undergraduate Linear Algebra

I have grown steadily unhappier with my linear algebra course. So this term, I am going to rewrite it in a radical way. I would like to make the experience a bit closer to my (successful) IBL Euclidean Geometry course. In EG, we use Euclid’s Elements as our “extant literature,” and then I have an IBL task sequence designed to go with it.

To make this project work, I need to write something analogous for Linear Algebra. For lack of a better title, I am calling this Elements of Linear Algebra. I would like to emulate the structure of Euclid’s work, too, where each book is just enough material to get to an important goal result. Then I can design tasks & homework for the students to do so that they work around the text and extend it. For context, here are the big results at the end of the first four books of Euclid’s Elements:

  1. The Pythagorean Theorem and its converse
  2. The equi-decomposability of rectilineal planar figures with squares
  3. If x lies outside a circle O, and a line through x meets O at points b and c, then the line xa is tangent to O if and only if (xa)^2 = (xb)(xc).
  4. the construction of a regular pentagon

Those are four beautiful theorems.

How should I choose the Beautiful Theorems for an undergraduate linear algebra course?

For context: (1) my course is is pre-rigorous, we don’t write “proofs.” Instead, we argue from examples to generality. (2) this course has been entirely stuck in Euclidean space, but it is not quite a matrix algebra course. (3) I have taught out of Strang for several years.

I want your feedback! Here is my current list of potential big results for the to explore. Each of these would be a chapter of my text.

  1. Descriptions of lines and planes in the plane and in 3-space using both standard forms and parametric forms.
  2. How to solve a system of equations, including how to decide if it is solvable, how big the solution set is, and a reasonably efficient algorithm for writing down the solution set.
  3. the invertible matrix theorem
  4. the fundamental theorem of linear algebra (borrowed from Strang — the four subspaces and how they fit together)
  5. How to find a ‘best approximate solution’ when there is not a given solution
  6. The spectral theorem for diagonalization of symmetric matrices

I would love to include the singular value decomposition, but I can barely get to #6 right now.

Note that these are just the big results! Each chapter would have other material in it to help us understand and contextualize the big result. For example, the invertible matrix theorem will necessitate determinants coming up in that chapter.

Anyway… What do you think?

An Important Part of Success

So far, this term seems to be off to a good start. I realize that one thing I am doing much better this term than last is really important. If I write it down, maybe I will always remember.

The attitude I present in the classroom is crucial to having a good first few weeks. In particular, this means projecting an overwhelmingly patient, cheery, positive, and helpful face, with as much energy as I can muster at any given moment.

This is especially important for my largish Math in Decision Making courses (55 students each). But it is also helping set a better tone for my linear algebra class.

Last term things were not so easy for me personally. It bled into my work. I did not consistently get across a positive attitude about students, their learning, and my involvement. This term, things are going better. I just have to keep it up for 13 more weeks.