I’m excited and happy to be teaching linear algebra again next semester. Linear algebra has it all — there’s computation that you can do by hand if you like that sort of thing, but also a strong incentive to use computers regularly and prominently. (How big is an incidence matrix that represents, say, Facebook?) There’s theory that motivates the computation. There’s computation that uncovers the theory. There’s something for everybody, and in the words of one of my colleagues, if you don’t like linear algebra then you probably shouldn’t study math at all.
Linear algebra is also an excellent place to use Peer Instruction, possibly moreso than any other sophomore-level mathematics course. Linear algebra is loaded with big ideas that all connect around a central question (whether or not a matrix is invertible). The computation is not the hard part of linear algebra — it…
This one is a bit more lecture-oriented than I intend most of the rest of them to be, so it’s a little longer than I expect most others will be. But I do break up the lecture a little bit with a “Concept Check”, which is the same thing as a ConcepTest except I’ve never warmed to that particular term (the word “test” puts students on edge, IMO).
If you have tried out any of Udacity’s courses or read my posts about taking Udacity courses, you will see some obvious inheritances here. I tried to keep the video short, provide simple but interesting examples, and give some measure of formative assessment in the video. I am exploring ways to make the Concept Check actually doable within YouTube — Camtasia 2 has an “interactive hotspot” feature I am trying to figure out — …
Interesting stuff from elsewhere on the web this week:
Danny Caballero, who does really interesting research on physics education at UC-Boulder, has just started up his own blog. Every post on it so far has been excellent, but his article “Which computational tool should we teach?” in particular is a great analysis of three major computational software tools from the standpoint of teaching physics students computational modeling.
Let me preface this article by saying that I really like Google Documents. It’s a fantastic set of tools that extends basic office functionality to the web in really compelling ways. I’ve been incorporating Google Docs pretty centrally in my courses for the last few years — for example, I no longer hand out paper syllabi on the first day of classes but instead write the syllabi on GDocs and distribute the links; and I’ve given final exams on Google Docs with links to data that are housed in Google Spreadsheets. I love being able to create a document on the web and just leave it there for students (or whoever) to come see, collaborate, and comment — without having to keep track of paper and with virtually zero chance of losing my data. (If Google crashes, we have much bigger problems than the loss of a set of quiz data.)
But like anything, Google Documents isn’t perfect — and in…
In my Linear Algebra class we use a lot of MATLAB — including on our timed tests and all throughout our class meetings. I want to stress to students that using professional-grade technological tools is an essential part of learning a subject whose real-life applications closely involve the use of those tools. However, there are a few essential calculations in linear algebra, the understanding of which benefits from doing by hand. One of those calculations is row-reduction. Nobody does this by hand; but doing it by hand is useful for understanding elementary row operations and for getting a feel for the numerical processes that are going on under the hood. And it helps with understanding later concepts, notably that of the LU factorization of a matrix.
I have students take a mastery exam where they have to reduce a 3×5 or 4×6 matrix to reduced echelon form by hand. They are not…
Over the weekend a minor smack-talk session opened up on Twitter between Maria Andersen and about half a dozen other math people about MathType versus \(\LaTeX\). Maria is on record as being pro-MathType and yesterday she claimed that \(\LaTeX\) is “not intuitive to learn”. I warned her that a pro-\(\LaTeX\) blog post was in the offing with those remarks, and so it comes to this. \(\LaTeX\) is accessible enough that every math teacher and every student in a math class at or above Calculus can (and many should) learn \(\LaTeX\) and use it for their work. I have been using \(\LaTeX\) for 15 years now and have been teaching it to our sophomore math majors for five years. I can tell you that students can learn it, and learn to love it.
Why use \(\LaTeX\) when MathType is already out there, bundled with MS Word and other office programs, tempting us with its…
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 …
1. Why is it that, in Google Spreadsheets, you can take a two-column set of numerical data and find the slope of the regresssion line for the data, you can find the y-intercept of the regression line, and you can make a scatterplot of the data — but you can’t plot the regression line on top of the scatterplot?
2. How come, in Google Documents, there’s no rudimentary equation editing? How come we can’t have a simple Equation Editor-like pallette system for mathematical typesetting, inline \(\LaTeX\) compiling (like WordPress.com blogs and Wikispaces wikis have), OpenOffice’s math typesetting syntax, or even just old-school MathML editing?
I’d be nearly ecstatic, and much more likely to actually use Google Docs for everyday purposes, if some of the smart people at Google could make either one of these two questions go away.
Good article here at The Productive Student giving five reasons why students should use \(\LaTeX\) as their word processor and not Microsoft Word:
1. Never worry about formatting again.
2. It looks way better. [By the way: Very nice article on LaTeX's typesetting at that link.]
3. It won’t crash: LaTeX is basically a plain text file. You can edit it anywhere, in any text editor, and it basically can’t crash on you. File size is very small which makes it very portable.
4. It’s great for displaying equations, which is why it’s the leading standard among sciencitifc scholars.
5. It fits in with the workflow of a student and allows you to do one thing well: Write.
The writer also shares some of his practices for writing papers (not necessarily math or science papers) with \(\LaTeX\), stressing \(\LaTeX\)’s ability to handle bibliographic data as the “killer feature”….
I’ve been noticing since upgrading to Leopard last week that PDF’s that are made using LaTeX do not always look right in Preview. Here’s the same PDF made using LaTeX (TeXShop, to be exact), opened three times in immediate succession using Preview (click to enlarge each):
The third one (rightmost) finally looks like it’s supposed to, but the other two have this strange-looking font substitution for text, and the math is just completely out of whack.
Again, this is the same PDF opened up, then closed, then opened again right after that, then again. No additional LaTeX builds were done. Also, the PDF viewer that comes with TeXShop had the same problems with fonts.
Anybody have a thought as to what’s going on here?
I am a mathematician and educator with interests in cryptology, computer science, and STEM education. I am affiliated with the Mathematics Department at Grand Valley State University in Allendale, Michigan. The views here are my own and are not necessarily shared by GVSU.
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