Category Archives: Linear algebra

May 15, 2010, 11:41 am

The semester in review

Plot of the vector field f(x,y) = (-y,x).

Image via Wikipedia

I’ve made it to the end of another semester. Classes ended on Friday, and we have final exams this coming week. It’s been a long and full semester, as you can see by the relative lack of posting going on here since around October. How did things go?

Well, first of all I had a record course load this time around — four different courses, one of which was the MATLAB course that was brand new and outside my main discipline; plus an independent study that was more like an undergraduate research project, and so it required almost as much prep time from me as a regular course.

The Functions and Models class (formerly known as Pre-calculus) has been one of my favorites to teach here, and this class was no exception. We do precalculus a bit differently here, focusing on using functions as data modeling …

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March 21, 2010, 7:32 pm

Calculus reform's next wave

There’s a discussion going on right now in the Project NExT email list about calculus textbooks, the merits/demerits of the Stewart Calculus textbook, and where — if anywhere — the “next wave” of calculus reform is going to come from. I wrote the following post to the group, and I thought it would serve double-duty fairly well as a blog post. So… here it is:

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I’d like to add my $0.02 worth to this discussion just because (1) I’m a longtime Stewart Calculus user, having used the first edition (!) when I was an undergrad and having taught out of it for my entire career, and (2) I’m also a fairly consistent critic of Stewart’s calculus and of textbooks in general.

I try to see textbooks from the viewpoints of my students. From that vantage point, I unfortunately find very little to say in favor of Stewart’s franchise of  books, including the current edition, all of the…

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February 27, 2010, 6:32 am

Is Khan Academy the future of education?

Salman Khan is a former financial analyst who quit his day job so that he could form Khan Academy — a venture in which he makes instructional videos on mathematics topics and puts them on YouTube. And he has certainly done a prolific job of it — to the tune of over a thousand short videos on topics ranging from basic addition to differential equations and also physics, biology, and finance.  Amazingly, he does this all on his own time, in a remodeled closet in his house, for free:

I can attest to the quality of his linear algebra videos, some of which I’ve embedded on the Moodle site for my linear algebra course. They are simple without being dumbed down, and what he says about the 10-minute time span in the PBS story is exactly right — it’s just the right length for a single topic.

What do you think about this? What role do well-produced, short, simple, free video…

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February 4, 2010, 10:14 pm

12 videos for getting LaTeX into the hands of students

There seem to be two pieces of technology that all mathematicians and other technical professionals use, regardless of how technophobic they might be: email, and \(\LaTeX\). There are ways to typeset mathematical expressions out there that have a more shallow learning curve, but when it comes to flexibility, extendability, and just the sheer aesthetic quality of the result, \(\LaTeX\) has no rival. Plus, it’s free and runs on every computing platform in existence. It even runs on WordPress.com blogs (as you can see here) and just made its entry into Google Documents in miniature form as Google Docs’ equation editor. \(\LaTeX\) is not going anywhere anytime soon, and in fact it seems to be showing up in more and more places as the typesetting system of choice.

But \(\LaTeX\) gets a bad rap as too complicated for normal people to use. It seems to be something people learn …

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January 20, 2010, 10:31 am

Courses and "something extra"

Some of the most valuable courses I took while I was in school were so because, in addition to learning a specific body of content (and having it taught well), I picked up something extra along the way that turned out to be just as cool or valuable as the course material itself. Examples:

  • I was a psychology major at the beginning of my undergraduate years and made it into the senior-level experiment design course as a sophomore. In that course I learned how to use SPSS (on an Apple IIe!). That was an “extra” that I really enjoyed, perhaps moreso than the experiment I designed. (I wish I still knew how to use it.)
  • In my graduate school differential geometry class (I think that was in 1995), we used Mathematica to plot torus knots and study their curvature and torsion. Learning Mathematica and how to use it for mathematical investigations were the “something extra” that I took from the …

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July 5, 2007, 11:49 am

Advice for effective studying

 ~Pmeerw Bg Ny Pictures Public Library Reading Room
Scott Young has an outstanding article at Lifehack.org today on 10 tips to study smart and save time. These three tips from the list are related to each other and offer very good advice that most students, especially new college students, never hear:

  • Leave No Islands – When you read through a textbook, every piece of information should connect with something else you have learned. Fast learners do this automatically, but if you leave islands of information, you won’t be able to reach them during a test.
  • Test Your Mobility – A good way to know you haven’t linked enough is that you can’t move between concepts. Open up a word document and start explaining the subject you are working with. If you can’t jump between sections, referencing one idea to help explain another, you won’t be able to think through the connections during a test.
  • Find Patterns – Look for patterns in information…

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July 2, 2007, 1:17 pm

The Big Picture of abstract algebra?

 English Images FarmarialI’ve been working here and there on my Modern Algebra class for this fall. As regular readers know, I am doing this course this time around without the use of a required textbook. One of the difficult, and good, things this approach imposes on me as the professor is that I cannot rely on the book to provide structure and order to the course. I have to do this myself. Before I can do any realistic planning, I first have to decide what I am going to cover and the order in which I am going to (try to) do it. And before I can do that, I have to face some questions that professors are surprisingly able to sidestep when using a textbook, namely: What is this course about? What themes unify, and therefore motivate, the material? And what are the core issues and questions that this course attempts to address?

Far too often, students can take a course in college or high school and make good…

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